1,393 results
Search Results
2. Reactive Gait Composition With Stability: Dynamic Walking Amidst Static and Moving Obstacles.
- Author
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Narkhede, Kunal Sanjay, Motahar, Mohamad Shafiee, Veer, Sushant, and Poulakakis, Ioannis
- Subjects
- *
BIPEDALISM , *ROBOTIC path planning , *LIMIT cycles , *DYNAMIC stability , *MATHEMATICS , *ROBOT motion - Abstract
This paper presents a modular approach to motion planning with provable stability guarantees for robots that move through changing environments via periodic locomotion behaviors. We focus on dynamic walkers as a paradigm for such systems, although the tools developed in this paper can be used to support general compositional approaches to robot motion planning with dynamic movement primitives (DMPs). By formulating the planning process as a switching system with multiple equilibria (SSME), we prove that the system's evolution remains within explicitly characterized trapping regions in the state space under suitable constraints on the frequency of switching among the DMPs. These conditions encapsulate the low-level stability limitations in a form that can be easily communicated to the planner. Furthermore, we show how the available primitives can be safely composed online in a receding horizon manner to enable the robot to react to moving obstacles. The proposed framework can be applied in a wide class of 3D bipedal walking models, and offers a modular approach for integrating readily available low-level locomotion control and high-level planning methods. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
3. In Vitro Simulation of Shoulder Motion Driven by Three-Dimensional Scapular and Humeral Kinematics
- Author
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Heath B. Henninger, Hema J. Sulkar, Tyler Knighton, Tucker Hermans, Linda Amoafo, Christopher W. Kolz, Yue Zhang, and Klevis Aliaj
- Subjects
Shoulder ,Shoulder Joint ,Biomedical Engineering ,Biomechanics ,Context (language use) ,Repeatability ,Kinematics ,Humerus ,Research Papers ,Biomechanical Phenomena ,Scapula ,medicine.anatomical_structure ,Cadaver ,Physiology (medical) ,medicine ,Humans ,Range of Motion, Articular ,Range of motion ,Biomedical engineering ,Mathematics - Abstract
In vitro simulation of three-dimensional (3D) shoulder motion using in vivo kinematics obtained from human subjects allows investigation of clinical conditions in the context of physiologically relevant biomechanics. Herein, we present a framework for laboratory simulation of subject-specific kinematics that combines individual 3D scapular and humeral control in cadavers. The objectives were to: (1) robotically simulate seven healthy subject-specific 3D scapulothoracic and glenohumeral kinematic trajectories in six cadavers, (2) characterize system performance using kinematic orientation accuracy and repeatability, and muscle force repeatability metrics, and (3) analyze effects of input kinematics and cadaver specimen variability. Using an industrial robot to orient the scapula range of motion (ROM), errors with repeatability of ±0.1 mm and
- Published
- 2022
4. Proper Orthogonal Decomposition-Based Method for Predicting Flow and Heat Transfer of Oil and Water in Reservoir
- Author
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Xianhang Sun, Ma Xu, Pan Yi, Bingfan Li, Weiqiu Huang, and Yang Shuangchun
- Subjects
0303 health sciences ,Renewable Energy, Sustainability and the Environment ,020209 energy ,Mechanical Engineering ,Flow (psychology) ,Physical system ,Finite difference method ,Energy Engineering and Power Technology ,Basis function ,02 engineering and technology ,Mechanics ,Research Papers ,03 medical and health sciences ,Fuel Technology ,Point of delivery ,Geochemistry and Petrology ,Principal component analysis ,Heat transfer ,Reservoir engineering ,0202 electrical engineering, electronic engineering, information engineering ,030304 developmental biology ,Mathematics - Abstract
Calculation process of some reservoir engineering problems involves several passes of full-order numerical reservoir simulations, and this makes it a time-consuming process. In this study, a fast method based on proper orthogonal decomposition (POD) was developed to predict flow and heat transfer of oil and water in a reservoir. The reduced order model for flow and heat transfer of oil and water in the hot water-drive reservoir was generated. Then, POD was used to extract a reduced set of POD basis functions from a series of “snapshots” obtained by a finite difference method (FDM), and these POD basis functions most efficiently represent the dynamic characteristics of the original physical system. After injection and production parameters are changed constantly, the POD basis functions combined with the reduced order model were used to predict the new physical fields. The POD-based method was approved on a two-dimensional hot water-drive reservoir model. For the example of this paper, compared with FDM, the prediction error of water saturation and temperature fields were less than 1.3% and 1.5%, respectively; what is more, it was quite fast, where the increase in calculation speed was more than 70 times.
- Published
- 2019
5. Design and Validation of a Low-Cost Bodyweight Support System for Overground Walking
- Author
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Mhairi K. MacLean and Daniel P. Ferris
- Subjects
030506 rehabilitation ,medicine.medical_specialty ,Rehabilitation ,medicine.medical_treatment ,Biomedical Engineering ,Biomechanics ,Medicine (miscellaneous) ,Overground walking ,Gait ,Load cell ,Design Innovation Papers ,03 medical and health sciences ,0302 clinical medicine ,Physical medicine and rehabilitation ,Vertical force ,medicine ,Support system ,0305 other medical science ,Constant force ,030217 neurology & neurosurgery ,Mathematics - Abstract
Walking with bodyweight support is a vital tool for both gait rehabilitation and biomechanics research. There are few commercially available bodyweight support systems for overground walking that are able to provide a near constant lifting force of more than 50% bodyweight. The devices that do exist are expensive and are not often used outside of rehabilitation clinics. Our aim was to design, build, and validate a bodyweight support device for overground walking that: (1) cost less than $5000, (2) could support up to 75% of the users' bodyweight (BW), and (3) had small (±5% BW) fluctuations in force. We used pairs of constant force springs to provide the constant lifting force. To validate the force fluctuation, we recruited eight participants to walk at 0.4, 0.8, 1.2, and 1.6 m/s with 0%, 22%, 46%, and 69% of their bodyweight supported. We used a load cell to measure force through the system and motion capture data to create a vector of the supplied lifting force. The final prototype cost less than $4000 and was able to support 80% of the users' bodyweight. Fluctuations in vertical force increased with speed and bodyweight support, reaching a maximum of 10% at 1.6 m/s and 69% BW support.
- Published
- 2020
6. Numerical Approximation of Elasticity Tensor Associated With Green-Naghdi Rate
- Author
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Wei Sun and Haofei Liu
- Subjects
0301 basic medicine ,0206 medical engineering ,Linear elasticity ,Finite Element Analysis ,Biomedical Engineering ,02 engineering and technology ,020601 biomedical engineering ,Research Papers ,Finite element method ,Elasticity ,03 medical and health sciences ,symbols.namesake ,Oxidative Stress ,030104 developmental biology ,Physiology (medical) ,Hyperelastic material ,Tangent modulus ,Jacobian matrix and determinant ,symbols ,Applied mathematics ,Computer Simulation ,Tensor ,Elasticity (economics) ,Tensor derivative ,Mathematics - Abstract
Objective stress rates are often used in commercial finite element (FE) programs. However, deriving a consistent tangent modulus tensor (also known as elasticity tensor or material Jacobian) associated with the objective stress rates is challenging when complex material models are utilized. In this paper, an approximation method for the tangent modulus tensor associated with the Green-Naghdi rate of the Kirchhoff stress is employed to simplify the evaluation process. The effectiveness of the approach is demonstrated through the implementation of two user-defined fiber-reinforced hyperelastic material models. Comparisons between the approximation method and the closed-form analytical method demonstrate that the former can simplify the material Jacobian evaluation with satisfactory accuracy while retaining its computational efficiency. Moreover, since the approximation method is independent of material models, it can facilitate the implementation of complex material models in FE analysis using shell/membrane elements in abaqus.
- Published
- 2017
7. A Zero-Dimensional Model and Protocol for Simulating Patient-Specific Pulmonary Hemodynamics From Limited Clinical Data
- Author
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Robin Shandas, Uyen Truong, Vitaly O. Kheyfets, D. Dunbar Ivy, Kendall S. Hunter, and Jamie Dunning
- Subjects
Male ,Patient-Specific Modeling ,medicine.medical_specialty ,Cardiac output ,Pulmonary Circulation ,Heart Ventricles ,Hypertension, Pulmonary ,0206 medical engineering ,Biomedical Engineering ,Hemodynamics ,Blood Pressure ,02 engineering and technology ,030204 cardiovascular system & hematology ,Pulmonary Artery ,03 medical and health sciences ,0302 clinical medicine ,Afterload ,Physiology (medical) ,Internal medicine ,medicine ,Humans ,Computer Simulation ,Bland–Altman plot ,Cardiac Output ,Child ,Simulation ,Mathematics ,Protocol (science) ,Models, Cardiovascular ,Stroke Volume ,Stroke volume ,medicine.disease ,020601 biomedical engineering ,Pulmonary hypertension ,Research Papers ,Preload ,Cardiology ,Female ,Algorithms ,Blood Flow Velocity - Abstract
In pulmonary hypertension (PH) diagnosis and management, many useful functional markers have been proposed that are unfeasible for clinical implementation. For example, assessing right ventricular (RV) contractile response to a gradual increase in pulmonary arterial (PA) impedance requires simultaneously recording RV pressure and volume, and under different afterload/preload conditions. In addition to clinical applications, many research projects are hampered by limited retrospective clinical data and could greatly benefit from simulations that extrapolate unavailable hemodynamics. The objective of this study was to develop and validate a 0D computational model, along with a numerical implementation protocol, of the RV–PA axis. Model results are qualitatively compared with published clinical data and quantitatively validated against right heart catheterization (RHC) for 115 pediatric PH patients. The RV–PA circuit is represented using a general elastance function for the RV and a three-element Windkessel initial value problem for the PA. The circuit mathematically sits between two reservoirs of constant pressure, which represent the right and left atriums. We compared Pmax, Pmin, mPAP, cardiac output (CO), and stroke volume (SV) between the model and RHC. The model predicted between 96% and 98% of the variability in pressure and 98–99% in volumetric characteristics (CO and SV). However, Bland Altman plots showed the model to have a consistent bias for most pressure and volumetric parameters, and differences between model and RHC to have considerable error. Future studies will address this issue and compare specific waveforms, but these initial results are extremely promising as preliminary proof of concept of the modeling approach.
- Published
- 2016
8. Development of a Subject-Specific Foot-Ground Contact Model for Walking
- Author
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Jennifer N. Jackson, Benjamin J. Fregly, and Chris J. Hass
- Subjects
Friction ,0206 medical engineering ,Biomedical Engineering ,02 engineering and technology ,Kinematics ,Walking ,Motion capture ,Models, Biological ,Sensitivity and Specificity ,Root mean square ,03 medical and health sciences ,0302 clinical medicine ,Center of pressure (terrestrial locomotion) ,Control theory ,Physiology (medical) ,Elastic Modulus ,medicine ,Pressure ,Humans ,Computer Simulation ,Ground reaction force ,Gait ,Mathematics ,Foot ,Viscosity ,Stiffness ,Reproducibility of Results ,Revolute joint ,020601 biomedical engineering ,Research Papers ,Reaction ,Stress, Mechanical ,medicine.symptom ,030217 neurology & neurosurgery - Abstract
Computational walking simulations could facilitate the development of improved treatments for clinical conditions affecting walking ability. Since an effective treatment is likely to change a patient's foot-ground contact pattern and timing, such simulations should ideally utilize deformable foot-ground contact models tailored to the patient's foot anatomy and footwear. However, no study has reported a deformable modeling approach that can reproduce all six ground reaction quantities (expressed as three reaction force components, two center of pressure (CoP) coordinates, and a free reaction moment) for an individual subject during walking. This study proposes such an approach for use in predictive optimizations of walking. To minimize complexity, we modeled each foot as two rigid segments—a hindfoot (HF) segment and a forefoot (FF) segment—connected by a pin joint representing the toes flexion–extension axis. Ground reaction forces (GRFs) and moments acting on each segment were generated by a grid of linear springs with nonlinear damping and Coulomb friction spread across the bottom of each segment. The stiffness and damping of each spring and common friction parameter values for all springs were calibrated for both feet simultaneously via a novel three-stage optimization process that used motion capture and ground reaction data collected from a single walking trial. The sequential three-stage process involved matching (1) the vertical force component, (2) all three force components, and finally (3) all six ground reaction quantities. The calibrated model was tested using four additional walking trials excluded from calibration. With only small changes in input kinematics, the calibrated model reproduced all six ground reaction quantities closely (root mean square (RMS) errors less than 13 N for all three forces, 25 mm for anterior–posterior (AP) CoP, 8 mm for medial–lateral (ML) CoP, and 2 N·m for the free moment) for both feet in all walking trials. The largest errors in AP CoP occurred at the beginning and end of stance phase when the vertical ground reaction force (vGRF) was small. Subject-specific deformable foot-ground contact models created using this approach should enable changes in foot-ground contact pattern to be predicted accurately by gait optimization studies, which may lead to improvements in personalized rehabilitation medicine.
- Published
- 2016
9. Origami Folding and Bar Frameworks
- Author
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Alejandro R. Diaz
- Subjects
Combinatorics ,Sequence ,Optimization problem ,Bar (music) ,Simple (abstract algebra) ,Mathematics of paper folding ,Folding (DSP implementation) ,Representation (mathematics) ,Vertex (geometry) ,Mathematics - Abstract
One of the more computationally demanding tasks in a process of synthesizing “from scratch” origami crease patterns designed for a given purpose involve a simulation capability to track the progression of the folding process as the pattern folds. This work presents an approach to simulate origami folding based on bar frameworks. The work is related to joint frameworks and projected polyhedral, as they apply to folding. The analysis starts from a representation of a crease pattern as an undirected graph G(E,V) formed by edges E and vertices V. A framework G(p) is an instance of G where the vertex locations are assigned positions according to a vector valued function p(t), where t marks the folding progression and t=0 represents the initial, flat configuration. The strategy presented is based on finding a sequence of instances {p(1), p(2), …} corresponding to an analytic flex p, i.e., functions such that edges in all G(p(t)) have the same length. The method is based on using a finite element description of a bar framework corresponding to a truss-like structure congruent with G(p). Solutions to an eigenvalue problem associated with this structure provide the means to update from p(t) to p(t+1). Two simple (purely geometric) optimization problems adjust the update to compensate for higher order effects, guaranteeing that the length of the edges remain constant. The methodology can be used to achieve configurations close to “flat folding”, provided that no interference of the faces occurs along the way. We expected that physically-motivated constraints (stresses, deformations, etc.) and sensitivity analysis computations will be more easily represented in this framework and therefore this formulation will have an advantage over more standard “origami mathematics” approaches. The approach is illustrated with an example of folding a simple 10-crease pattern.Copyright © 2014 by ASME
- Published
- 2014
- Full Text
- View/download PDF
10. Trunk Angular Kinematics During Slip-Induced Backward Falls and Activities of Daily Living
- Author
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Jian Liu and Thurmon E. Lockhart
- Subjects
Male ,Motion analysis ,Movement ,Physics::Medical Physics ,Biomedical Engineering ,Poison control ,Kinematics ,Sitting ,Upper trunk ,Physiology (medical) ,Activities of Daily Living ,medicine ,Humans ,Simulation ,Mathematics ,Aged ,Mechanical Phenomena ,Torso ,Geodesy ,Trunk ,Research Papers ,Sagittal plane ,Biomechanical Phenomena ,medicine.anatomical_structure ,Accidental Falls ,Female - Abstract
Prior to developing any specific fall detection algorithm, it is critical to distinguish the unique motion features associated with fall accidents. The current study aimed to investigate the upper trunk angular kinematics during slip-induced backward falls and activities of daily living (ADLs). Ten healthy older adults (age = 75 ± 6 yr (mean ± SD)) were involved in a laboratory study. Sagittal trunk angular kinematics were measured using optical motion analysis system during normal walking, slip-induced backward falls, lying down, bending over, and various types of sitting down (SN). Trunk angular phase-plane plots were generated to reveal the motion features of falls. It was found that backward falls were characterized by a simultaneous occurrence of a slight trunk extension and an extremely high trunk extension velocity (peak average = 139.7 deg/s), as compared to ADLs (peak average = 84.1 deg/s). It was concluded that the trunk extension angular kinematics of falls were clearly distinguishable from those of ADLs from the perspective of angular phase-plane plot. Such motion features can be utilized in future studies to develop a new prior-to-impact fall detection algorithm.
- Published
- 2014
11. Muscle Synergies May Improve Optimization Prediction of Knee Contact Forces During Walking
- Author
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Jonathan P. Walter, Benjamin J. Fregly, David Lloyd, Thor F. Besier, Allison Kinney, Scott A. Banks, and Darryl D. D'Lima
- Subjects
Knee Joint ,medicine.medical_treatment ,Biomedical Engineering ,Knee replacement ,Inverse ,Electromyography ,Walking ,Models, Biological ,Contact force ,Control theory ,Physiology (medical) ,medicine ,Humans ,Computer Simulation ,Range of Motion, Articular ,Muscle, Skeletal ,Root-mean-square deviation ,Gait ,Postural Balance ,Mathematics ,Aged ,medicine.diagnostic_test ,Explained sum of squares ,Biomechanical engineering ,Research Papers ,Female ,Range of motion ,Algorithms ,Biomedical engineering ,Muscle Contraction - Abstract
The ability to predict patient-specific joint contact and muscle forces accurately could improve the treatment of walking-related disorders. Muscle synergy analysis, which decomposes a large number of muscle electromyographic (EMG) signals into a small number of synergy control signals, could reduce the dimensionality and thus redundancy of the muscle and contact force prediction process. This study investigated whether use of subject-specific synergy controls can improve optimization prediction of knee contact forces during walking. To generate the predictions, we performed mixed dynamic muscle force optimizations (i.e., inverse skeletal dynamics with forward muscle activation and contraction dynamics) using data collected from a subject implanted with a force-measuring knee replacement. Twelve optimization problems (three cases with four subcases each) that minimized the sum of squares of muscle excitations were formulated to investigate how synergy controls affect knee contact force predictions. The three cases were: (1) Calibrate+Match where muscle model parameter values were calibrated and experimental knee contact forces were simultaneously matched, (2) Precalibrate+Predict where experimental knee contact forces were predicted using precalibrated muscle model parameters values from the first case, and (3) Calibrate+Predict where muscle model parameter values were calibrated and experimental knee contact forces were simultaneously predicted, all while matching inverse dynamic loads at the hip, knee, and ankle. The four subcases used either 44 independent controls or five synergy controls with and without EMG shape tracking. For the Calibrate+Match case, all four subcases closely reproduced the measured medial and lateral knee contact forces (R2 ≥ 0.94, root-mean-square (RMS) error < 66 N), indicating sufficient model fidelity for contact force prediction. For the Precalibrate+Predict and Calibrate+Predict cases, synergy controls yielded better contact force predictions (0.61 < R2 < 0.90, 83 N < RMS error < 161 N) than did independent controls (-0.15 < R2 < 0.79, 124 N < RMS error < 343 N) for corresponding subcases. For independent controls, contact force predictions improved when precalibrated model parameter values or EMG shape tracking was used. For synergy controls, contact force predictions were relatively insensitive to how model parameter values were calibrated, while EMG shape tracking made lateral (but not medial) contact force predictions worse. For the subject and optimization cost function analyzed in this study, use of subject-specific synergy controls improved the accuracy of knee contact force predictions, especially for lateral contact force when EMG shape tracking was omitted, and reduced prediction sensitivity to uncertainties in muscle model parameter values.
- Published
- 2014
12. Economics of d-Limonene Recovery
- Author
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Gordon P. Gerow
- Subjects
D limonene ,Pulp and paper industry ,Mathematics - Abstract
d-Limonene is the main volatile constituent of citrus peel oil, and the collected volatile portion of oil is usually referred to as d-Limonene in the trade. The later definition will be used throughout this paper rather than the exact chemical definition. Paper published with permission.
- Published
- 1974
- Full Text
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13. Pulp Wash System Development
- Author
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Herman L. Jones, Ronald B. McKinnis, and Richard A. Andrews
- Subjects
Orange juice ,System development ,Soluble solids ,Pulp (paper) ,engineering ,CITRUS JUICE ,engineering.material ,Pulp and paper industry ,Mathematics - Abstract
The use of pulp wash as an aid in the production of citrus juice has gained acceptance since 1957. Earlier use is known, but real recognition seemed to await a certain period in the development of frozen orange juice concentrate, and a freeze. The history of this product could be divided into three time periods each approximately equal. The first period of time was certainly formative in which the product enjoyed all of the advantages of novelty. The second period of time was characterized by increasing competition and need for lowering costs. This required that the plants measure the fruit in terms of pounds of soluble solids and that they recover as product all that could be had without an unquestionable damage to quality. The demand for more recovery of the soluble solids exceeded the capability of any mechanical finishing equipment to distinguish between the juice left on a quite dry pulp and the pulp, which still had good juice on it. This brought about fresh thinking and new processing ideas, including one of gently rinsing the juice from a wet pulp. This became known as “Pulp Wash” and was developed during the third period of time. Paper published with permission.
- Published
- 1964
- Full Text
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14. Sargeant Electronic Evaporator
- Author
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William R. Erickson
- Subjects
Brix ,CITRUS JUICE ,Pulp and paper industry ,Evaporator ,Mathematics - Abstract
The Sargeant Radio-Frequency Evaporator is a radically new approach to the concentration of citrus juices above the level of 54° Brix. With your indulgence, I would like to explain this principle by using various flow diagrams. Paper published with permission.
- Published
- 1963
- Full Text
- View/download PDF
15. Optimal Control for Partially Observed Nonlinear Interval Systems.
- Author
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Dabbous, T. E.
- Subjects
- *
NONLINEAR systems , *INTERVAL analysis , *DIFFERENTIAL equations , *COMPUTER simulation , *OPTIMAL control theory , *PONTRYAGIN'S minimum principle - Abstract
In this paper, we consider the optimal control problem for a class of systems governed by nonlinear time-varying partially observed interval differential equations. The control process is assumed to be governed by linear time varying interval differential equation driven by the observed process. Using the fact that the state, observation, and control processes possess lower and upper bounds, we have developed sets of (ordinary) differential equations that describe the behavior of the bounds of these processes. Using these differential equations, the interval control problem can be transformed into an equivalent ordinary control problem in which interval mathematics and extension principle of Moore are not required. Using variational arguments, we have developed the necessary conditions of optimality for the equivalent (ordinary) control problem. Finally, we present some numerical simulations to illustrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
16. Separated Flows Around the Rear Window of a Simplified Car Geometry.
- Author
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Rouméas, Mathieu, Gilliéron, Patrick, and Kourta, Azeddine
- Subjects
GEOMETRY ,MATHEMATICS ,EUCLID'S elements ,SIMULATION methods & models ,MODELS & modelmaking ,LATTICE theory ,TRANSPORT theory - Abstract
A 3D numerical simulation based on the lattice Boltzmann method is carried out on a simplified car geometry (initially proposed by Ahmed, Ramm, and Falting, 1984, SAE Technical Paper series No. 840300) to analyze and establish a method for controlling the near-wake flow topology of a generic blunt body model. The results indicate the existence of a complex flow topology consisting of transverse and longitudinal vortices emanating from flow separations that occur on the top and the lateral edges of the slanted rear window, respectively. The topology of each structure is detailed and the numerical results are compared with the experimental results in the literature. The results presented in this paper can then be used to develop and parametrize active control solutions conducive to improving the aerodynamic performances of automobile vehicles. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
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17. On Higher Order Point-Line and the Associated Rigid Body Motions.
- Author
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Yi Zhang and Kwun-Lon Ting
- Subjects
- *
QUATERNION functions , *MATHEMATICS , *ALGEBRA , *DIFFERENTIAL geometry - Abstract
This paper presents a study on the higher-order motion of point-lines embedded on rigid bodies. The mathematic treatment of the paper is based on dual quaternion algebra and differential geometry of line trajectories, which facilitate a concise and unified description of the material in this paper. Due to the unified treatment, the results are directly applicable to line motion as well. The transformation of a point-line between positions is expressed as a unit dual quaternion referred to as the point-line displacement operator depicting a pure translation along the point-line followed by a screw displacement about their common normal. The derivatives of the point-line displacement operator characterize the point-line motion to various orders with a set of characteristic numbers. A set of associated rigid body motions is obtained by applying an instantaneous rotation about the point-line. It shows that the ISA trihedrons of the associated rigid motions can be simply depicted with a set of ∞2 cylindroids. It also presents for a rigid body motion, the locus of lines and point-lines with common rotation or translation characteristics about the line axes. Lines embedded in a rigid body with uniform screw motion are presented. For a general rigid body motion, one may find lines generating up to the third order uniform screw motion about these lines. [ABSTRACT FROM AUTHOR]
- Published
- 2007
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18. A Descriptive Geometry-Based Solution to a Geometrical Problem in Rotary Shaving of a Shoulder Pinion.
- Author
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Radzevich, Stephen P.
- Subjects
- *
SHAVING , *INVOLUTES (Mathematics) , *MATHEMATICS , *GEOMETRY , *PIVOT bearings , *BEARINGS (Machinery) , *MACHINERY - Abstract
A novel descriptive-geometry-based (DGB) approach for determining of limitation on parameters of rotary shaving operation of shoulder gear is reported in the paper The paper covers determination: (a) of the maximum feasible outside diameter oft he shaving cutter: (b) of the minimum required overlap in rotary shaving operation; and (c) of the minimum required face-width of the shaving cutter. Insufficiency of location, and migration of the pivot point is investigated as well. It is proven that instead of consideration of the pivot point itself, it is required to consider size and relative disposition of the auxiliary rack of the pinion, and of the auxiliary, rack of the shaving cutter. The developed solution is the exact and not an approximate one. Due to that it is still valid for any value of the crossed-axis angle, even in cases where it exceeds 10 deg. The results are valid for all four basic methods of rotary shaving. Application of the results enables avoiding of the pinion tooth bias. Taken as a whole, the topic covered in this paper will enable one determination of proper values of parameters (a) through (c) of rotary shaving operation, which are the dominating limiting factors of rotary shaving operation. The developed DGB approach can be readily put into practice. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
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19. New mathematical definition and calculation of axial rotation of anatomical joints.
- Author
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Miyazaki S and Ishida A
- Subjects
- Biomechanical Phenomena, Humans, Rotation, Joints physiology, Mathematics
- Abstract
In the field of joint kinematics, clinical terms such as internal-external, or medical-lateral, rotations are commonly used to express the rotation of a body segment about its own long axis. However, these terms are not defined in a strict mathematical sense. In this paper, a new mathematical definition of axial rotation is proposed and methods to calculate it from the measured Euler angles are given. The definition and methods to calculate it from the measured Euler angles are given. The definition is based on the integration of the component of the angular velocity vector projected onto the long axis of the body segment. First, the absolute axial rotation of a body segment with respect to the stationary coordinate system is defined. This definition is then generalized to give the relative axial rotation of one body segment with respect to the other body segment where the two segments are moving in the three-dimensional space. The well-known Codman's paradox is cited as an example to make clear the difference between the definition so far proposed by other researchers and the new one.
- Published
- 1991
- Full Text
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20. Investigation on Methods for Uncertainty Quantification of Constitutive Models and the Application in BEPU
- Author
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Qingwen Xiong, Jianqiang Shan, and Junli Gou
- Subjects
Constitutive equation ,Applied mathematics ,Uncertainty quantification ,Mathematics - Abstract
The best estimate plus uncertainty (BEPU) method is recommended by IAEA for nuclear safety analysis. Most of the existing BEPU methodologies rely on the uncertainty propagation of input parameters, while uncertainties of the constitutive models in best estimate codes tend not to be valued or even neglected. A structural method is proposed in this paper to quantify the uncertainties of the constitutive models. Different constitutive models will be classified according to the characteristics and corresponding method could be utilized for each model based on the method. Specific uncertainty quantification (UQ) methods adopted in this paper include the non-parametric curve estimation method, inverse method and design of experiment (DOE) method, and a model selection technique is adopted to opt the optimal model among all alternative models. The structural method is applied to the uncertainty evaluation of LOFT LP-02-6 experiment. Important models are identified, uncertainties of these models are quantified and propagated to the peak cladding temperature (PCT) through code calculations. Uncertainty of the PCT is quantified and the result shows that the calculated values could well envelop the experimental value.
- Published
- 2018
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21. Stability of Milling Operations With Asymmetric Cutter Dynamics in Rotating Coordinates.
- Author
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Comak, Alptunc, Ozsahin, Orkun, and Altintas, Yusuf
- Subjects
- *
MATHEMATICS , *DYNAMICS , *ANALYTIC geometry , *FORCE & energy , *MILLING (Metalwork) - Abstract
High-speed machine tools have parts with both stationary and rotating dynamics. While spindle housing, column, and table have stationary dynamics, rotating parts may have both symmetric (i.e., spindle shaft and tool holder) and asymmetric dynamics (i.e., two-fluted end mill) due to uneven geometiy in two principal directions. This paper presents a stability model of dynamic milling operations with combined stationary and rotating dynamics. The stationary modes are superposed to two orthogonal directions in rotating frame by considering the time- and speed-dependent, periodic dynamic milling system. The stability of the system is solved in both frequency and semidiscrete time domain. It is shown that the stability pockets differ significantly when the rotating dynamics of the asymmetric tools are considered. The proposed stability model has been experimentally validated in high-speed milling of an aluminum alloy with a two-fluted, asymmetric helical end mill. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
22. Linear Stability Analysis of a Waveboard Multibody Model With a Minimal Set of Equations
- Author
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Emilio Freire, D. García-Vallejo, Aki Mikkola, and A. G. Agúndez
- Subjects
Set (abstract data type) ,Nonlinear system ,Linear stability analysis ,Mathematical analysis ,Torsion (mechanics) ,Equations of motion ,Stability (probability) ,Eigenvalues and eigenvectors ,Mathematics - Abstract
In this paper, the stability of a waveboard, the skateboard consisting in two articulated platforms, coupled by a torsion bar and supported of two caster wheels, is analysed. The waveboard presents an interesting propelling mechanism, since the rider can achieve a forward motion by means of an oscillatory lateral motion of the platforms. The system is described using a multibody model with holonomic and nonholonomic constraints. To perform the stability analysis, the nonlinear equations of motion are linearized with respect to the forward upright motion with constant speed. The linearization is carried out resorting to a novel numerical linearization procedure, recently validated with a well-acknowledged bicycle benchmark, which allows the maximum possible reduction of the linearized equations of motion of multibody systems with holonomic and nonholonomic constraints. The approach allows the expression of the Jacobian matrix in terms of the main design parameters of the multibody system under study. This paper illustrates the use of this linearization approach with a complex multibody system as the waveboard. Furthermore, a sensitivity analysis of the eigenvalues considering different scenarios is performed, and the influence of the forward speed, the casters’ inclination angle and the tori aspect ratios of the toroidal wheels on the stability of the system is analysed.
- Published
- 2021
- Full Text
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23. Analysis and Evaluation of Piecewise Linear Systems With Coulomb Friction Using a Hybrid Symbolic-Numeric Computational Method
- Author
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Amir Shahhosseini, Meng-Hsuan Tien, and Kiran D'Souza
- Subjects
Piecewise linear function ,Mathematical analysis ,Coulomb friction ,Mathematics - Abstract
A general formulation of piecewise linear systems with discontinuous force elements is provided in this paper. It has been demonstrated that this class of nonlinear systems is of great importance due to their ability to accurately model numerous scientific and engineering phenomena. Additionally, it is shown that this class of nonlinear systems can demonstrate a wide spectrum of nonlinear motions and in fact, the phenomenon of weak chaos is observed in a mechanical assembly for the first time. Despite such importance, efficient methods for fast and accurate evaluation of piecewise linear systems’ responses are lacking and the methods of the literature are either incompatible, very slow, very inaccurate, or bear a combination of the aforementioned deficiencies. To overcome this shortcoming, a novel symbolic-numeric method is presented in this paper that is able to obtain the analytical response of piecewise linear systems with discontinuous elements in an efficient manner. Contrary to other efficient methods that are based on stationary steady state dynamics, this method will not experience failure upon the occurrence of complex motion and is able to capture the entirety of the dynamics.
- Published
- 2021
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24. A Viscoplastic Model for Alloy 617 for Use With the ASME Section III, Division 5 Design by Inelastic Analysis Rules
- Author
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T.-L. Sham and Mark Messner
- Subjects
Viscoplasticity ,business.industry ,Alloy ,Structural engineering ,Division (mathematics) ,engineering.material ,Finite element method ,Creep ,Section (archaeology) ,Computer software ,engineering ,Inelastic analysis ,business ,Mathematics - Abstract
The rules for the design of high temperature reactor components in Section III, Division 5, Subsection HB, Subpart B (HBB) of the ASME Boiler and Pressure Vessel Code contain two options for evaluating the deformation-controlled design limits on strain accumulation and creep-fatigue: design by elastic analysis and design by inelastic analysis. Of these options design by inelastic analysis tends to be less overconservative and produce more efficient designs. However, the HBB currently does not provide approved material models for use with the inelastic analysis rules, limiting their widespread use. A nonmandatory appendix has been developed to provide general guidance on appropriate material models and provide reference material models suitable for use with the design by inelastic analysis approach. This paper describes a viscoplastic model for Alloy 617 suitable for use with the HBB rules proposed for incorporation into the new appendix. The model represents the high temperature creep, creep-fatigue, and tensile response of Alloy 617 and accurately accounts for rate sensitivity across a wide range of temperatures. The focus in developing the model was on capturing key features of material deformation required for accurately executing the HBB rules and on developing a relatively simple model form that can be implemented in commercial finite element analysis software. The paper validates the model against an extensive experimental database collected as part of the Alloy 617 Code qualification effort as well as against specialized experimental tests examining the effect of elastic follow up on stress relaxation and creep deformation in the material.
- Published
- 2021
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- View/download PDF
25. Antiwindup Design for Zero-Phase Repetitive Controllers.
- Author
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Flores, J. V., Gomes da Silva, Jr., J. M., Sbarbaro, D., Turner, M. C., and Salton, A. T.
- Subjects
- *
FACTORIZATION , *ELECTRIC controllers , *MATHEMATICS , *QUANTUM mechanics , *FACTORIZATION of operators - Abstract
This paper addresses the antiwindup problem for linear systems equipped with the zero-phase repetitive controller (ZPRC). The antiwindup compensator is designed using a coprime factorization technique and conditions to characterize the sets of admissible references and disturbances are proposed. A numerical example illustrates the application and potentialities of the proposed methodology. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
26. Framework for Key Influences on Tensile Strain Capacity of Flawed Girth Welds.
- Author
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Hertelé, Stijn, Denys, Rudi, Horn, Anthony, Van Minnebruggen, Koen, and De Waele, Wim
- Subjects
WELDED joints ,TENSILE strength ,MATHEMATICS ,NUMERICAL analysis - Abstract
A key influence factor in the strain-based assessment of pipeline girth weld flaws is weld strength mismatch. Recent research has led to a framework for tensile strain capacity as a function of weld flow stress (FS) overmatch. This framework is built around three parameters: the strain capacity of an evenmatching weldment, the sensitivity of strain capacity to weld FS overmatch, and the strain capacity at gross section collapse (GSC). A parametric finite element study of curved wide plate (CWP) tests has been performed to identify the influence of various characteristics on each of these three parameters. This paper focuses on flaw depth, tearing resistance of the weld, stress-strain behavior of the base metal, and weld geometry. Influences of these characteristics are mostly found to be limited to one or two of the three framework parameters. A preliminary structure is proposed for equations that further develop the strain capacity framework. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
27. The Bauschinger Effect's Influence on the Stress Intensity Factors of a Semi-Elliptical Crack Emanating From an Erosion at the Bore of a Fully Autofrettaged Pressurized Cylinder.
- Author
-
Ma, Q., Levy, C., and Perl, M.
- Subjects
PRESSURIZED cylinders ,DURABILITY ,BAUSCHINGER effect ,STRENGTH of materials ,MATHEMATICS - Abstract
The benefits of autofrettage for thick-walled cylindrical vessels as a means of improving the vessel's durability and sustainability have been addressed in the published literature. However, the presence of the Bauschinger effect (BE) complicates the overall effect of autofrettage, especially when complex three-dimensional crack geometries emanating from erosions at the cylinder bore are considered. In this paper, the BE's impact on the stress intensity factors (SIFs) on such cracks is investigated. The effect of various erosion geometrical configurations on the mode I SIF distribution along the front of a semi-elliptical crack, emanating from the deepest line of the erosion surface (DLES) at the bore of an autofrettaged, pressurized thick-walled cylinder of outer-to-inner radius ratio, Ro/Ri = 2, is investigated. Both autofrettage with BE (BEDA) and Hill's ideal autofrettage residual stress field (BEIA) are considered and simulated by an equivalent thermal load. The SIFs are determined for the semi-elliptical cracks of various crack depths to wall thickness ratio, a/t = 0.05-0.25, and ellipticities, a/c, ranging from 0.5 to 1.5, emanating from the DLES via Ansys software and the nodal displacement method. Three groups of erosion geometries are considered: (a) arc erosions of constant relative depth, d/t, equal to 5% and with relative radii of curvature, r′/t, between 5% and 30%; (b) semi-elliptic erosions of constant relative depth, d/t, of 5% with erosion ellipticity, d/h, varying from 0.3 to 2.0; and (c) semicircular erosions of relative depth, d/t, between 1% and 10% of the wall thickness. KIP, the SIF due to pressurization, is highly dependent on the stress concentration ahead of the DLES which directly relates to the erosion geometry. It is found that the absolute value of KIA, the SIF due to autofrettage, is just slightly reduced by the presence of the erosion. Its change solely depends on, and is directly proportional to, the erosion depth. Thus, the combined SIFs of deep cracks are found to be significantly enhanced by the presence of autofrettage and might result in a shortening of the vessel's fatigue life by up to an order of magnitude. Counteracting this, the combined SIFs are found to be significantly higher for BEDA cases than for BEIA cases. Therefore, the vessel's fatigue life can be profoundly influenced by the presence of the BE. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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28. Fully-Plastic Strain-Based J Estimation Scheme for Circumferential Surface Cracks in Pipes Subjected to Reeling.
- Author
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Parise, Luís F. S., Ruggieri, Claudio, and O'Dowd, Noel P.
- Subjects
SURFACE cracks ,UNDERWATER pipelines ,POWER plants ,MATHEMATICS ,STIFFNESS (Mechanics) - Abstract
Modern installation techniques for marine pipelines and subsea risers are often based on the reel-lay method, which introduces significant (plastic) strains on the pipe during reeling and unreeling. The safe assessment of cracklike flaws under such conditions requires accurate estimations of the elastic-plastic crack driving forces, ideally expressed in a strain-based formulation to better account for the displacement controlled nature of the reeling method. This paper aims to facilitate such assessments by presenting a strain-based expression of the well-known Electric Power Research Institute (EPRI) estimation scheme for the J integral, which is directly based upon fully plastic descriptions of fracture behavior under significant plasticity. Parametric finite element simulations of bending of circumferentially cracked pipes have been conducted for a set of crack geometries, pipe dimensions, and material hardening properties representative of current applications. These provide the numerical assessment of the crack driving force upon which the nondimensional factors of the EPRI methodology, which scale J with applied strain, are derived. Finally, these factors are presented in convenient graphical and tabular forms, thus allowing the direct and accurate assessment of the J integral for circumferentially cracked pipes subjected to reeling. Further results show that crack driving force values estimated using the proposed methodology and the given g1 factors are in very close agreement to those obtained directly from the finite element simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
29. Protection Against Local Failure for Impulsively Loaded Vessels.
- Author
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Clayton, Alan M. and Duffey, Thomas A.
- Subjects
MATHEMATICS ,FORCE density ,PRESSURE regulators ,DIAPHRAGMS (Mechanical devices) ,ARITHMETIC - Abstract
Significant changes have been incorporated in design limits for pressurized vessels in Section VIII, Division 3 of the ASME Code, starting in 2007. There is now a local damage-mechanics based strain-exhaustion limit as well as a separate global plastic collapse limit. In addition, Code Case 2564 (Sec. VIII, Div 3) has recently been approved to address impulsively loaded vessels. Recent studies (Nakamura, T., Kaguchi, H., and Kubo, S., 2000, "Failure Strain of Thin Cylindrical Vessel Subjected to Dynamic Internal Pressure," Design and Analysis of Pressure Vessels and Piping, Vol. 399, R. Baliga, ed., pp. 47-54 and Duffey, T. A., 2011, "Plastic Instabilities in Spherical Vessels for Static and Dynamic Loading," ASME J. Pressure Vessel Technol., 133(5), p. 051210) have shown that local strain limits play a particularly important role for these impulsively loaded vessels. In this paper, the new local strain-exhaustion procedure, originally intended for static-pressure-loaded vessels, is evaluated for adequacy in conservatively predicting failure for impulsively loaded vessels. Based upon symmetrically loaded cylindrical shell geometry, it is found that direct extension of the new local failure rules in the ASME Code to impulsively loaded vessels is unconservative. However, a hoop-strain local failure criterion predicts failures reasonably well. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
30. Qualitative and Semi-Quantitative Model for Estimating the Probability of Failure at River Crossings
- Author
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Millan Sen, Rodolfo B. Sancio, David Vance, Patricia Varela, and Kourosh Abdolmaleki
- Subjects
Probability of failure ,Statistics ,Semi quantitative ,Mathematics - Abstract
Pipeline river crossings are typically managed by using a combination of flood monitoring, ground inspections, integrity assessments, and remediations. Using a probabilistic model to assess the likelihood of failure at river crossings would enable combined consideration of all factors that contribute to the failure threat, provide site rankings to support discrete mitigation prioritizations, allow for evaluation of whether a crossing is acceptable in regard to a risk target, and provide a “check” to the deterministic integrity management methods. This paper describes two models for estimating the pipeline probability of failure at river crossings. The first model is a qualitative scoring model that can be easily implemented by operators and consultants. This model employs a weighting-factors approach to consider the multiple variables that contribute to pipeline exposures and overstress given exposure. The results may be applied to threat rank diverse crossings, as well estimate the probability of failure at a crossing relative to that at historical failure sites. The second model is a semi-quantitative model that 1) estimates the likelihood of a crossing exposure occurring, 2) estimates the associated scour length, 3) assesses the pipelines critical span length, and 4) quantifies the probability that a span length longer than the critical span length could form. This model may be applied to achieve the same goals as the qualitative model, and also compare the probability of failure at a river crossing to a reliability target. Due to the complexity of this model and the paper length limits, it is conceptually described within this paper. The results demonstrated that the model output site rankings correlated reasonably with those estimated by pipeline integrity program managers, the scour depth and length prediction results were consistent with measured historical scours, and the pipeline probability of failure at the assessed river crossings were within expected ranges.
- Published
- 2020
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- View/download PDF
31. On the Formulation of Nonreflecting Boundary Conditions for Turbomachinery Configurations: Part II — Application and Analysis
- Author
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Nina Wolfrum, Daniel Schlüß, Maximilian Beck, Christian Frey, and Patrick Bechlars
- Subjects
business.industry ,Computation ,Turbomachinery ,Mechanics ,Boundary value problem ,Computational fluid dynamics ,Vorticity ,business ,Mathematics - Abstract
The flow in turbomachinery components is complex due to the relative motion of rotating and non-rotating elements. A proper design and prediction of physical phenomena requires reliable CFD tools. One important aspect is the incorporation of sophisticated algorithms at the boundaries of the computational domain. For inviscid, one-dimensional and two-dimensional Euler-flows there exist analytical solutions for the formulation of a boundary condition. Realistic applications, however, are viscous and consist of a complex three-dimensional character. Nevertheless, the analytical 2D nonreflecting boundary conditions are commonly used in CFD codes for their high computational efficiency and numerical robustness. The application becomes more challenging when the boundaries are close to geometrical features such as blades and vanes. In practical applications, the position of the boundaries is dictated by geometrical constraints and hence the proximity to the blading cannot always be avoided. The interaction of rotating and non-rotating geometrical features in a turbomachine produces complex flow patterns that propagate in the form of acoustic, vorticity and entropy waves. A boundary condition must be implemented in such a way that waves can propagate undisturbed out of the computational domain. Any reflection may unphysically affect the solution within the computational domain which is especially harmful to sensitive values such as unsteady aeroelastic quantities. But also steady-state computations may suffer from errors produced by reflective boundary conditions. The following paper is the second of two papers on the formulation of unsteady boundary conditions based on a two-dimensional analytical approach. The first part of this paper [6] explains how to extend 2D nonreflecting boundary conditions to real 3D annular domains by applying them in certain conical rotational surfaces. Two different formulations are discussed referring to the orientation of said rotational surfaces. In the first case the surfaces are oriented perpendicular to the boundary panel. In the second case the surfaces are aligned with the circumferentially averaged meridional flow velocity. In the present paper a thorough analysis of the two different approaches will be given. Both formulations of the boundary algorithm are validated on the basis of several elementary model flows. The behavior is analyzed for various unsteady wave patterns of different propagation directions with respect to the boundary. It will be shown that the alignment of the rotational surfaces with the meridional flow has a beneficial effect on the reflective behavior for the majority of the investigated flow conditions. The boundary conditions are then tested on realistic turbomachinery components in order to analyze their applicability on complex flows.
- Published
- 2020
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- View/download PDF
32. On the Formulation of Nonreflecting Boundary Conditions for Turbomachinery Configurations: Part I — Theory and Implementation
- Author
-
Patrick Bechlars, Maximilian Beck, Nina Wolfrum, Daniel Schlüß, and Christian Frey
- Subjects
Unsteady flow ,Turbomachinery ,Mechanics ,Boundary value problem ,Mathematics - Abstract
With unsteady flow simulations of industrial turbomachinery configurations becoming more and more affordable there is a growing need for accurate inlet and outlet boundary conditions as numerical reflections alone can lead to incorrect trends in engine efficiency, noise and aeroelastic analysis parameters. This is the first of two papers on the formulation of unsteady boundary conditions which have been implemented for both time-domain and frequency-domain solvers. Giles’ original idea for steady solvers to formulate the boundary condition in terms of characteristics generalizes to frequency-domain solvers. The boundary condition drives the value of the incoming characteristics to ideal values that are computed using the modal decomposition of linearized 2D Euler flows. The present paper explains how to generalize 2D nonreflecting boundary conditions to real 3D annular domains by applying them in certain conical rotational surfaces. For a flow with zero radial component and an annular boundary that is perpendicular to the machine axis, these surfaces are the cylindrical streamsurfaces. For more general flows and geometries, however, there is no natural choice for the rotational surfaces. In this paper, two choices are discussed: the surfaces that are generated by the boundary normals and those that are defined by the circumferentially averaged meridional velocity. The impact of the boundary condition on the stability of the harmonic-balance solver is analyzed by studying the pseudo-time evolution of certain energy integrals. For a model problem which consists of a small disturbance of an inviscid flow, the increase or decrease of this energy integral is shown to be directly related to the normal characteristic variables along the boundary. This shows that the actual boundary condition should be formulated as a control problem for the normal characteristics. Moreover, the application of the harmonic balance solver to a simple duct configuration with prescribed disturbances demonstrates that using the characteristics based on the meridional velocity may prevent the solver from converging. In contrast, the 2D theory can be formulated in a different surface without impairing the robustness of the overall approach. These findings are illustrated by a simple test case. The impact of the choice of the rotational surface for the 2D theory is studied for various duct segments and a low-pressure turbine configuration in the second paper. There it is shown that applying the 2D theory to the meridional-velocity surfaces may be advantageous in that it leads to more accurate results.
- Published
- 2020
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33. A Random Method for Calculation of Hoisting Drag
- Author
-
Jianming Yang, Stephen Butt, Hongyuan Qiu, and Geoff Rideout
- Subjects
Drag ,Random method ,Mechanics ,Finite element method ,Mathematics - Abstract
In reality, downhole conditions are highly unpredictable due to many uncertain and inconsistent factors, such as the uncertainty of the friction and contact between drillstring and bore-hole. As friction and contact are crucial components in torque and drag calculation, it is meaningful and practical to consider their uncertainty. This paper presents a random method for calculation of hoisting drag. Firstly, the finite element method (FEM) is used for hoisting drag calculation of a directional drilling well using Adanoy’s method in the deterministic case. Then two strategies are taken to model the random component in the downhole. The first strategy considers the randomness of the downhole friction. Instead of being a deterministic value, the friction coefficient is considered as Gaussian. The second strategy considers the randomness of contact between drillstring and wellbore. As a result, the drillstring is no longer continuously contacting with the wellbore in the curved section of well profile, which can help avoid overestimating torque and drag. Parametric studies on both strategies are conducted. Monte Carlo (MC) simulation is employed for statistical analysis. The probability density distributions and mean values of drag will be studied. The methodology can be extended into torque or drag calculation in lowering, ream in and ream out drilling conditions. Results from this paper indicate that surface hoisting drag is nearly Gaussian when the friction coefficient is Gaussian. The contact loss leads to considerable reduction in the surface hoisting drag when contact uncertainty is considered. The work of this paper will help estimate the range of surface drag and torque, which allows the well planner to develop a risk assessment for a challenging well trajectory.
- Published
- 2020
- Full Text
- View/download PDF
34. Evaluation of Metal Seals With for Interval Control Valve With Roundness Error Intelligent Well Considering Roundness Error
- Author
-
Yiwei Yang, Hongwu Zhu, Dongsheng He, Yan Zheng, Chuan Li, Liangbin Xu, and Yufa He
- Subjects
Control valves ,Roundness error ,Control theory ,Interval (mathematics) ,Mathematics - Abstract
Intelligent wells armed with the interval control valve (ICV) are more and more widely applied in the oilfields. In an ICV, the metal seal pair composed of the metal seal ring and the sliding sleeve is designed to isolate the produced fluid flow between the casing annulus and the tubing. The evaluation of the metal seals for ICVs is necessary to enhance the reliability. In this paper, the influences of medium pressure and initial interference on the contact mechanical behaviors of the metal seal for the ICV are studied by using finite element analysis (FEA) when both of the metal seal pair elements have roundness errors. The results indicate that when the both long axes of the metal seal pair’s elliptical sections coincide or are orthogonal, the contact stresses on the core area for the seal face present cosine or sine curve distributions. Each distribution curve becomes smoother with the increase of medium pressure, initial interference or the reduction of sliding sleeve roundness error. And for the contact stress distribution curves, the maximum at the peaks and troughs and the average increase with the increase of the medium pressure, the initial interference and the roundness error of the sliding sleeve. Moreover, when the angle between the metal seal pair elliptical sections’ long axes increases from 0 ° to 90 °, the contact stress distribution curves on the core area for the seal face change from cosine to sine type, and the maximum at the peaks and troughs and the average first decrease and then increase. The relationship curves between the maximum or average contact stress and the angle of two long axes are approximately symmetrical about the line θ = 45° . This paper provides a simulation evaluation for the ICV metal seal pair with roundness error.
- Published
- 2020
- Full Text
- View/download PDF
35. Technical Basis for Proposed Revisions to ASME Section III Code Case N-891 on Maximum Allowable Indentation Depths in HDPE Pipe to Extend Applicability to PENT Ratings Up to 10,000 Hours
- Author
-
Douglas Scarth, Prabhat Krishnaswamy, Phillip Rush, and Douglas Munson
- Subjects
Basis (linear algebra) ,business.industry ,Section (archaeology) ,Indentation ,Code (cryptography) ,Structural engineering ,High-density polyethylene ,business ,Mathematics - Abstract
Mandatory Appendix XXVI of Section III of the ASME B&PV Code contains rules for the construction of Class 3 pressure piping systems comprised of PE4710 High Density Polyethylene (HDPE) with a minimum Pennsylvania Notched Test (PENT) rating of 2,000 hours. Appendix XXVI contains acceptance standards for the maximum allowable depths of gouges, cuts or other surface conditions that are characterized as indentations. The acceptance standards are very conservative, in particular for large diameter HDPE pipes. Less restrictive maximum allowable indentation depths for PE4710 HDPE pipes with a minimum PENT rating of 2,000 hours were previously developed based on analyses of tests on HDPE pipes containing scratches. These less restrictive maximum allowable indentation depths were published in the ASME Section III Code Case N-891 as an alternative to the acceptance standards in Appendix XXVI. The PENT rating of PE4710 HDPE material can significantly exceed 2,000 hours, and the current maximum allowable indentation depths in Code Case N-891 are overly-restrictive for the higher PENT ratings. Maximum allowable indentation depths for PENT ratings up to 10,000 hours have been developed, and are proposed to be implemented into a revision of Code Case N-891 and Appendix XXVI. The technical basis for the maximum allowable indentation depths for these higher PENT ratings is provided in this paper. The proposed revisions to Code Case N-891 include a provision to permit use of results from accelerated PENT testing at a higher temperature and stress level than standard PENT test conditions. The technical basis for the use of results from accelerated PENT testing is also provided in this paper.
- Published
- 2020
- Full Text
- View/download PDF
36. INCEFA-PLUS Project: The Impact of Using Fatigue Data Generated From Multiple Specimen Geometries on the Outcome of a Regression Analysis
- Author
-
Jean-Christophe Le Roux, Joshua L. Waters, Peter Gill, Norman Platts, Jack Beswick, Philippe Spätig, and Alec McLennan
- Subjects
Materials science ,Statistics ,Regression analysis ,Outcome (game theory) ,Mathematics - Abstract
The INCEFA-PLUS project (INcreasing Safety in NPPs by Covering gaps in Environmental Fatigue Assessment) aims to generate and analyse Environmentally-Assisted Fatigue (EAF) experimental data studying parameters such as mean strain, hold times and surface finish. To understand the implications of these parameters for environmental fatigue assessments, these tests were carried out at 300 °C in air and light water reactor primary coolant environments (at 230 °C and 300 °C). Over the duration of this project around 230 fatigue data points were generated by different organisations using a common testing methodology, but with differing specimen geometries. Of these 230 data points, 23 were obtained from tests done using hollow specimen designs. Recent work comparing the fatigue lives of hollow to those of solid specimens indicates that on average the use of hollow specimens results in reduced fatigue lives. This has been explained in terms of the additional hoop and radial strains applied to the specimen due to the internal pressure of the hollow specimen. Given the examples published in the literature on the topic, the comparison of data generated using hollow and solid specimen geometries within the INCEFA-PLUS database has been a particular concern. This paper aims to explore the differences between hollow and solid specimen geometries within the INCEFA-PLUS database, highlight the potential risks of including both geometries in a single analysis, and discusses the approach taken by the project to mitigate the identified risks. The work presented in this paper details three approaches for the data obtained from hollow specimens: 1) exclude the data, 2) include the data as is, or 3) include the data with a correction on the strain amplitude. The strain amplitude correction will be based on the theoretical basis presented in Gill et al. [1], and extended to account for the different hollow specimen geometries used across the INCEFA-PLUS programme. This work demonstrates the robustness of the data analysis performed on the INCEFA-PLUS database to the use of differing specimen geometries. It also develops an explanation for the apparent difference in fatigue life between tests conducted on hollow and solid specimens under test conditions that are nominally the same. Furthermore, this paper builds on the mechanistic understanding presented in Gill et al. [1] and generalises across several Laboratories.
- Published
- 2020
- Full Text
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37. Significance of Ms and Validation of Reference Stress Solutions for Crack Like Flaws: Part 1
- Author
-
Greg Thorwald and Yoichi Ishizaki
- Subjects
Stress (mechanics) ,Reference stress ,business.industry ,Structural engineering ,business ,Mathematics - Abstract
This is Part 1 of two papers discussing the significance of two key factors of crack like flaw assessment in the Fitness for Service assessment. While FEM analysis technology has been advancing amazingly in recent years, and FEM based fitness-for-service assessment of damaged components, such as crack like flaws and local metal loss assessment, has become mainstream in assessments, it is still important to understand the reference stress solution and the role of each factor in the failure mode to operate the damaged component safely until the end of its life. In API 579-1/ASME FFS-1[1], Part 9, Assessment of Crack like Flaws, those reference stress solutions were developed based on the limit load analysis using Folias factor Mt and surface correction factor Ms. Folias factor Mt and surface correction factor Ms, are factors that account for the bulging effect around flaws. Those factors enable prediction of a maximum allowable pressure of a damaged cylindrical shell from a simple flat plate model that contain same size of defected area. As for Folias factor, Mt, it is well known to express the relationship between the reference stress of a through-wall crack flat plate and a through-wall crack cylinder. The application of Mt is clearly defined in ASME/API 579 FFS-1 part 9C [1], as well as papers by Folias et al. [2][3]. The significance of the surface correction factor for surface flaw, Ms, has not been commonly understood well enough in general. Unfortunately, API 579-1/ASME FFS-1[1] also does not clearly mention its significance and how Ms is to be applied in the stress analysis. Also the detailed discussion of the derivation process of each reference solution was rooted in several papers with different nomenclature and slightly different definition of factors, which can be very confusing. At a glance, surface correction factor, Ms, looks like a similar factor to Mt, and it is tempting to simply apply Ms to primary membrane stress term like Mt, but that is not correct. Eventually, an incorrect application of Ms would lead to an incorrect discussion of a flaw characterization. Often, there is a question about ASME/API 579 FFS-1[1] Part 9C reference stress solutions, especially for ASME/API 579 FFS-1[1] eq.9C.76, from the misunderstanding meaning of the Ms factor. Addressing this issue is important to maintain the understanding and integrity of the Fitness-For-Service technology. In this Part 1 of two papers, authors reviewed and reorganized step by step procedure of each reference stress solutions for flat plates and cylinders. Through this discussion, authors clarified the significance of Mt and Ms that are defined in ASME/API 579 FFS-1[1] Part 9C. In part 2, validation of equations obtained in this paper is discussed based on FEM analysis.
- Published
- 2020
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38. Effect of Friction Coefficients Regarding Bolt Self-Loosening
- Author
-
Yasumasa Shoji
- Subjects
business.industry ,Structural engineering ,Thread (computing) ,business ,Mathematics - Abstract
As there have been many researches for bolt self-loosening and a lot of knowledge have been accumulated, the phenomena has been understood more and more clearly. On the other hand, it is quite difficult to achieve both non-self-loosening and easy bolting tasks. In practical situations, easy and stable bolting is more focused and torque control is employed for tension control in the fields. For the stable bolting, friction of the threads is reduced by lubrication. However, the effect of this friction reduction is not yet investigated in the aspect of self-loosening. In this paper, the effect of frictions between male and female threads and between nut and bearing surface is investigated by FEA simulations. This provides information how self-loosening can be controlled. In this paper, the motion of the fastened plate transverse to the bolt axis is considered. This motion is known as the easiest motion to make self-loosening in experience and also as shown so in the author’s previous researches. The friction seems to increase self-loosening and also decrease self-loosening at the same time. It seems that the friction on the bearing surface drives self-loosening and friction on the thread surfaces prevents it. In this paper, both the frictions are examined in the relative manner with the Finite Element Analyses.
- Published
- 2020
- Full Text
- View/download PDF
39. Mathematical Description of Projectile Shot Exit Dynamics (Set-Forward).
- Author
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Carlucci, D. E., Frydman, A. M., and Cordes, J. A.
- Subjects
- *
MATHEMATICAL programming , *INTERIOR ballistics , *AERIAL projectiles , *FINITE element method , *MUZZLES (Firearms) , *MILITARY engineers - Abstract
The dynamics or "ringing" of a projectile structure at gun-muzzle exit has been observed to cause a large number of electronics failures in projectiles as well as possible safety concerns with respect to components impacting one another or structural components of the projectile coming apart. Current numerical tools allow accurate calculation of the muzzle exit event given that the engineer understands the forces acting on the projectile. Dynamic response of a structure is well understood by persons working in the field; however, engineers who do not regularly deal with dynamic analyses generally have difficulty interpreting results from both analyses and tests. This paper details the mathematics associated with this event so that the engineer confronted with a dynamics related issue can have a reference for understanding and interpretation. The results of a simple model show that accelerometer data should be used with caution and-the support of a finite element analysis of the projectile structure with the proper pressure decay is usually necessary. Recommendations for use of measured acceleration data for modeling and simulation are provided. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
40. Capability Estimation of Geometrical Tolerance With a Material Modifier by a Hasofer-Lind Index.
- Author
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Tahan, Antoine S. and Cauvier, Jason
- Subjects
- *
MATHEMATICAL models , *DISTRIBUTION (Probability theory) , *MATHEMATICAL functions , *MATHEMATICS , *STATISTICAL process control - Abstract
This paper considers a way of measuring a process capability index in order to obtain the geometric tolerance of a pattern of position elements according to the ASME Y14.5 standard. The number of elements present in the pattern, as well as its material condition (least LMC or maximum MMC), are taken into consideration during the analysis. An explicit mathematical model will be developed to identify the distribution functions (PDF and CDF) of defects on the location and diameter. Using these distributions and the Hasofer-Lind index, we will arrive at a new definition of process capability--meaning the value of tolerances that can meet the threshold of x% compliance. Finally, our method is validated using a variety of typical case studies. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
41. A Fast Correction for Elastic Quarter-Space Applied to 3D Modeling of Edge Contact Problems.
- Author
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Guilbault, Raynald
- Subjects
HERTZIAN contacts ,NUMERICAL analysis ,CORRECTION factors ,FINITE element method ,ALGORITHMS ,MATHEMATICS - Abstract
Applying the Hertz theory to some non-Hertzian contact problems can produce acceptable results. Nevertheless, including the influence of free surfaces requires numerical methods, many of. which are based on the Boussinesq-Cerruti solution. This paper presents a new approach, which is better capable of releasing quarter-space free surfaces from shear and normal internal stresses without engendering any increase in calculation times. The mirrored pressure for shear correction is multiplied by a correction factor (ψ), which accounts for the normal load. The expression ψ is derived from the Hetényi correction process, and the resulting displacements show an enhanced correspondence with validation finite element method models; with an imposed fluctuating pressure, the maximum edge displacement error was -21.90% for a shear load correction (Poisson coefficient = 0.3), and introducing the ψ factor reduced the deviation to -9.55%, while for u of 0.15, the maximum error was -11.30%, which was reduced to +0.60% with the ψ factor. This study introduces the factor ψ, in a 3D elastic contact algorithm. The resulting calculation scheme is then able to simulate any point or line Contact problems. Compared with coincident ends and sharp edge contact validation values, the model shows high conformity levels. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
42. Performance of Mechanical Bandpass Filters Used in Energy Scavenging in the Presence of Fabrication Errors and Coupling.
- Author
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Shahruz, S. M.
- Subjects
BANDPASS filters ,MATHEMATICS ,MATHEMATICAL models ,MATHEMATICAL statistics ,STATISTICS ,MATHEMATICAL variables ,RANDOM variables ,ELECTRIC filters ,MATHEMATICAL ability - Abstract
In this paper several mathematical models that are more realistic representations of mechanical bandpass filters are studied. Such filters can be used in energy scavengers to convert energy from vibration sources into small amount of electricity. A mechanical bandpass filter is an ensemble of cantilever beams where at the tip of each beam a mass, known as the proof mass, is mounted. A beam with a proof mass at its tip is called a beam-mass system. By studying a variety of models representing the filter dynamics, it will be unraveled to what extent fabrication errors in beam-mass systems of a filter and/or the coupling of such systems can alter the bandpass behavior of a fabricated filter. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
43. An Alternative to F. Y. M. Wan's Single Equation for an Elastic Right Circular Conical Shell.
- Author
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Simmonds, J. G.
- Subjects
- *
EQUATIONS , *BENDING (Metalwork) , *CALCULUS , *COMPUTER networks , *MATHEMATICS , *DIFFERENTIAL equations , *BESSEL functions , *DIFFERENTIAL inclusions , *EXISTENCE theorems - Abstract
In 1970, F Y. M. Wan derived a single, complex-valued ordinary differential equation for an elastically isotropic right circular conical shell ("On the Equations of the Linear Theory of Elastic Conical Shells," Studies AppI. Math., 49, pp. 69-83). The unknown was the nth Fourier component of a complex combination of the midsurface normal displacement and its static-geometric dual, a stress function. However an attempt to formally replace the Fourier index n by a partial derivative in the circumferential angle θ results in a partial differential equation, which is eighth order in θ. The present paper takes as unknowns the traces of the bending strain and stress resultant tensors, respectively, and derives static-geometric dual partial differential equations of fourth order in both the axial and circumferential variables. Because of the explicit appearance of Poisson ratios of bending and stretching, these two equations cannot be combined into a single complex-valued equation. Reduced equations for beamlike (axisymmetric and lateral) deformations are also derived. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
44. Accounting for High Stress Gradient by a Modified Weibull Failure Theory.
- Author
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Ekwaro-Osire, S., Khandaker, M. P. H., and Gautam, K.
- Subjects
- *
WEIBULL distribution , *STRAINS & stresses (Mechanics) , *PROBABILITY theory , *GEOMETRIC function theory , *DISTRIBUTION (Probability theory) , *STRUCTURAL analysis (Engineering) , *MECHANICS (Physics) , *MATHEMATICS , *GEOMETRY - Abstract
A high stress gradient occurs in a component when the stress, due to external loading, rises asymptotically. The Weibull failure theory overestimates the probability of failure for components with high stress gradients generated due to the geometric irregularities, material mismatch, thermal mismatch, and contact loading. A modified Weibull failure theory is proposed in this paper The method is based on the weight function method. The modified Weibull failure theory was applied to two specimens, and the results showed the ability of the proposed theory to handle high stress gradients. The theory considers variable equivalent stress intensity factors along the faces of cracks; hence, it considers the strength of a specimen to be dependent on the stress field. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
45. A Generalized Fault Classification for Gas Turbine Diagnostics at Steady States and Transients.
- Author
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Loboda, Igor, Yepifanov, Sergiy, and Feldshteyn, Yakov
- Subjects
- *
GAS turbines , *TURBINES , *THERMODYNAMICS , *DYNAMICS , *PROBABILITY theory , *MATHEMATICS - Abstract
Gas turbine diagnostic techniques are often based on the recognition methods using the deviations between actual and expected thermodynamic performances. The problem is that the deviations generally depend on current operational conditions. However, our studies show that such a dependency can be low. In this paper, we propose a generalized fault classification that is independent of the operational conditions. To prove this idea, the probabilities of true diagnosis were computed and compared for two cases: the proposed classification and the conventional one based on a fixed operating point. The probabilities were calculated through a stochastic modeling of the diagnostic process. In this process, a thermodynamic model generates deviations that are induced by the faults, and an artificial neural network recognizes these faults. The proposed classification principle has been implemented for both steady state and transient operation of the analyzed gas turbine. The results show that the adoption of the generalized classification hardly affects diagnosis trustworthiness and the classification can be proposed for practical realization. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
46. Kinematic and Geometric Analysis of a Pure-Rolling Epicyclic Train.
- Author
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Chao Chen, Xiang Zhang, and Jorge Angeles
- Subjects
- *
MATHEMATICS , *KINEMATICS , *ENGINEERING design , *ATMOSPHERIC boundary layer - Abstract
This paper reports an innovative design of epicyclic (planetary) cam trains based on pure-rolling contact, intended to overcome the drawbacks of gear trains, such as Coulomb friction and backlash. The kinematic relations of the mechanism with a given speed-reduction ratio are analyzed; accordingly, the profiles of the sun cam and ring cam, key elements of the mechanism, are obtained. Furthermore, the condition for undercutting avoidance of the ring cam is derived. For mechanical design, different layouts of the epicyclic cam trains are discussed for the structure and transmission optimization. Finally, an epicyclic cam-roller speed reducer is designed and prototyped. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
47. A Preconditioning Mass Matrix to Avoid the Ill-Posed Two-Fluid Model.
- Author
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Zanotti, Angel L., Méndez, Carlos G., Nigro, Norberto M., and Storti, Marie
- Subjects
- *
FLUID models in geophysics , *MATHEMATICS , *MATRICES (Mathematics) , *EIGENVALUES , *EQUATIONS , *NUMERICAL analysis - Abstract
Two-fluid models are central to the simulation of transport processes in two-phase homogenized systems. Even though this physical model has been widely accepted, an inherently nonhyperbolic and nonconservative ill-posed problem arises from the mathematical point of view. It has been demonstrated that this drawback occurs even for a very simplified model, i.e., an inviscid model with no interfacial terms. Much effort has been made to remedy this anomaly and in the literature two different types of approaches can be found. On one hand, extra terms with physical origin are added to model the interphase interaction, but even though this methodology seems to be realistic, several extra parameters arise from each added term with the associated difficulty in their estimation. On the other hand, mathematical based-work has been done to find a way to remove the complex eigenvalues obtained with two-fluid model equations. Preconditioned systems, characterized as a projection of the complex eigenvalues over the real axis, may be one of the choices. The aim of this paper is to introduce a simple and novel mathematical strategy based on the application of a preconditioning mass matrix that circumvents the drawback caused by the nonhyperbolic behavior of the original model. Although the mass and momentum conservation equations are modified, the target of this methodology is to present another way to reach a steady-state solution (using a time marching scheme), greatly valued by researchers in industrial process design. Attaining this goal is possible because only the temporal term is affected by the preconditioner. The obtained matrix has two parameters that correct the nonhyperbolic behavior of the model: the first one modifies the eigenvalues removing their imaginary part and the second one recovers the real part of the original eigenvalues. Besides the theoretical development of the preconditioning matrix, several numerical results are presented to show the validity of the method. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
48. Determination of Singularity-Free Zones in the Workspace of Planar 3-P_RR Parallel Mechanisms.
- Author
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Mehdi Tale Masouleh and Cle´ment Gosselin
- Subjects
- *
ALGORITHMS , *MATHEMATICS , *MECHANICS (Physics) , *ALGEBRA - Abstract
This paper presents an algorithm for the determination of singularity-free zones in the workspace of the planar 3-P_RR mechanism. The mathematical derivation of the algorithm is first given. Numerical examples are then included to demonstrate the application of the proposed approach. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
49. Modeling of Crack Propagation in Thin-Walled Structures Using a Cohesive Model for Shell Elements.
- Author
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Zavattieri, Pablo D.
- Subjects
- *
FINITE element method , *NUMERICAL analysis , *MATHEMATICAL analysis , *MATHEMATICS , *ALGEBRA - Abstract
A cohesive interface element is presented for the finite element analysis of crack growth in thin specimens. In this work, the traditional cohesive interface model is extended to handle cracks in the context of three-dimensional shell elements. In addition to the traction-displacement law, a bending moment-rotation relation is included to transmit the moment and describe the initiation and propagation of cracks growing through the thickness of the shell elements. Since crack initiation and evolution are a natural outcome of the cohesive zone model without the need of any ad hoc fracture criterion, this model results in automatic prediction of fracture. In particular, this paper will focus on cases involving mode I/III fracture and bending, typical of complex cases existing in industrial applications in which thin-walled structures are subjected to extreme loading conditions (e.g., crashworthiness analysis). Finally, we will discuss how the three-dimensional effects near the crack front may affect the determination of the cohesive parameters to be used with this model. [ABSTRACT FROM AUTHOR]
- Published
- 2006
- Full Text
- View/download PDF
50. Nonlocality Effect in Atomic Force Microscopy Measurement and Its Reduction by an Approaching Method.
- Author
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Ming Hu, Haiying Wang, Mengfen Xia, Fujiu Ke, and Yilong Bai
- Subjects
- *
MICROSCOPY , *MEASUREMENT , *OPTICS , *ENGINEERING , *MATHEMATICS , *INFINITY (Mathematics) - Abstract
In AFM measurements of surface morphology, the locality is a traditional assumption, i.e., the load recorded by AFM is simply the function of the distance between the tip of AFM and the point on a sample right opposite the tip [Giessibl, F J., 2003, "Advances in Atomic Force Microscopy," Rev. Mod. Phys., 75, pp. 949-983]. This paper presents that nonlocality effect may play an important role in atomic force microscopic (AFM) measurement. The nonlocality of AFM measurement results from two different finite scales: the finite scale of the characteristic intermolecular interaction distance and the geometric size of AFM tip. With a coupled molecular-continuum method, we analyzed this nonlocality effect in detail, it is found that the non locality effect can be formulated by a few dimensionless parameters characterizing the ratio of the following scales: the characteristic intermolecular interaction distance between the AFM tip and the sample, the characteristic size of the tip and the characteristic nano-structure and/or the nanoscale roughness on the surface of a sample. The present work also suggests a data processing algorithm—the approaching method, which can reduce the nonlocality effect in AFM measurement of surface morphology effectively. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
- View/download PDF
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