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Nowadays there are various calculation methods for solving a wide range of problems in construction, hydrodynamics, thermal conductivity, aerospace research and many other areas of industry. Analytical methods that make up one class for solving problems, and numerical calculation methods that make up another class, including those implemented in computing complexes, are used for the design and construction of various thin-walled structures such as shells. Due to the fact that thin-walled spatial structures in the form of various shells are widely used in many areas of human activity it is useful to understand and know the capabilities of different calculation methods. Research works on the study of the stress-strain state of the torse shell of equal slope with an ellipse at the base are not widely available at the moment. For the first time the derivation of the differential equations of equilibrium of momentless theory of shells to determine the normal force Nu from the action of uniformly distributed load tangentially directed along rectilinear generatrixes to the middle surface of the torse of equal slope with a directrix ellipse is presented in this article. The parameters of the stress state of the studied torse are also obtained by the finite element method and the variational-difference method. The SCAD software based on the finite element method and the program SHELLVRM written on the basis of the variational-difference method are used. The numerical results of the parameters of the stress state of the studied torse are analyzed, and the advantages and disadvantages of the analytical method and two numerical calculation methods are determined.

Fracture toughness is an important index in safety evaluation for materials and structures. Its convenient and accurate characterization has attracted extensive attention. For small specimens, traditional testing methods of fracture toughness are not suitable due to limitations in sample size and shape. In this work, a new formula is proposed to determine the fracture toughness of glasses using scratch tests with a Vickers indenter based on dimensional analysis and finite element analysis. Fracture toughness of glasses could be calculated with elastic modulus, crack depth of scratched materials and normal force applied during the scratch tests. The effects of plastic deformation and interfacial friction between the Vickers indenter and scratched materials are considered, and the crack shape is consistent with experimental observations. The proposed formula is verified by comparing the fracture toughness of soda-lime and borosilicate glasses obtained from scratch tests with those obtained via indentation tests. This work provides an alternative method to determine the fracture toughness of glass materials.

Purpose. Perform numerical analysis of the station structure. Take into account in the process of mathematical modeling the process of construction of station tunnels of a three-vaulted station. Obtain the regularities of the stress-strain state of the linings, which is influenced by the processes of soil excavation and lining construction. Methodology. To achieve this goal, a series of numerical calculations of models of the deep contour interval metro pylon station was performed. Three finite-element models have been developed, which reflect the stages of construction of a three-vaulted pylon station. Numerical analysis was performed on the basis of the finite element method, implemented in the calculation complex Lira for Windows. Modeling of the stress-strain state of the station tunnel linings and the soil massif was performed using rectangular, universal quadrangular and triangular finite elements, which take into account the special properties of the soil massif. Station tunnel linings are modeled by means of rod finite elements. Findings. Isofields of the stress-strain state in finite-element models reflecting the stages of construction are obtained. The vertical displacements and horizontal stresses that are characteristic of a three-vaulted pylon station are analyzed. The analysis of horizontal stresses proved that at the stage of opening of the middle tunnel the scheme of pylon operation is rather disadvantageous. The analysis of bending moments and normal forces was also carried out and the asymmetry of their distribution was noted. Originality. Based on the obtained patterns of distribution of stress-strain state and force factors, it is proved that numerical analysis of the station structure during construction is necessary to take measures to prevent or reduce deformation of frames that are in unfavorable conditions. Practical value. In the course of research, the regularities of changes in stresses, displacements, bending moments and normal forces in the models of the pylon station, which reflect the sequence of its construction, were obtained.

Analyzing the chip formation process by means of the finite element method (FEM) is an established procedure to understand the cutting process. For a realistic simulation, different input models are required, among which the material model is crucial. To determine the underlying material model parameters, inverse methods have found an increasing acceptance within the last decade. The calculated model parameters exhibit good validity within the domain of investigation, but suffer from their non-uniqueness. To overcome the drawback of the non-uniqueness, the literature suggests either to enlarge the domain of experimental investigations or to use more process observables as validation parameters. This paper presents a novel approach merging both suggestions: a fully automatized procedure in conjunction with the use of multiple process observables is utilized to investigate the non-uniqueness of material model parameters for the domain of cutting simulations. The underlying approach is two-fold: Firstly, the accuracy of the evaluated process observables from FE simulations is enhanced by establishing an automatized routine. Secondly, the number of process observables that are considered in the inverse approach is increased. For this purpose, the cutting force, cutting normal force, chip temperature, chip thickness, and chip radius are taken into account. It was shown that multiple parameter sets of the material model can result in almost identical simulation results in terms of the simulated process observables and the local material loads.

For the kilometer-level electromagnetic launch system, a high-speed double-sided linear permanent magnet (PM) linear motor is presented in this paper. To enhance the average thrust force, reduce the thrust ripple and normal force of linear motor, a segmented trapezoidal PM shaping method is proposed. Compared with conventional PM shaping method, the segmented trapezoidal PMs achieves less force ripple, greater average force and lower manufacturing difficulty. The risk of PM demagnetization fault has been taken into account. To reduce the losses in the mover of the linear motor, a non-metallic light-weight mover structure is proposed. The effectiveness of segmented trapezoidal PMs and non-metallic light-weight mover are verified by the finite element method and experiment.

The normal force that exists between primary and secondary of a linear motor plays an important role in Magnetically Levitated (MagLev) trains. In the particular case of the superconducting magnetic levitation (SML) method, based on the diamagnetic property of high-temperature superconductors (HTS) in the proximity of rare-earth permanent magnets, this issue is even more critical, as there is no control of the levitation gap, which changes according to the load. In this article, the previous experience of traction systems of MagLev trains in commercial operation serves as a background for the study and will be reviewed. The experience of other SML projects will also be considered to reach the proposed topology, similarly to the process of genetic evolution. The proposed solution for the normal force issue consists of a linear induction motor (LIM) optimized for an urban SML vehicle. Analytical equations and simulations with the finite element method (FEM) are presented. An innovative workbench for velocity tests was developed to measure the parameters of interest. Simulation and experimental results confirm the improved performance of the proposed LIM. The final results with the short primary LIM, designed and tested, showed excellent results. The LIM can be qualified as 3 times low: low-cost solution, for low-speed SML vehicles, and with low-normal force amplitudes.

Pipe belt conveyor is a new type of environmentally friendly and efficient bulk conveying equipment. In the design of the roller, the belt and the driving motor of pipe belt conveyor, the sag resistance is a key parameter. Meanwhile, the normal force between the conveyor belt and the roller group is the other important factor need be considered and has a great influence on the sag resistance. This paper analyzes a pipe belt conveyor with a diameter of 150 mm to study the calculation method of normal force. And the relationship between the normal force and the sag resistance is explored. Firstly, the normal force is decomposed into three components related to the forming force of belt, material gravity and belt gravity. So it can be expressed as a linear combination of these three quantities, and the coefficients of each component are obtained based on the dynamic analysis of belt-roller. The results show that the coefficient is mainly affected by the material filling rate, and is almost not affected by the distance between the rollers and the density of the material. The calculation method of the normal force is eventually obtained. Secondly, the normal force in the case of different material filling rates is tested by experiments, and the calculation method of the normal force is verified. Thirdly, the variation law of the sag resistance in the case of different roller group spacing and material filling rate is studied by the dynamic model. It is found that the roller group spacing and material filling rate affects the sag resistance by changing the normal force. There is a power function relationship between the sag resistance and the normal force. In the case of different roller group spacing and material filling rate, the relationship among the sag resistance and the normal force remains unchanged. This study results are of great significance to the design of pipe belt conveyor.

The friction model in the tool-chip interface has significant influences on predicting chip forms, cutting forces, and cutting tool temperatures, when simulating the chip formation using the finite element method. In this paper, the friction behavior in the tool-chip interface was investigated experimentally and numerically under cutting conditions. The friction tests were performed with different workpiece materials (AISI 1045 and Direct Aged Inconel 718) in combination with uncoated and coated cemented carbide cutting tools. Various process normal forces were applied to achieve different contact pressures. The experimental results showed strong influences of relative speeds, contact pressures, and contact temperatures on apparent friction coefficients. In addition, an advanced friction model was proposed and validated with 3D FE-simulations of the friction test.

Three-dimensional tactile sensing in smart devices is witnessing an increasing demand. In this study, a three-dimensional tactile sensor is proposed according to the principle of triboelectricity by using polydimethylsiloxane (PDMS) and polyethylene oxide (PEO) films. Use of PDMS-ZnO composite films increases the output voltage of the electrodes. The sensor is designed with a cross beam-shaped pressure head to enable sensing normal forces in five directions. The working mechanism of the sensor is analyzed using the finite element method. The calculation results indicate a linear relationship between the output voltage and the force. The simulation results also demonstrate that the output voltage is linearly correlated with the applied force in the range of 1–30 N. Test results show that the sensor can sense the magnitude, frequency, and direction of the force as well as measure the duration of the force. The hardness of the object has a significant effect on the output voltage. Finally, the sensor is tested on a manipulator grasping an object to demonstrate its ability to sense the contact and sliding of the object.

Permanent magnet linear synchronous motors have the advantages of high thrust density, high acceleration, high speed, and high efficiency, which are widely used in CNC lathes, lithography machines, rail transportation, etc. In high-speed, high-precision servo control systems, detent force fluctuation caused by end effect can easily cause problems such as speed fluctuation, mechanical vibration and electromagnetic noise, which affect the servo performance of permanent magnet linear synchronous motors. Aiming at the detent force fluctuation caused by the end effect of permanent magnet linear synchronous motor, this paper proposes a stepped double auxiliary pole method. The method has a good suppression effect on the end normal force fluctuation and the end thrust fluctuation, which improves the servo performance of the permanent magnet linear synchronous motor in the high-precision servo system. In the traditional methods of suppressing the fluctuation of end detent force, two common methods are using a magnetic isolation aluminum plate and optimizing the auxiliary pole size. The former needs a magnetic isolation aluminum plate to connect the auxiliary pole and the primary mover. Therefore, it needs to add the connection device to connect those three parts. The connection device complicates the auxiliary pole part and increases manufacturing difficulty. The latter does not change the manufacturing process, but in the early design process, the optimum size of the auxiliary needs to be considered. Compared with these two methods, the one proposed in this paper avoids the complex structure of magnetic isolation aluminum plate, the stepped double auxiliary pole is integrated with the primary mover. Moreover, it has a fixed structure with optimum size. Therefore, the method in the paper does not change the manufacturing process, improves the strength of the initial pole structure, and reduces design period. Finally, the finite element analysis by ANSYS was performed to illustrate the correctness and effectiveness of the method.

The problem of local buckling delamination around interface edge cracks in a sandwich PZT/Metal/PZT rectangular thick plate is studied within the scope of the 3D linearized buckling instability theory. Crack faces have an insignificant initial imperfection, and the plate is compressed by uniformly distributed normal forces acting on two opposite ends of the plate. The evolution of the initial imperfection is investigated, and the critical buckling forces for the plate are found. A mathematical modeling of the problem considered is performed using the 3D exact geometrically nonlinear electroelasticity theory within the framework of a piecewise homogeneous body model. The corresponding boundary-value problems are solved numerically by employing a 3D finiteelement method. Numerical results for the critical forces and the effect problem parameters on these forces are presented and discussed.

In the interaction between rubber tire and granular terrain, the dynamic behavior of granular terrain is significantly affected not only by the shape of soil grains, but also by the deformation contact of tread rubber. Therefore, the effect of these two factors should be considered in tire–sand interactions. In this study, an improved contact model including the effect of sand grain shape and tread rubber deformation is developed for dealing with the interaction between rubber tire and sand terrain. In sand–sand contact model, the interaction between sand grains takes the form of surface contact instead of conventional point contact, where the contact calculation contains four interactions, i.e., normal force, tangential force, rolling resistance and twisting resistance. And in tread–sand contact model, the contact between tread rubber and sand grains is surface contact, which includes the rolling resistance and twisting resistance on the grains caused by rubber deformation during contact. As a result, the complete and realistic evaluation of contact forces is accomplished. Next, a comparison of sandpile simulation of coarse particles and experiment is carried out to verify the effectiveness of the sand–sand contact model. Finally, the novel contact model is applied to tire–sand interaction simulations and compared with the single-wheel experiments. The results indicate that the proposed contact model can be a powerful tool to simulate the interactions between rubber tire and sand terrain.

This paper shows the influence of the air-gap length variations in a low speed linear induction motor behavior. Changes in the air-gap length produces variations in the equivalent circuit model parameters of the low speed linear induction motor, altering the mechanical characteristics of the motor. This analysis is extended to the dynamic model of the linear induction motor. A new dynamic model is proposed to take into account the air-gap variations and an expression to calculate the dynamic normal force developed by the motor is presented. The proposed models are compared to the static and dynamic computational simulations using the finite element method. The results show the proposed model has a good correspondence with the computational simulations.

We have investigated an entirely 3D printed capacitive sensor. Using a combination of 4 variable capacitors it allows to simultaneously measure shear and normal forces. To guide the design and analysis the behavior of the sensor has been modeled using both finite element method (FEM) simulations and an analytical model. The sensor was tested in a mechanical test setup by means of a linear actuator, loading the sensor with a force from various angles. The sensor showed it was able to measure both the normal and shear force components with a maximum noise floor of 1.5 N.

En el presente estudio se realizó el análisis cinemático y de esfuerzos de un rodillo aireador con cuchillas. Se obtuvieron las trayectorias de las cuchillas del rodillo aireador, las cuales incluyen los movimientos de rotación y de traslación sobre el terreno. Se calcularon áreas longitudinales bajo el suelo y volúmenes de las grietas para cuchillas de forma rectangular (Tipo A), triangular simétrica (Tipo 1) y triangular asimétrica (Tipo 2). Los resultados del análisis cinemático reportan que las cuchillas de tipo A modifican considerablemente el suelo con respecto a las otras dos cuchillas. Se calcularon esfuerzos normales numéricamente y por elemento finito, obteniendo para la cuchilla tipo 1 esfuerzos calculados numéricamente de 4.52 MPa en la zona superior del elemento y -7.06 MPa en la zona inferior del mismo. Los esfuerzos normales calculados por elemento finito, se encontraron en el rango de 3.66 a 6.52 MPa para la parte superior del elemento y -7.8 MPa para la parte inferior del mismo. Para la cuchilla tipo 2 se obtuvo un esfuerzo normal de forma numérica de 8.83 MPa. Los esfuerzos normales calculados por elemento finito se encontraron en el rango de 3.95 a 12.86 MPa.

A novel double-sided permanent magnet linear synchronous motor (PMLSM) is proposed in this paper, which forms a three-phase balanced structure by arranging a specific distance between the single phase-group concentrated-coil (PGCC) windings. First, the model of the double-sided PMLSM is established. Then, the air gap magnetic field and operating principle of the proposed motor are theoretically analyzed. Finally, based on the analysis of the air gap magnetic field, the cogging normal force of the proposed PMLSM is theoretically analyzed and verified by the finite element method (FEM).

This paper describes an eddy current brake (ECB) device consisting of AC excitation and ferromagnetic railway. The braking force can be generated with non-contact and low noise caused by the reaction between the eddy current and excitation current. In this paper, the structure of the brake is introduced detailedly. In addition, the three-dimensional finite element analysis (FEA) model of ECB is established. Meanwhile, the experiment system of the rail ECB is built to study the braking characteristics. The validity of FEA simulation is verified by experimental results. It is found that with the increase of speed, the braking force increases linearly to a maximum value first, then slowly decreases, while the normal attractive force decreases continuously. The braking characteristic matches the requirements for the high-speed running trains which need large braking force and low normal force in the deceleration process, so it can be used as an auxiliary braking method in the high-speed railway.

Complex profile broaches are widely used in the manufacture of complex parts of aero-engines, but the forces in the broaching process are difficult to predict and control. A new numerical model for broaching force with complex profile tools was presented, which considered the area and arc length of the curved shear zone boundary. The area and arc length were calculated by the curve function of the boundary, which is firstly predicted by FEM simulation. Then, an experimental device was set up to carry out the broaching experiment with straight profile tools and complex profile tools in accordance with the progressive depth of the cut. Based on the experiments, the traditional broaching model and the modified model with the complex profile tool have been established. Compared with the traditional force model, the accuracy of the modified model has been moderately improved. Furthermore, the modified main broaching force (Y direction) model and the normal force (Z direction) model show a significant improvement in accuracy of 4.8% and 9.7%, respectively, which suggests that the projection area of curved shear zone A1 and the projection arc length of curved shear zone l1 have a big impact on the broaching process. It is firmly believed that the modified model proposed in this paper can provide guidance for the design of complex profile tools and facilitate the efficient and high-precision machining of complex parts.

Nowadays, the development of robust finite element models is vital to research cost-effectively the optimal cutting parameters of a composite machining process. However, various factors, such as the high computational cost or the complicated nature of the interaction between the workpiece and the cutting tool significantly hinder the modelling of these types of processes. For these reasons, the numerical study of common machining operations, especially in composite machining, is still minimal. This paper presents a novel approach comprising a mixed multidirectional composite damage mode with composite edge trimming operation. An ingenious finite element framework which infer the cutting edge tool wear assessing the incremental change of the machining forces is developed. This information is essential to replace tool inserts before the tool wear could cause severe damage in the machined parts. Two unidirectional carbon fibre specimens with fibre orientations of 45° and 90° manufactured by pre-preg layup and cured in an autoclave were tested. Excellent machining force predictions were obtained with errors below 10% from the experimental trials. A consistent 2D FE composite damage model previously performed in composite machining was implemented to mimic the material failure during the machining process. The simulation of the spring back effect was shown to notably increase the accuracy of the numerical predictions in comparison to similar investigations. Global cutting forces simulated were analysed together with the cutting tool tooth forces to extract interesting conclusions regarding the forces received by the spindle axis and the cutting tool tooth, respectively. In general terms, vertical and normal forces steadily increase with tool wear, while tangential to the cutting tool, tooth and horizontal machining forces do not undergo a notable variation.

When a fingerpad presses into a hard surface, the development of the contact area depends on the pressing force and speed. Importantly, it also varies with the finger's moisture, presumably because hydration changes the tissue's material properties. Therefore, we collected data from one finger repeatedly pressing a glass plate under three moisture conditions, and we constructed a finite element model that we optimized to simulate the same three scenarios. We controlled the moisture of the subject's finger to be dry, natural, or moist and recorded 15 pressing trials in each condition. The measurements include normal force over time plus finger-contact images that are processed to yield gross contact area. We defined the axially symmetric 3D model's lumped parameters to include an SLS-Kelvin model (spring in series with parallel spring and damper) for the bulk tissue, plus an elastic epidermal layer. Particle swarm optimization was used to find the parameter values that cause the simulation to best match the trials recorded in each moisture condition. The results show that the softness of the bulk tissue reduces as the finger becomes more hydrated. The epidermis of the moist finger model is softest, while the natural finger model has the highest viscosity.

A moving axle finite element (FE) was developed to study the contact between a wheel and curved rail, where the FE can simulate multi-point contact with sticking, sliding, and separation modes. The possible contact region is inputted as a number of nodes along the wheel and rail surfaces, while the wheel nodes are simulated as cubic-splines. The rail node to wheel cubic-splines contact method is then used to find the normal and shear forces, where the normal and tangential stiffness values obtained from the three-dimensional (3D) FE analysis for an actual wheel and rail are used to model the force–displacement relationship. A simple theoretical solution for curved railways was used to validate the proposed FE in 3D analyses. The results show that good agreement with the theoretical and FE solutions for the contact normal force, shear force, wheel sliding, and wheel separation under various train speeds, curve radius, cant angles, and friction coefficients. This FE can be used in combination with other elements to simulate a train traveling on a curved track system, in which only the standard Newton–Raphson and Newmark’s methods are required in the FE main program.

This article introduces a novel double-sided linear hybrid excitation flux switching machine (DSLHEFSM) with yokeless secondary suitable for long stroke applications. The significant to this novel machine is the elimination of the secondary yoke, which can reduce the volume of the secondary. To reduce cost, ferrite magnets with reduced volume as compared to conventional design are utilized. In order to increase the thrust force density and reduce thrust force ripple under load conditions, the impact of some main design parameters, including split ratio, AC winding slot area, stator pole alignment, stator pole width, stator pole height and turn-on angle are investigated through finite element analysis. The electromagnetic performances of the LHEFSM are analysed including flux linkage, detent force, normal force, no-load EMF, force-velocity curve. Within the same volume constraint and electrical loading, the proposed model achieved higher average thrust force than the conventional model.

Phase-shift or pole-shift method can reduce the detent force of the double-sided permanent magnet linear synchronous motor (DS-PMLSM) dramatically. However, this method causes a decrease in thrust and an increase in normal force simultaneously. To overcome this drawback, a novel slot-shift structure whose slots on the two sides of the primary component are staggered by an optimal distance is proposed in this paper. The models of the detent force including the end force and cogging force is established theoretically, and then verified by finite element analysis. The windings in the upper primary and the lower primary are arranged differently to improve the average thrust. The thrust characteristics of the DS-PMLSM under different shifted distances are analyzed and compared in detail. Furthermore, the primary component employing two kinds of core laminations is proposed to reduce both the dc component and ripple of the normal force. Finally, a DS-PMLSM prototype is tested, and the experimental results are compared with the analytical results to verify the effectiveness of the theoretical and simulation research.

The impact of uncertainty on the reliability of slope design is often significant. Spatial variability of soil properties has been recognized as an important factor influencing the reliability of the slope. This paper aims to investigate the influence of isotropic spatially variable tensile strength on the reliability of reinforced slope. For slope safety assessment, random finite element method represents a rigorous tool to combine spatially variable tensile strength into reliability analysis of slope stability. Numerical results showed that the spatial autocorrelation distance and the coefficient of variation of tensile strength for isotropic random field have a large influence on the probability of failure and on the normal forces when the isotropic autocorrelation distance is small in combination with a higher value of coefficient of variation of tensile strength.

Traditionally, straggering the primaries of the double-sided permanent magnet linear synchronous motor (DS-PMLSM) is beneficial in helping to reduce the detent force caused by the longitudinal end effect, but leading to a reduction of the average thrust. To overcome this disadvantage, this paper provides a novel DS-PMLSM, which adopts the structure of staggering two primaries and rearranging windings. First, the characteristics of the voltage and detent force are analyzed theoretically and verified by finite element (FEM) simulations. The inductance, thrust, and normal forces are then compared with the traditional DS-PMLSM. Furthermore, the geometrical parameters are optimized to improve the thrust. Finally, one DS-PMLSM prototype is tested. The detent force and back electromotive force tested results verify the effectiveness of the topology proposed in this research.

Confining pressure is an important factor that affects the rock breakage efficiency of Tunnel Boring Machines (TBMs). This study analyses the influence of the confining pressure on the rock breakage process, rock breakage efficiency and fragmentation distribution after crushing using a coupled FEM-DEM method. First, the parameters of the rock numerical model are calibrated using numerical uniaxial compression tests and Brazilian tests. Second, the rock breakage by the cutter is simulated under different confining pressures, and the influence of the confining pressure on the rock breakage process is determined. Third, using a post-processing program developed for extracting the induced fragments, the distribution of fragments after rock fragmentation is obtained, which accurately provides the fractured area of the rock to determine the variation of the specific energy (SE) with confining pressure. Finally, the equivalent length distributions of the fragments are analysed using the fractal method. The results show that the confining pressure has a significant inhibitory effect on the propagation of median cracks. The angle of the lateral crack increases with increasing confining pressure, and the length of the crack first increases and then decreases. The maximum normal force and the maximum indentation distance also increase first and then decrease with increasing confining pressure. The SE first increases with increasing confining pressure; however, when the confining pressure reaches the first critical value, the SE begins to decrease with increasing confining pressure and then continues to increase after the confining pressure reaches the second critical value. The variation of the fractal dimension with the confining pressure is similar to the variation of the SE with the confining pressure.

Indentation and scratch models are proposed to numerically investigate effects of compressive prestress on film’s mechanical responses. In indentation, normal stress distributions are strongly dependent on film thickness; the applied force and the maximum normal stresses with a prestress are much larger than without prestress. For various film thicknesses the change in the normal force in scratch between the non-prestressed and prestressed films is 4%–23%. The scratch friction coefficient is larger with prestress than without prestress. With biaxial or uniaxial prestress the material becomes more difficult to deform or to slide at the contact surface compared with cases without prestress.

This paper applies the topology optimization (TO) technique to the design of custom compression casts/braces on two-manifold mesh surfaces. Conventional braces or casts, usually made of plaster or fiberglass, have the drawbacks of being heavy and unventilated to wear. To reduce the weight and improve the performance of a custom brace, TO methods are adopted to optimize the geometry of the brace in the three-dimensional (3D) space, but they are computationally expensive. Based on our observation that the brace has a much smaller thickness compared to other dimensions and the applied loads are normal forces, this paper presents a novel TO method based on thin plate elements on the two-dimensional manifold (2-manifold) surfaces instead of 3D solid elements. Our working pipeline starts from a 3D scan of a human body represented by a 2-manifold mesh surface, which is the base design domain for the custom brace. Similar to the concept of isoparametric representation, the 3D design domain is mapped onto a two-dimensional (2D) parametric domain. An Finite Element Analysis (FEA) with bending moments is performed on the parameterized 2D design domain, and the Solid Isotropic Material with Penalization (SIMP) method is applied to optimize the pattern in the parametric domain. After the optimized cast/brace is obtained on the 2-manifold mesh surface, a solid model is generated by our design interface and then sent to a 3D printer for fabrication. Compared with the optimization method with solid elements, our method is more efficient and controllable due to the high efficiency of solving FEA in the 2D domain.

Since the 1960s, the Inconel Alloy 718 has been a standard nickel-based superalloy due to its high strength, balanced mechanical properties, and strong corrosion resistance at relatively low costs and has been widely used in critical aircraft engine components. With the aim of improving productivity and product quality by implementing advanced tools and new process designs, models such as the FE model are utilized to predict the machining performance such as the cutting forces, the tool life, and the surface integrity. In the research area of FEM chip formation simulation, the influence of flank wear on predictions has not been investigated, especially not on the underestimation of the cutting normal force. In this paper, a 2D FEM chip formation model with the coupled Eulerian-Lagrangian (CEL) method has been built to predict cutting forces as well as other material loadings (Brinksmeier et al. Procedia CIRP 13:429–434, 2014; Buchkremer and Klocke Wear 376-377:1156–1163, 2017) in the machining of Direct Aged 718. In order to validate the performance of the FE model, fundamental investigations have been performed in orthogonal cutting with different cutting parameters. Two kinds of cemented carbide cutting tools with different cobalt contents have been applied to achieve different tool wear behaviors. Moreover, the underestimation of the cutting normal force by FEM chip formation simulation has been investigated and solved in consideration of the flank wear. The introduced FE-modeling approach shows precise predictions in terms of the cutting forces and the chip formation.

Delamination of rigid objects from an elastic substrate with finite thickness is a fundamental problem underlying applications such as marine fouling release coatings or anti-icing coatings. Most existing theoretical studies assume that delamination is driven by forces normal to the substrate surface, while in practice the delamination force may also include shear components that are parallel to the substrate surface. In this work, we consider a model system where a rigid cylindrical punch is detached from an elastic substrate under normal force, shear force or both. Our focus is to determine the pull-off force and to reveal the delamination mechanics under various geometrical and loading conditions, specifically the substrate thickness and the position and angle of the delamination force. To gain theoretical insights, we first study a plane strain model where a long rigid strip is adhered to an elastic half-space, and obtain an analytical solution revealing how the pull-off force depends on the loading position and angle. Moreover, we develop a three-dimensional finite element model to simulate the delamination of a rigid cylindrical punch from an elastic substrate with finite thickness. Three delamination modes are identified from finite element results: Mode-I crack propagation, Mode-II crack propagation, and interface cavitation. For the first two modes, we obtain empirical formulas to calculate the pull-off force using adhesion energy, substrate modulus, contact radius and substrate thickness. We also find that the analytical solution derived from the plan strain model can serve as a qualitative guide to estimate the effect of loading position and angle on the pull-off force.

Linear flux switching machines (LFSMs) are one of the recently emerging and competitive candidates for long stroke applications due to high thrust force density, low cost and robust secondary, and high reliability. In the past decade, permanent magnet linear flux switching machines (PMLFSMs) with continuous secondary is researched by numerous researchers. However, cost of rare earth permanent magnet and iron material for continuous secondary in case of long stroke application makes PMLFSMs not an economical choice. In order to incorporate advantages of segmented secondary, such as: less use of stator iron, high power factor, and less critical saturation, a novel complementary dual mover field excited linear flux switching machine (FELFSMs) with segmented secondary and parallel magnetic structure is proposed and investigated in this paper. Furthermore, geometry-based deterministic optimization approach based on finite element analysis (FEA) is adopted to uplift overall thrust force profile, reduce secondary iron volume, and balance magnetic circuit of the machine. During optimization process, magnitude difference of flux flow between ac winding tooth and dc winding tooth is observed, that compel designers to go for unequal primary teeth design. Finally, optimal ac and dc current densities of geometrically optimized model and without any cooling arrangements are investigated for maximum average thrust force and minimum thrust force ripple ratio.

The deformation compatibility relationship of the general contact object under external normal force and the single secondary internal gear pairs of involute RV reducer under a load torque is derived. By transforming the deformation coordination relationship into a linear programming form, a mathematical model for the analysis of the single secondary internal gear pairs with the tooth surface contact of the involute RV reducer is established. An improved simplex method is used to solve the linear programming problem. The calculation results are compared with the ANSYS simulation values from the three aspects of contact tooth pairs, gear tooth load and tooth surface contact force. The results show that the values obtained by the two methods are almost the same on the contact tooth pairs and the tooth load. In terms of tooth surface contact force, the contact area calculated using the finite element linear programming method is slightly smaller than the ANSYS results, but most of the errors are below 12%, indicating that the tooth surface contact conditions obtained using the two calculation methods are consistent. The accuracy and effectiveness of the finite element-linear programming method are thus verified.

The snapthrough and free vibration response of bistable cross-ply [ 90 n / 0 n ] composite laminates is investigated. Thin unsymmetric composite laminates possess more than one equilibrium position when cooled to room temperature due to the difference in thermal expansion of the plies. Bistable cross-ply laminates have cylindrical shapes at room temperature provided appropriate side-length-to-thickness ratio is used. The laminate is modelled according to the classical lamination plate theory taking into account the von Karman geometric nonlinearity . The strains and displacements are approximated via a simplified Rayleigh-Ritz model that depends on only four time-dependent parameters for the general dynamic response. The simplified model is validated against experimental and finite element results and an acceptable agreement is obtained. The laminate’s length-to-thickness ratio is key to assess the existence of bistability. The model is used to investigate the snapthrough response of an 8-ply [ 90 4 / 0 4 ] laminate that is subjected to three loading schemes: concentrated moments, normal forces, and tangential forces . The variations of the principal curvatures and the lateral displacement of the laminate with the applied forces are shown. The significance of the force location is also found a crucial element in finding the snapthrough force. The free vibration that takes place in the vicinity of a stable equilibrium position is studied and the variation of the fundamental frequency with the laminate size is presented.

This paper analyzes the flux characteristics and normal force of the double-sided switched reluctance linear machine (SRLM) under the asymmetric air gap. The magnetic equivalent circuit (MEC) of the machine and the details of the flux paths configuration at six distinct mover positions under the asymmetric air gap are included. Then, six special mover position magnetization curves are calculated by solving the MEC with the method of Gauss–Seidel. The magnetic flux-linkage model and thrust model based on six distinct mover positions are established by analytical polynomial. Three-dimensional (3-D) finite-element method (FEM) simulation and the experimental study with the prototype hardware are carried out to validate the accuracy of the MEC model calculated for the flux linkage and normal force. The six distinct mover positions flux linkage and normal force calculated by the MEC are consistent with the 3-D FEM calculated data and experimental data. It indicates that the proposed method to calculate the flux linkage and the normal force is feasible and effective. The dynamic analysis is also conducted. The simulated phase current waveforms are also consistent with the experimental results. It indicates that the presented method can be used to simulate the phase current under the asymmetry air gap effectively. The normal force under different asymmetry rates is analyzed, which provides the theoretical basis for reducing the unbalanced force of the double-sided SRLM.

A double-gap magnetorheological (MR) cell is designed, constructed, and validated using finite element method magnetostatics simulations, computational fluid dynamics calculations, and experimental data with Newtonian fluids and conventional MR fluids for a range of particle concentrations and external magnetic field strengths. This new cell is a generalization of the twin-gap device. It is capable of reaching very large magnetic field strengths and shear rates, avoiding normal force overload. More importantly, it is optimized for magnetic field homogeneity.A double-gap magnetorheological (MR) cell is designed, constructed, and validated using finite element method magnetostatics simulations, computational fluid dynamics calculations, and experimental data with Newtonian fluids and conventional MR fluids for a range of particle concentrations and external magnetic field strengths. This new cell is a generalization of the twin-gap device. It is capable of reaching very large magnetic field strengths and shear rates, avoiding normal force overload. More importantly, it is optimized for magnetic field homogeneity.

Traditionally, application of the conventional logarithmic spiral in limit equilibrium (LE) analyses has been limited to homogenous materials. Herein, a modification of the conventional logarithmic spiral LE approach is proposed to account for transitions in soil conditions and provide insight into the internal statics associated with this approach, termed the compound log-spiral (CLS). Comparing both factor of safety (FS) and failure surfaces for a range of frictional strength combinations, the CLS approach demonstrates good agreement with results derived from both generalized, commercially available rigorous LE analyses and finite element analyses. The utility of the CLS method is further demonstrated through an example where the stability of a heavily stratified seacliff is considered. The proposed method satisfies equilibrium at a limit state without resorting to internal statistical assumptions associated with traditional LE approaches. Furthermore, it enables the explicit determination of internal statics, such as inter-slice shear forces, inter-slice normal forces, inter-slice angle, line of thrust, and normal stress distributions, which is a less-than-trivial task for the complex slip surface geometry realized in heterogeneous slope failures. Subsequently, the reasonableness of results could be assessed.

Previous research into the friction behaviour of elastomers has typically focused on the effects of velocity, contact pressure, counter surface and lubrication on the coefficient of friction. O-ring type elastomer seals are common in many different industries. Friction plays a critical role during the setting and in service of these components. An experimental O-ring friction testing rig has been developed that can measure the effects of sliding speed and hydrostatic pressure on elastomer friction. Finite element analysis (FEA) packages can adopt fixed friction coefficients or ones that are pressure dependent. For the latter case, the dependence of the frictional behaviour is typically obtained from the instantaneous stress response at any given pressure and then related to the normal force response. The friction rig described in this paper uses industry standard dimensions for the O-ring gland, the pre-compression levels, extrusion gap size and pressure rating. The coefficient of friction is derived by dividing the measured friction force by the normal force, which was determined using an FEA modelling approach, as it could not be measured directly. Finally, a relationship between the frictional velocity and surface roughness is obtained in order to provide a frequency dependent Coefficient of Friction (CoF) that is easily translatable between surfaces.

This contribution focuses on the analytical and finite element modelling of the thermo-mechanical behaviour of a friction-pendulum bearing device for passive seismic isolation. Influences of some crucial factors, such as the magnitude and the rate of change of the sliding velocity, the weight of the superstructure, and the rise in temperature on the force-displacement relationship characterizing the isolator, are studied. Numerical results obtained for a realistic testing protocol (plausible value of the applied normal force and sliding velocity) are presented.

The discontinuous joints are an essential type of natural joints. The normal force, joint persistency, and distribution exert great influences on the shear resistance of the rock joints. By simulating the uniaxial compression experiment and Brazilian test, the material parameters and the basic size standard for meshing were determined. The symmetrical discontinuous joint distribution of three types were established, the cohesive elements were inserted between the solid elements, and the numerical simulation of the shear test was conducted. The effects of joint distribution, joint continuity, and normal stress on the shear resistance of joint rock were investigated, and the law of crack evolution was analyzed. The results showed that the shear process of discontinuous joints can be divided into four stages: elastic stage, strengthening stage, plastic stage, and residual stress stage. For the scattered joint distribution, the rock bridge can provide more reinforcement for the joints, which enhances the shear resistance of the joints, the stress concentration point at the end of the joint is easy to accumulate more fracture energy, which induces the initiation of the cracks, and under the influence of unbalanced torque, the both-sided joint distribution is more likely to produce tension damage.

Measurement of load information on the plantar (lower) surface of the foot can provide valuable insights to help identify pathologies like diabetic foot ulcers. Studies have shown that both plantar pressure and shear stress play an important role in foot disorders, especially ulcer formation. However, in this context shear stress is much less studied in comparison with pressure distribution, mainly due to the lack of reliable measurement technologies. In this paper, we propose a triaxial force sensor for measuring plantar loading. The sensor consists of an array of sensing coils combined with an elastomeric spacer and a conductive target. Under loading, the sensor demonstrates differential variations in inductance which are digitized by built-in conditioning circuitry and decoupled. A 3D finite element (FE) model was developed for the system as a design tool. This was validated experimentally and demonstrated a high agreement to the results. In experimental evaluation with multiaxial loading the sensor showed precise operation over the operating range (RMSE: 0.05 N for shear (-1.5 N - 1.5 N) and 0.70 N for normal force (0-13 N) measurements). The FE model was then used to investigate the effect of undesirable tilting of the target. The results indicated that it is important to minimize the tilting of the target for robust operation in real-world scenarios.

A metamodel considering material plasticity is presented for computationally efficient prediction of wheel–rail normal contact in railway switches and crossings (S&C). The metamodel is inspired by the contact theory of Hertz, and for a given material, it computes the size of the contact patch and the maximum contact pressure as a function of the normal force and the local curvatures of the bodies in contact. The model is calibrated based on finite element (FE) simulations with an elasto-plastic material model and is demonstrated for rail steel grade R350HT. The error of simplifying the contact geometry is discussed and quantified. For a moderate difference in contact curvature between wheel and rail, the metamodel is able to accurately predict the size of the contact patch and the maximum contact pressure. The accuracy is worse when there is a small difference in contact curvature, where the influence of variation in curvature within the contact patch becomes more significant. However, it is shown that such conditions lead to contact stresses that contribute less to accumulated plastic deformation. The metamodel allows for a vast reduction of computational effort compared to the original FE model as it is given in analytical form.

The give paper is closely connected with the analysis of the normal force relating to the winding mechanism referring to production or manufacturing of raw tyres. The attention is mainly paid to the calculation of normal force during the manufacturing process when the individual constituents of raw tyre are pressed-in. The dynamic analysis as well as the calculation of the given normal force was done for raw truck tyre. The simulation of the movement and dynamic analysis for the given kinematic conditions as well as appropriate input values were solved in Solid Works - modeling computer program. Courses of normal forces for the first one set and the second one set of winding arms in dependence on lever position are in graphitic form. Based on the dynamical analysis, it can be concluded that, the second one set of winding arms does not have any influence on the quality of the produced car tyre.