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This paper presents a Piezoelectric Micromachined Ultrasonic Transducer (PMUT) array targeting mid-air haptic feedback applications. Compared to existing bulk ultrasound transducer technologies, this array implements polymer-based micromachined ultrasound transducers fabricated in a display-compatible, large area technology. It is, thus, a good candidate for direct integration on top of large displays and allows to fabricate dense PMUT arrays for a fine non-contact haptic experience at interesting price point.

This proposal aims at demonstrating the suitability of two different non-intrusive and versatile methods to determine the (cumulated) probability density function of a physical quantity of interest that depends on a couple of stochastically varying parameters. The first one is based on numerical integration using a triangulation of the parameter space, similar to matrix assembly in the finite element method. The second one, the statistical order reduction methods, utilizes orthogonal polynomials to identify an efficient “design of experiments” together with weighting factors for the data to be determined according to the identified design. Both methods are compared to each other and to the classical Monte Carlo method with respect to reliability and performance. As practically relevant benchmark problem, the determination of a cable shield's transfer impedance is studied.

A (3+1)-D generalized B-type KP-Boussinesq equation, which was recently formulated in the literature, is investigated here from Lie group standpoint. A solution is obtained by Lie symmetry reductions and direct integration in terms of incomplete elliptic integral. Furthermore, hyperbolic and trigonometric functions solutions are derived by invoking the (G′/G)- expansion method. Finally, we construct conservation laws of the aforementioned equation by utilizing the multiplier method and conservation theorem due to Ibragimov. Keywords: A (3+1)-dimensional generalized BKP-Boussinesq equation, Lie point symmetries, Exact solutions, Incomplete elliptic integral, (G′/G)-expansion method, Conservation laws

This paper presents the starting situation and some interim results of a research project with the aim of a fully electrified short-range public transportation in a German town called Solingen. It gives an insight to the existing trolleybus infrastructure and the benefits of second life battery usage. Following, the design configuration of a refurbished trolleybus battery system for stationary usage in substations is shown and evaluated. Based on this a new silicone carbide power electronic for a direct integration of stationary battery systems are proposed and evaluated. Available semiconductors for the prototype are specified and compared by measurements. The results show that the integration of trolleybus batteries can be done with high system efficiency.

The sign problem of relativistic field theories at finite fermion chemical potential has been approached by deforming the domain of integration into complex field space. We present a method for selecting a deformed manifold of integration which is a local maximum of the average phase, and demonstrate this method on the three-dimensional Thirring model. Finally, we compare the performance of this method, in the heavy-dense limit, to direct integration on the Lefschetz thimbles., Comment: 7 pages; proceedings from LATTICE2018

To achieve resource efficiency and an increased performance, as well as a higher safety and more features for vehicles, lightweight composites are a central sphere of activity for automotive innovations. This becomes particularly striking if the focus is not only a reduced vehicle weight but also an efficient overall concept. In addition to compatible material technologies and component design, new electronic solutions are of interest. A research contribution at the Robert Bosch Company deals with the direct integration of a current automotive acceleration sensor in fiber-reinforced polymer (FRP) parts. The sensor is part of the passive vehicle safety. Primarily, the principal application of the currently mounted sensor as an integrated part of the vehicle structure was proven. Sensor-integrated parts were evaluated on their sensing functionality as well as their structural performance. The present research is done to use the integrated sensor for a secondary feature. The study shows that the sensor can also be an indicator for the condition of its surrounding FRP structure. Hence, the sensor integration makes it possible to derive a secondary feature for automobiles by using the current sensor for future functionalized lightweight structures.

In this paper we study the calculation of multiloop Feynman integrals that cannot be expressed in terms of multiple polylogarithms. We show in detail how certain types of two- and three-point functions at two loops, which appear in the calculation of higher order corrections in QED, QCD and in the electroweak theory (EW), can naturally be expressed in terms of a recently introduced elliptic generalisation of multiple polylogarithms by direct integration over their Feynman parameter representation. Moreover, we show that in all examples that we considered a basis of pure Feynman integrals can be found.

We calculate the four-loop massless QCD corrections with two closed quark lines to quark and gluon form factors. The results for the gluon form factor and the singlet part of the quark form factor are given for the first time. From our analytic expressions for the form factors, we determine the corresponding cusp anomalous dimensions. The relevant Feynman integrals are obtained with novel integral reduction techniques and direct integration methods.

ISAR imaging technology has been applied in various fields such as object identification, radar detecting, object quality test and so on. Several ISAR imaging algorithms are realized and compared by running efficiency, imaging quality in the paper. FFT algorithm is fast but its quality is limited by angle rotation range, Direct Integration algorithm is unlimited but its efficiency is very poor. Compared to the both, CBP algorithm (Convolution Back Projection) is fast and unlimited by applied sceneries. CBP algorithm can form high-resolution ISAR image and has a low cost of running time.

Highly stretchable strain sensors, with embedded microchannels filled with conductive liquid, have been widely used in various applications in soft robotics for detecting different types of deformation modes, when attached to human or robot bodies. One of recent applications that draws an attention is direct integration of soft sensors with soft actuators for proprioceptive feedback. However, it is not easy to obtain a high resolution in curvature sensing when combined with bending actuators in which curvature is indirectly measured from strain sensing, since the placement of soft sensors are limited to the location where the strain sensitivity is relatively small. Therefore, we propose a new design of high gauge factor strain sensors using a multi-material structure. By alternately arranging low and high stiffness elastomers, the structure experiences amplified strain changes on each of the low-stiffness regions. The gauge factor was significantly increased as high as over three times of a conventional single material sensor. In this paper, the design and fabrication of the proposed sensor are described with an analytical model. The sensor was tested while integrated with a PneuNet bending actuator for curvature detection as an application.

The purpose of this paper is to find conformal vector fields of some perfect fluid Kantowski-Sachs and Bianchi type III space-times in the f(R) theory of gravity using direct integration technique. In this study there exists only eight cases. Studying each case in detail, we found that in two cases proper conformal vector fields exist while in the rest of six cases conformal vector fields become Killing vector fields. The dimension of conformal vector fields is either 4 or 6., 12 pages

In the context of improving energy efficiency and thermal comfort in the building, the use of phase change materials (PCMs) is one of the suggested solutions. The proposed integration solutions concern the building envelope as well as the applications related to its operation. The study of the incorporation of PCM in the walls of the building was the subject of numerous works. However, the antisymmetric character of storing/recovering energy management in the walls is less controlled and do not fit the optimal conditions. In this study, a solution based on the direct integration of a stabilized PCM (gel) in an envelope including ventilation channels, was proposed to overcome this problem of antisymmetry storing/recovering and fitting with different fixed ambient conditions. The final aim is to develop the optimization strategy of a wall combining the heavy inertia offered by the PCM, intra-ventilation control and the contribution to air renewal energy demand. In this context, an experimental study of a concrete block system is conducted to test the thermal response of this configuration by the application of cyclic solicitations. The comprehension of this integrated constructive solution essentially passes by the possession of validated numerical tools. For this, two models have been developed. The first model using the electrical–thermal analogy, based on an RC equivalence, is distinguished by its relative simplicity and weak time computing demand. Each of these two factors, R and C summarise the system properties and has a direct influence on the building transient simulations over a year. The second one is based on direct numerical simulation DNS of the energy and fluid flow equations using commercial code COMSOL Multiphysics. Such DNS is time consuming and could not be used to simulate over a year but aims only to validate the first RC circuit approach. A comparison of these two models with the idealised experimental data was carried out and allowed the validation of the thermal behaviour of the solution based on the integration of the PCM with core ventilation.

This paper presents the three-dimensional analysis of laminated composite rectangular plates with general boundary and loading conditions using the strong sampling surfaces (SaS) formulation and the extended differential quadrature (EDQ) method proposed by the first author. The strong SaS formulation is based on the choice of SaS parallel to the middle surface and located at Chebyshev polynomial nodes to introduce the displacements of these surfaces as plate unknowns. This choice of unknowns with the use of Lagrange polynomials in the through-thickness approximations of displacements, strains and stresses leads to an efficient laminated plate formulation. The outer surfaces and interfaces are not included into a set of SaS that makes it possible to minimize uniformly the error due to Lagrange interpolation. Therefore, the strong SaS formulation based on direct integration of the equilibrium equations of elasticity in the transverse direction in conjunction with the EDQ method can be applied effectively to high-precision calculations for the composite rectangular plates with different boundary conditions. This due to the fact that in the SaS/EDQ formulation the displacements, strains and stresses of SaS are interpolated in a rectangular domain using the Chebyshev-Gauss-Lobatto grid and Lagrange polynomials are also utilized as basis functions. Such a technique allows the use of only first order derivatives in the equilibrium equations that simplifies the implementation of the EDQ method.

This study provides a quasi-three-dimensional (quasi-3D) dynamic model for rotating pre-twisted functionally graded (FG) blades based on the three-dimensional elasticity shell theory and Carrera unified formulation. The material properties of the pre-twisted FG blades alter continuously in the direction of the thickness. The boundary conditions (clamped-end and free-edge) are realized by utilizing the well-known penalty method. Initial centrifugal stress field due to the high rotating speed is determined by two centrifugal stress solving methods, direct integration of centrifugal forces (DICF) and static analysis under centrifugal forces (SACF). The modified Fourier spectral approach is utilized to construct the displacement variables of the higher-order configurations. Eigenvalue problems are obtained by using the Hamilton's principle on the base of the kinetic, strain, centrifugal potential and boundary potential energy. The results of the theoretical model display a good agreement with the reference data and FEM results. Parametric studies are then performed to assess the applicability of the centrifugal stress solving methods and investigate the effects of the centrifugal shear stress, rotating speed, pre-twisted angle, penalty factors as well as the volume fraction index on the vibration characteristics of the pre-twisted FG blades. It is expected that the quasi-3D solutions for the rotating pre-twisted FG blades will serve as benchmarks in future researches.

Principal component analysis (PCA) has proved to be a powerful technique for processing NMR data. It is particularly useful in signal quantitation where it often provides better results compared to a direct integration of individual signals. In the present work, we recapitulate the principles and theoretical framework underlying PCA-based quantitation with a special focus on T1 relaxometry. We show that under commonly encountered conditions, this approach can provide up to ~4-fold improvement in scatter of points in magnetization build-up curves compared to direct integration. Best practices to optimize the PCA performance in measuring the total magnetization are discussed, including minimization of the number of signal-related principal components and a proper selection of FT parameters and data quantitation intervals. For signals consisting of distinct relaxation components, formulas are provided for resolving the components relaxation and illustrated on a real-data example. In addition to the problem of quantitation, the use of PCA in denoising of partially relaxed spectra is discussed in connection with such applications as line shape analysis and monitoring relaxation of individual spectral components.

The fully anisotropic response of composite beams is an important consideration in diverse applications including aeroelastic responses of helicopter rotor and wind turbine blades. Our goal is to present exact analytical solutions for the first time for coupled deflection of Euler–Bernoulli composite beams. Towards this goal, two approaches are proposed: (1) obtaining the exact analytical solutions directly from the governing equations of Euler–Bernoulli composite beams and (2) extraction of the solutions from Timoshenko composite beam solutions. For the direct solution approach, based on Euler–Bernoulli theory, new variationally-consistent field equations are obtained, in which four degrees of freedom, i.e. in-plane bending, out-of-plane bending, twist and axial elongation are fully coupled. By expressing the coupled system of differential equations in a compact matrix form, a novel expression for the eccentricity of neutral axes from the midplane, as well as the shift in shear centre from the centre of beam, is obtained. This eccentricity matrix serves to decouple the bending in the two principal directions from in-plane and twist deformations. Then, the general closed-form analytical solutions for the decoupled system are derived simply using direct integration. Additionally, the analogous closed-form analytical solutions are retrieved from the previously obtained Timoshenko composite beam solution and it is proven that they are identical to those obtained from the current direct approach for conditions where Euler–Bernoulli beam theory apply. To study the effects of anisotropy, numerical results are obtained for a number of examples with different composite stacking sequences showing various coupled behaviours. The results are compared against the Chebyshev collocation method as well as against less comprehensive analytical solutions available in the literature, noting that excellent agreement is observed, where expected. The present exact solutions can serve as benchmark problems for assessing the accuracy and convergence of various analytical and numerical methods.

This work proposes a chemical mechanism tabulation method using artificial neural networks (ANNs) for turbulent combustion simulations. The method is employed here in the context of the Large-Eddy Simulation (LES)–Probability Density Function (PDF) approach and the method of stochastic fields for numerical solution, but can also be employed in other methods featuring real-time integration of chemical kinetics. The focus of the paper is on exploring an ANN architecture aiming at improved generalization, which uses a single multilayer perceptron (MLP) for each species over the entire training dataset. This method is shown to outperform previous approaches which take advantage of specialization by clustering the composition space using the Self-Organizing Map (SOM). The ANN training data are generated using the canonical combustion problem of igniting/extinguishing one-dimensional laminar flamelets with a detailed methane combustion mechanism, before being augmented with randomly generated data to produce a hybrid random/flamelet dataset with improved composition space coverage. The ANNs generated in this study are applied to the LES of a turbulent non-premixed CH4/air flame, Sydney flame L. The transported PDF approach is used for reaction source term closure, while numerical solution is obtained using the method of stochastic fields. Very good agreement is observed between direct integration (DI) and the ANNs, meaning that the ANNs can successfully replace the integration of chemical kinetics. The time taken for the reaction source computation is reduced 18-fold, which means that LES–PDF simulations with comprehensive mechanisms can be performed on modest computing resources.

This paper presents and discusses a hybrid-mixed stress (HMS) finite element model for the static and dynamic analysis of 2D reinforced concrete frame structures. It is assumed a physically non-linear behaviour for both concrete and steel. In this model, both the stress and the displacement fields are approximated in the domain of each element. Complete sets of orthonormal Legendre polynomials are used as approximation functions. The use of these functions makes possible the definition of analytical closed form solutions for the computation of all structural operators when a physically linear behaviour is assumed and leads to the development of very effective p- refinement procedures. Due to the nature of the HMS formulation, it is possible to consider the use of both inverse and direct integration schemes at the cross-section level. The time integration procedure uses classical step-by-step techniques, such as Newmark and α-HHT method. The latter is used in order to supress some numerical noise that may occur in the iterative procedure involved in the solution of dynamic non-linear problems. Three different types of damage models, with and without permanent strains, are used to model concrete behaviour. To validate the model, to illustrate its potential and to assess its accuracy and efficiency, several numerical examples are discussed, and comparisons are made with solutions provided by other numerical techniques.

This paper studies the Sasa-Satsuma equation, which is used to describe the nonlinear phenomenon of pulse propagation in optical fiber communication. By using the direct integration method, all envelope traveling wave patterns are given, including singular solutions, solitary wave solutions and elliptic function double periodic solutions. These patterns show completely the behaviors of dynamics of the model.

A mathematical model for the study of reaction kinetics and molecular weight distributions in miniemulsion polymerization systems with oil-soluble initiators is presented. The mathematical model allows the computation of the evolution of the complete molecular weight distribution with chain lengths of up to 105 mers in miniemulsion polymerization by direct integration in reasonable computational time. Also, no restriction in the kinetic regime is needed, as the model is able to represent both compartmentalized and pseud-bulk systems. The model was validated with experimental results for methyl methacrylate and styrene homopolymerizations, with two different oil-soluble initiators, and adequately represented both the kinetics and molecular weight distributions of these systems. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2128–2140, 2017

The creation of fabrics capable of dynamically communicating information would have a great impact on future smart fabric technologies for applications ranging from fashion and entertainment to biomedical monitoring. Typically, state-of-the-art displays are fabricated onto flexible substrates and then mounted onto textiles. However, recent progress in fabricating electroluminescent (EL) fiber-shaped devices that can be directly integrated into knitted and woven structure has unlocked new opportunities for developing fabric-integrated displays. Here, a novel method of directly integrating an EL system into a network of fibers to create a dynamic knit display is presented. A 4-pixel prototype with individually controllable pixels disposed within a knitted fabric matrix is demonstrated. The control system and structure of isolated pixels in the knit fabric matrix are explained. Important display features based on the prototype performance that demonstrate the current and future potential of this structure are reported.

This paper presents a numerical dynamic analysis of a self-supporting transmission line (TL) latticed steel tower, for the purpose of compare the results with those obtained in an experimental dynamic analysis of a full-scale tower. The main objective of this work is to calibrate the structural damping ( c ) in the numerical model until the damping ratio ( ζ ) results the same that in the experimental analysis, since the damping is a fundamental parameter in numerical analysis, which can change significantly the response of the structure, especially in terms of dynamic amplification. It should be noted that in this type of structure is crucial perform a structural analysis most accurate possible, given the fact that in a TL are built hundreds of identical towers and the collapse of one can lead to a cascading failure. The dynamic characteristics, such as the frequencies and normal modes were evaluated in a modal analysis, using the ANSYS © program v. 15.0, and also through the direct numerical integration method, using an explicit approach (central finite differences). The experimental tower was tested using impulsive loads, which were reproduced in the numerical model to allow comparison with the experimental results. In the modal analysis were employed models commonly used in actual designs, that is, with space truss and space frame members. For the direct integration method, was used a program developed in FORTRAN, in which only space truss elements are allowed, necessitating the adoption of the fictitious bars to eliminate internal instabilities. The consideration of the damping in the direct integration method was taken in a simplest form, that is, proportional to the mass. Finally, the numerical values found were very close to the experimental response, setting the value of structural damping for use in such projects of this type of tower.

A sensitivity-based finite element model updating approach is presented to identify the local damages in axially functionally graded (AFG) beams. The local damage is simulated by a reduction in the elemental Young's modulus of the beam. In the forward analysis, free vibration analysis is conducted to obtain the natural frequency of the beam. Then forced vibration responses of the beam under external force are obtained from Newmark direct integration. In the inverse analysis, an objective function is established and a sensitivity-based finite element model updating approach is used to identify the local damages in the beam. Two numerical examples are investigated to illustrate the correctness and efficiency of the proposed method. Damage identification results from measured natural frequencies and the dynamic responses from different excitation forces are compared. The effects of measurement noise on the identification results are investigated. Studies in this paper indicate that the proposed method is efficient and robust for identifying damages in the axially functionally graded beams. Good identified results can be obtained from the short time histories of a few number of measurement points and the first several natural frequencies.

The effect of soil-structure interaction (SSI) on the dynamic responses of seismically isolated three-span continuous reinforced concrete (RC) bridge is investigated. Also, tuned mass damper(s) (TMD/s) is/are installed to control undesirable bearing displacement, even under the SSI effect. The TMDs are placed at the mid-span of the bridge and each tuned with a modal frequency, while controlling up to first few modes as desirable. The soil surrounding the foundation of pier is modeled by frequency independent coefficients. Dynamic analysis is carried out in time domain using direct integration method. In order to specify the effects of the SSI, the responses of the non-isolated, isolated, and controlled isolated bridge are compared. It is observed that the soil surrounding the pier has significant effects on the bearing displacement of the isolated RC bridges. In addition, it is observed that the seismic responses of isolated RC bridge reduced significantly with installation of the TMDs.

Based on the concept of isoparametric mapping, a generic approach for investigating the bending and shear deformation in a non-prismatic elastic beam with corrugated steel webs (CSWs) was presented in this study. The strain field of an actual element (namely, the non-prismatic beam segments) is expressed as a function of the local coordinates in the parent element. Continually, the solution of the bending and shear deformation of the non-prismatic beam segment can be transformed into the integration of strain in the parent element under local coordinates. Since it is usually laborious to solve the displacement field by direct integration of strain in a non-prismatic beam segment using global coordinates. In addition, this study found that shear deformation cannot be ignored in the actual design of this type of structure because the thin-walled section has a small shear stiffness. In contrast, for a composite beam with CSWs, shear deformation occurs beyond bending deformation and becomes a major contributor of total deformation in some critical sections. Finally, experimental study of the mechanical properties of a non-prismatic beam with CSWs is conducted for the first time. The experimental results further demonstrate the validity of the proposed theoretical analysis methods.

In this paper, 1-soliton and two kinds of peaked solitary wave solutions of nonlinear longitudinal wave equation in magneto–electro–elastic circular rod are presented for the first time. The soliton ansatz will be applied to give 1-soliton solution; then, peaked solitary wave solutions are obtained by using direct integration with boundary condition and symmetry condition. At last, numeric graphs are provided for solitary wave solutions.

Shell and tension surface structures are characterized by complex curved geometries with a potential for structural efficiency and formal quality. To unveil this potential, it is essential to define, modify and analyse complex geometries in an integral way. Describing complex, free-form geometries, within a computer-based design process, non-uniform rational B-Splines (NURBS)-based methods can be considered as standard within the common working process. The mathematical description of geometry with NURBS within a finite element-based analysis has become known as isogeometric analysis (IGA). As the basic descriptions of design and analysis models are equivalent, transforming steps (such as “meshing”, etc.) become irrelevant, and it is possible to fully unify the design and analysis environment. For the direct integration of isogeometric-based structural analysis into the design process the authors developed an interface for the computer aided design (CAD) environment that can directly access a broad field of analysis tasks (such as structural analysis, form-finding, etc.). As a result, the designing architect or engineer is capable of instantly estimating the structural qualities of arbitrary geometries. The integration of architectural and structural design by IGA with CAD enables an integrated design approach. This will be demonstrated in the context of the design of shell structures. To support the design process, the interface contains tools to provide important values such as strain energy to, for example, evaluate the structural efficiency of a random shell geometry within an early design stage. This strongly supports the designer to meet different design criteria derived from either structural or formal aspects. After a brief introduction of the isogeometric analysis method, this paper will highlight the potentials of this method through a variety of case studies. In each study both engineering and architectural design aspects will be addressed by comparing the process and the results of finite element analysis, and highlighting the integrated variability of design.

A new mathematical appoach using the inverse Radon equation for restoration of images in problems of linear two-dimensional x-ray tomography is formulated. In this approach, Fourier transformation is not used, and it gives the chance to create the practical computing algorithms having more reliable mathematical substantiation. Results of software implementation show that for especially for low number of projections, the described approach performs better than standard X-ray tomographic reconstruction algorithms.

Based on the idea of collocation methods, a spline-based integration method for the stability prediction of systems governed by time-periodic delay differential equations (DDEs) is presented. A B-spline curve is adopted to approximate the solution of the DDEs using the direct integration technique. The stability of the dynamic system is then predicted using the Floquet theory based on the established state transition matrix. The proposed method can apply to time-periodic DDEs where the delay and the period are incommensurate, and the proposed method is extended to study the stability of milling processes as well. For stability analysis of variable pitch cutters, the proposed method use one or multiple B-spline curves to approximate the solution of the DDEs according to the relationship between the cutter angles and the radial immersion, which can describe exactly the free vibration of the cutter. Compared with the numerical integration method and the Chebyshev collocation method, the simulation results demonstrate that the proposed technique is more efficient and accurate for stability prediction at low radial immersion cases in milling processes with variable pitch cutters.

A unique formulation of the solution to a spinning, nearly axisymmetric rigid-body is presented. Direct integration of the linearized equations of motion gives accurate results for nearly axisymmetric inertia ellipsoids while avoiding the complexity of more general formulations. The simplicity of the formulation lends itself to a better understanding of the system behavior. Specifically, the motion of the spin axis for this nearly axisymmetric case is described by an oblate epicycloid, providing an extension of the classic epicycloid solution for axisymmetric objects.

We revisit the integer lattice (IL) method to numerically solve the Vlasov-Poisson equations, and show that a slight variant of the method is a very easy, viable, and efficient numerical approach to study the dynamics of self-gravitating, collisionless systems. The distribution function lives in a discretized lattice phase-space, and each time-step in the simulation corresponds to a simple permutation of the lattice sites. Hence, the method is Lagrangian, conservative, and fully time-reversible. IL complements other existing methods, such as N-body/particle mesh (computationally efficient, but affected by Monte-Carlo sampling noise and two-body relaxation) and finite volume (FV) direct integration schemes (expensive, accurate but diffusive). We also present improvements to the FV scheme, using a moving mesh approach inspired by IL, to reduce numerical diffusion and the time-step criterion. Being a direct integration scheme like FV, IL is memory limited (memory requirement for a full 3D problem scales as N^6, where N is the resolution per linear phase-space dimension). However, we describe a new technique for achieving N^4 scaling. The method offers promise for investigating the full 6D phase-space of collisionless systems of stars and dark matter., 9 pages, 5 figures, 1 table, mnras

Probabilistic fatigue analysis of offshore structures requires the numerical simulation of a huge number of loading cases to compute the long-term multi-dimensional integral associated to the fatigue damage assessment. This paper proposes the implementation of the univariate dimension-reduction method developed by Rahman and Xu [1] in order to compute the long-term fatigue damage more efficiently. This method is particularly attractive because it reduces significantly the number of simulations by decomposing the N-dimensional integral associated to expected long-term fatigue damage assessment into the sum of N one-dimensional integrals. In addition, this paper compares the univariate-dimension reduction method with the brute force direct integration methodology and other methods based on Taylor expansions, such as perturbation approach and asymptotic expansion method discussed by Low and Cheung [2]. Two comprehensive examples are included to show the effectiveness of the method. At first, the performance of the univariate dimension-reduction method is evaluated by assessing the fatigue damage of a theoretical structure represented by a single stress response amplitude operator (RAO). Then, in order to show a case of practical application, the fatigue damage is evaluated for a Steel Lazy Wave Riser (SLWR) connected to an FPSO in a water depth of 2200 m.

This paper deals with the problems investigating of parameters that influence the dynamic behaviour of the carrying structure of type H portal cranes with high carrying capacities excited by the motion of the crane and the load swing. The introduction of the paper presents the importance of the problem of the dynamics of structures. In accordance with the given problem, dynamic spatial models of the boom and portal of the crane were formed and solved. The main part of the paper presents a modal analysis and determines dynamic responses of the space structure with the application of the finite element method and direct integration. The influence of changes in speed and acceleration on the dynamic response of the structure was analysed. The influence of the change of boom rotation angle on the dynamic response of the structure was also analysed. The investigation results provide significant bases and conclusions for designing portal cranes and continuation of research in this field.

The paper presents the project of an open source C/C++ library of analytical solutions to micromechanical fields within media with ellipsoidal heterogeneities. The solutions are based on Eshelby's stress-free, in general polynomial, eigenstrains and equivalent inclusion method. To some extent, the interactions among inclusions in a non-dilute medium are taken into account by means of the self-compatibility algorithm. Moreover, the library is furnished with a powerful I/O interface and conventional homogenization tools. Advantages and limitations of the implemented strategies are addressed through comparisons with reference solutions by means of the Finite Element Method., Comment: 28 pages, 10 figures, 7 tables

The nonlinear vibrations of a water-filled circular cylindrical shell subjected to radial harmonic excitation in the spectral neighbourhood of the lowest resonances are investigated experimentally and numerically by using a seamless aluminium sample. The experimental boundary conditions are close to simply supported edges. The presence of exact one-to-one internal resonance, giving rise to a travelling wave response around the shell circumference and non-stationary vibrations, is experimentally observed and the nonlinear response is numerically reproduced. The travelling wave is measured by means of state-of-the-art laser Doppler vibrometers applied to multiple points on the structure simultaneously. Chaos is detected in the frequency region where the travelling wave response is present. The reduced-order model is based on the Novozhilov nonlinear shell theory retaining in-plane inertia and the nonlinear equations of motion are numerically studied (i) by using a code based on arclength continuation method that allows bifurcation analysis in case of stationary vibrations, (ii) by a continuation code based on direct integration and Poincare maps that evaluates also the maximum Lyapunov exponent in case of non-stationary vibrations. The comparison of experimental and numerical results is particularly satisfactory.

Engineering structures often have nonlinear characteristics. Many of these nonlinear systems could be modelled as piecewise linear. The dynamic analysis of such systems can be carried out by the direct integration of the mathematical model of the system. In this article, solution schemes are identified and qualified studying a single degree-of-freedom system and evaluated studying real-life engineering structures. As an alternative, a modified Newmark method with iteration for nonlinear forces and half-step error monitoring is presented. The modified scheme has been found to be efficient and accurate.

This study investigates in to the dynamic response of an inclined cross-ply laminated composite beam traversed by a moving mass. For this purpose, a finite element method based on the classical lamination theory is used. By taking the effects of inertial, Coriolis and centrifugal forces, the property matrices of the moving mass element are extracted. To calculate the overall property matrices of the entire system, we should combine the property matrices of each moving mass element and the overall property matrices for the inclined beam itself. Newmark direct integration method is employed to solve the equation of motion. In order to evidence this study, the numerical results of the isotropic beam are compared to the analytical solution and other numerical results. In addition, the effects of moving mass speed, the Coriolis force, centrifugal force, the frictional force and the inclined angle of beam are studied. Finally, The dynamic response of symmetric cross-ply laminated beam due to moving mass have been compared to the results of an isotropic simple beam.

A combined analysis method is developed in the present paper for studying the dynamic properties of a type of geometrically nonlinear vibration isolator, which is composed of push–pull configuration rings. This method combines the geometrically nonlinear theory of curved beams and the Harmonic Balance Method to overcome the difficulty in calculating the vibration and vibration transmissibility under large deformations of the ring structure. Using the proposed method, nonlinear dynamic behaviors of this isolator, such as the lock situation due to the coulomb damping and the usual jump resulting from the nonlinear stiffness, can be investigated. Numerical solutions based on the primary harmonic balance are first verified by direct integration results. Then, the whole procedure of this combined analysis method is demonstrated and validated by slowly sinusoidal sweeping experiments with different amplitudes of the base excitation. Both numerical and experimental results indicate that this type of isolator behaves as a hardening spring with increasing amplitude of the base excitation, which makes it suitable for isolating both steady-state vibrations and transient shocks.

High-speed machining of thin-walled workpiece is widely used in aerospace industry. To optimize the machining parameters in milling operations, the related process stability is required to be predicted. Compared to the existing two-dimensional (2D) milling stability model, a more completed three-dimensional (3D) regenerative process stability prediction model of thin-walled workpiece is presented based on the newly developed dynamic model. The efficiency and accuracy of the regenerative milling stability can be improved in the presented 3D model. The analysis procedure of the stability of flexible dynamic milling is developed in details. The 3D stability lobes are calculated according to the full discretization method and direct integration scheme. To verify the accuracy of presented 3D stability model, the thin-walled workpiece milling sound pressure signal and surface quality are determined in experiments.

This paper proposes an indirect method for the identification of moving vehicular parameters using the dynamic responses of the vehicle. The moving vehicle is modelled as 2-DOF system with 5 parameters and 4-DOF system with 12 parameters, respectively. Finite element method is used to establish the equation of the coupled bridge–vehicle system. The dynamic responses of the system are calculated by Newmark direct integration method. The parameter identification problem is transformed into an optimization problem by minimizing errors between the calculated dynamic responses of the moving vehicle and those of the simulated measured responses. Glowworm swarm optimization algorithm (GSO) is used to solve the objective function of the optimization problem. A local search method is introduced into the movement phase of GSO to enhance the accuracy and convergence rate of the algorithm. Several test cases are carried out to verify the efficiency of the proposed method and the results show that the vehicula...

In this article a variable order variable step size technique in backwards difference form is used to solve nonlinear Riccati differential equations directly. The method proposed requires calculating the integration coefficients only once at the beginning, in contrast to current divided difference methods which calculate integration coefficients at every step change. Numerical results will show that the variable order variable step size technique reduces computational cost in terms of total steps without effecting accuracy.

The prototype of mold oscillator that uses a non-sinusoidal generator was modified using Inverse dynamics and Multi-body dynamics. We maintained a basic structure of the mold oscillator including the motor, the gear, the leaf-spring and the caster. To reduce the coupling effect, the non-sinusoidal generator was replaced by a hollow cylinder that had non-sinusoidal surface. The system parameters were obtained from previous research [1], and a new design of the connecting rod between the cylinder and the leaf spring was analyzed by sensitivity analysis. A definition of the detailed system component including gear mesh, and non-sinusoidal surface, Lagrange's equation, Fourier series, and Cam profile synthesis was used to define an equation of motion. The response of oscillating system was derived by a direct integration method. The model was simulated according a specific assumption for each component, and a control system corresponding to real operation was applied. Dynamic responses are displacement, velocity and acceleration of each component. All responses from these simulations were analyzed in the time-frequency region by Fast Fourier transform. Using the model, sensitivity analysis about design variables was also executed about operating performance.

Usually, solar heat in combi systems is used via a buffer storage. In contrast to that, the solar collectors may be connected directly to the space heating circuit in order to store the heat in the building itself. Such a direct solar integration is investigated within system simulations for different layouts and heating elements. The simulations show significant reductions in the final energy demand as well as an increasing solar yield due to less thermal losses of the storage tank compared to the usual solution with one buffer storage. A prototype of one of the investigated heating concepts within a single family house proofs the functionality of the system concept and the high solar yield, particularly at low radiation levels. Since only a few manufacturers provide such system solutions with a direct solar integration, the results may have an important impact on the future development of combi systems.

Seismic qualification by test is widely used as a way to show the integrity and functionality of equipment that is related to the overall safety of nuclear power plants. Another means of seismic qualification is by direct integration analysis. Both approaches require a series of time histories as an input. However, in most cases, the possibility of using real earthquake data is limited. Thus, artificial time histories are widely used instead. In many cases, however, response spectra are given. Thus, most of the artificial time histories are generated from the given response spectra. Obtaining the response spectrum from a given time history is straightforward. However, the procedure for generating artificial time histories from a given response spectrum is difficult and complex to understand. Thus, this paper presents a simple time-domain method for generating a time history from a given response spectrum; the method was shown to satisfy conditions derived from nuclear regulatory guidance.

The authors present an analytical solution for two-layered beam with interlayer slip. Timoshenko’s kinematic assumptions are used for both layers imposing the constraint of equal cross-sectional rotation. A linear constitutive equation between the horizontal slip and the interlaminar shear force is considered. The applied loads act in the plane of symmetry of composite beam and the material and geometrical properties do not depend on the axial coordinate. Analytical solution for the deflection, slip, cross-sectional rotation and internal forces are derived. The effect of the cross-sectional shear deformation to the deflection is analyzed. Closed form solutions are given for the stresses. A Rayleigh-Betti type reciprocity relation for composite shear deformable beam with interlayer slip is formulated, whose applications are illustrated by some examples.

The vibration analysis of bar element systems with continuous variable parameters using the direct integration method is proposed. The method is based on analytical solutions of the appropriate differential equations. By using this method, the problem of free flexural vibrations of a straight bar with arbitrary, continuously varying transverse stiffness and mass per unit length is solved. Formulas in analytical form are derived for dynamic parameters of bar structures, and the procedure for their numerical implementation is presented. Free vibrations of a truncated cone and chimney with a variable wall thickness are studied.

Large nonlinear rotor-bearing system is an important structure in rotating machinery, such as NC machine. Due to the mass imbalance of the system, vibrations induced by centrifugal forces inevitably exist in rotating machinery. So, nonlinear dynamic response of a complex rotor-bearing system was dealt with in this paper. The system considered was modeled using the finite element method and has 124 DOFs (degrees of freedom). A linear reduction method was used and a reduced-order dynamic model of the system with two DOFs had been obtained. Harmonic balance method was applied to the reduced-order dynamic model of the system and an approximate analytical expression of the solution for nonlinear dynamic response of the system at steady state was derived. The analytical solution obtained from the reduced-order dynamic model of the system was compared with the numerical one obtained from the direct integration of the equations of motion of the original system.

This work outlines the use of a black-box fast multipole method to accelerate the far-field computations in an isogeometric boundary element method. The present approach makes use of T-splines to discretise both the geometry and analysis fields allowing a direct integration of CAD and analysis technologies. A black-box fast multipole method of O(N) complexity is adopted that minimises refactoring of existing boundary element codes and facilitates the use of different kernels. This paper outlines an algorithm for implementing the open-source black-box fast multipole method BBFMM3D 1 within an existing isogeometric boundary element solver, but the approach is general in nature and can be applied to any boundary element surface discretisation. The O(N) behaviour of the approach is validated and compared against a standard direct solver. Finally, the ability to model large models of arbitrary geometric complexity directly from CAD models is demonstrated for potential problems.

In this study, the dynamic behaviour of a rotating Timoshenko beam when under the actions of a variable magnitude load moving at non-uniform speed is carried out. The effect of cross-sectional dimension and damping on the flexural motions of the elastic beam was neglected. The coupled second order partial differential equations incorporating the effects of rotary and gyroscopic moment describing the motions of the beam was scrutinized in order to obtain the expression for the dynamic deflection and rotation of the vibrating system using an elegant technique called Galerkin’s Method. Analyses of the solutions obtained were carried out and various results were displayed in plotted curve. It was found that the response amplitude of the simply supported beam increases with an increase in the value of the foundation reaction modulus. Effects of other vital structural parameters were also established.