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Purpose: The purpose of this study is to apply the topology and parameter optimization (TPO) to interior permanent magnet (IPM) motors to obtain the optimized shape with higher torque, lower ripple and sufficient mechanical strength. Design/methodology/approach: The constraints regarding the maximum stress, connectivity and mesh quality were considered to achieve not only high electrical performance but also high mechanical strength. To enhance the accuracy of the finite element analysis of the elastic analysis, this paper used body-fitted mesh adaptation technique to avoid the stress concentration. Findings: The proposed method in this study resulted in feasible shapes with sufficiently high strength compared to previous studies. It is also shown that TPO yielded IPM motors with higher torque compared to topology optimization (TO) with fixed parameters. Practical implications: Different from the existing studies on topology optimization of IPM motors, the mechanical strength is even considered by evaluating the stress values. Therefore, in the practical phase, geometries can be designed that are less likely to be damaged due to deformation, even in the high-speed rotation range. Originality/value: This paper performed TO and parameter optimization (PO) simultaneously, considering not only the electrical performance but also the mechanical strength. Furthermore, the mechanical strength was evaluated more precisely by devising the elastic analysis conditions and mesh generation. [ABSTRACT FROM AUTHOR]

This paper documents the first attempt to apply the localized Fourier collocation method (LFCM), a recently published meshless collocation method, for solving 2D and 3D elastostatic problems. The approach first divides the entire domain into a series of intersecting sub-domains. Within each sub-domain, the unknown functions are approximated by utilizing the pseudo-spectral Fourier collocation technique. The method integrates the merits of the rapid convergence of the pseudo-spectral method and the high sparsity of the localized discretization technique. This combination results in a novel framework that is highly suitable for large-scale and high-precision engineering simulations. Extensive numerical experiments, involving both 2D and 3D elastostatic problems, are presented to showcase the precision and efficiency of the current method. The source codes for numerical examples studied in this work are also provided. [ABSTRACT FROM AUTHOR]

In this paper, a peridynamic differential operator (PDDO) method is developed to analyze the static and dynamic responses of size-dependent elastic structures in the frame of a consistent couple stress theory (CCST). The displacement governing equations together with the boundary conditions of the couple-stress static problems are transformed from the local differential form to the nonlocal integral form through a fourth-order PDDO and then solved by a meshfree scheme. For dynamic cases, the time-domain problems are first transformed into frequency domain by Fourier transform, then solved by the PDDO meshless method in the frequency domain. The time-domain results are finally obtained by using an exponential window method (EWM). The size effects on the static and dynamic responses of some typical elastic problems are investigated by the developed PDDO method. A very high level of computational accuracy is achieved by comparing with the analytical solutions and the existing numerical results. [ABSTRACT FROM AUTHOR]

• We introduce a new numerical method, GDDR, for elastic- plastic analysis of plates. • This method considerably increases the accuracy of solution. • GDDR method noticeably decreases required number of iterations and process time. • The proposed method can strongly predict deflections and stresses in plates. In the present paper, two different numerical methods, generalized differential quadrature (GDQ) and dynamic relaxation method (DR) are employed to analyze elastic-plastic plates. These methods are initially evaluated for elastic beams and then they are utilized for elastic-plastic plates analysis. A new method, GDDR (Generalized Differential Dynamic Relaxation), is developed by the combination of two mentioned methods. The proposed method is validated by theoretical analysis for elastic problems, Abaqus simulation and experimental study for elastic-plastic plates. Reduction in the number of required discretizing nodes, lower computational time and decrease in the number of iterations (about 80%) are the advantages of introduced method compared with the conventional ones. Moreover, this method improves the accuracy of solutions, especially in terms of stresses, by increasing the differentiation accuracy of nodes for elastic-plastic analysis. Comparing the errors of proposed GDDR method with conventional DR method shows about 70% reduction in mean squared error. Moreover, this new method is able to solve problems by using only 3 nodes in each direction, while other methods need at least 8. [ABSTRACT FROM AUTHOR]

• Non-intrusive stochastic smoothed finite element model (SS-FEM) is formulated. • The SS-FEM is used to solve the homogeneous and multi-material mechanical structures under uncertainties. • The spatial variability in material parameters is characterized by random field based on KL expansion. A random field of homogeneous and multi-material structures with uncertain scenarios is addressed by constructed the generalized stochastic cell-based smoothed finite element model. Smoothed finite element method (S-FEM) is "Jacobian-free", which is not only overcomes the limitations of "overly-stiff" and low accuracy of the standard FEM, but also demonstrates strong resistance to mesh distortion. This paper proposes an efficient non-intrusive stochastic smoothed finite element method (SS-FEM) based on cell-based smoothing domains (SD) for the stochastic analysis of elastic problems, which describe much more realistically real physical systems under uncertain scenarios. This SS-FEM starts from the Gaussian random field based on representation related to the spatial variability in material parameters based on the Karhunen-Loève (KL) expansion, and then establishes the basic formulation that considers the effects of uncertainties. A generalized solving framework based on numerical integration is further developed. The non-intrusive dimension reduction method is also adopted to obtain the statistical moments and probability density function. The proposed SS-FEM can capture the structural stochastic responses under uncertainty condition by combining gradient smoothing technology and uncertainty quantification. A number of engineering examples are compared with the solution of Monte Carlo simulation to demonstrate both the accuracy and the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

A body force concentrated at a point and moving at a high speed can induce shear-wave Mach cones in dusty-plasma crystals or soft materials, as observed experimentally and named the elastic Cherenkov effect (ECE). The ECE in soft materials forms the basis of the supersonic shear imaging (SSI) technique, an ultrasound-based dynamic elastography method applied in clinics in recent years. Previous studies on the ECE in soft materials have focused on isotropic material models. In this paper, we investigate the existence and key features of the ECE in anisotropic soft media, by using both theoretical analysis and finite element (FE) simulations, and we apply the results to the non-invasive and non-destructive characterization of biological soft tissues. We also theoretically study the characteristics of the shear waves induced in a deformed hyperelastic anisotropic soft material by a source moving with high speed, considering that contact between the ultrasound probe and the soft tissue may lead to finite deformation. On the basis of our theoretical analysis and numerical simulations, we propose an inverse approach to infer both the anisotropic and hyperelastic parameters of incompressible transversely isotropic (TI) soft materials. Finally, we investigate the properties of the solutions to the inverse problem by deriving the condition numbers in analytical form and performing numerical experiments. In Part II of the paper, both ex vivo and in vivo experiments are conducted to demonstrate the applicability of the inverse method in practical use. [ABSTRACT FROM AUTHOR]

This paper presents an axisymmetric BEM analysis of layered elastic halfspace with volcano-shaped mantle and cavity under internal gas pressure. The problem is of interest to understand the behavior of volcanoes, tectonic earthquakes and other oil and gas reservoirs. The volcano-shaped mantle ground topography and the internal spherical or ellipsoidal cavity are added to the conventional model of layered halfspace. The analysis uses the axisymmetric boundary element method (BEM) associated with the fundamental solution of a multilayered elastic fullspace subject to the concentrated ring-body force. The BEM is further verified for its high efficiency and accuracy by comparing its result with the analytical and FEM solutions for the problem of a homogeneous elastic halfspace whose spherical cavity is under internal pressure. The BEM is used to examine the effect of the volcano-shaped mantle, the cavity shape, the layered material properties and the internal pressure on the elastic behavior of the halfspace under the internal pressure loading within the cavity. The displacements and stresses at the external and internal boundaries and within the layered halfspace are presented and analyzed in detail. The presence of the volcano-shaped mantle can reduce significantly the swelling ground movement induced by the expansive pressure in the cavity in the layered halfspace. The cavity shape can have significant effect to the location and magnitude of the maximum tensile principal hoop stress on the cavity surface induced by its internal pressure. [ABSTRACT FROM AUTHOR]

This paper presents a new solution for the free vibration analysis of moderately thick viscoelastic plates with different shapes, based on free vibration analysis of elastic plates. The advantage of this method is that all natural frequencies and viscous damping can be easily calculated with low computational cost and high precision. Also, critical damped natural frequencies of Mindlin viscoelastic plates are calculated. The constitutive equation is written utilizing the Boltzmann integral law with constant bulk modulus. The Laplace transformation is used to convert equations from the time domain to the Laplace domain. The displacement vector is approximated using the separation of variables method. Besides, the effects of material and geometrical properties on the natural frequency, viscous damping, and critical damped natural frequency of viscoelastic Mindlin plates are investigated. [ABSTRACT FROM AUTHOR]

The localized method of fundamental solutions is a recent domain-type meshless collocation method with the fundamental solutions of governing equations as the radial basis functions. This approach forms a sparse system matrix and has a higher efficiency than the traditional method of fundamental solutions. In this paper, a modified version of the localized method of fundamental solutions is developed for bending analysis of simply supported and clamped thin elastic plates. Some auxiliary nodes on the boundary are firstly introduced to provide additional weight coefficients, which contribute to the construction of the determined system of equations and avoid the over-determined equation system of the localized method of fundamental solutions for bending analysis of thin elastic plates. Several numerical experiments with simply supported or clamped boundary conditions are provided, and numerical results are in good agreement with the analytical or COMSOL Multiphysics solutions. [ABSTRACT FROM AUTHOR]

This paper presents a unified framework to describe the static equilibrium modeling and analysis of elastic rods with large deformations. Through an innovative combination of the Hamiltonian principle in arc coordinates and nonlinear optimization based on the principle of minimum potential energy, our method enables us to support the nonlinear statics model and deal with the different complex constraints of an elastic rod, including the end restraint, self-contact, through-hole, and surface contact Based on the idea of dynamic analogy, the equilibrium shape of an elastic rod is described by the movement and rotation of the moving coordinate system along an arc relative to the static coordinate system. Euler parameters are used as generalized variables to describe the strain energy and the external force potential energy of the elastic rod. Taking the total potential energy of the elastic rod as the objective function and different contact forms as the constraint conditions, a nonlinear optimization model is introduced to describe the equilibrium shape of the elastic rod. Based on a primal–dual interior-point method, the model is solved numerically. Considering various constraints and initial conditions, the geometric shape of the elastic rod is simulated. The simulation results show that the unified model proposed in this paper can effectively deal with the static equilibrium problem of elastic rods with large deformations for multiple complex constraints. • A unified framework for static equilibrium modeling of elastic rods was presented. • A position and orientation matrix were used to handle complex constraints. • An improved primal–dual​ interior point algorithm was used to solve the model. • Our method can effectively deal with large deformation under multiple complex constraints. [ABSTRACT FROM AUTHOR]

This paper presents an efficient and accurate boundary element method (BEM) for the elastic analysis of axisymmetric problems in vertically non-homogeneous solids without or with cavity. This BEM uses the fundamental solution of the elastic field in a multilayered elastic solid induced by the body force uniformly concentrated at a circular ring. This solution is also called Yue's solution. The effective integration methods are used for dealing with the integrals in the discretized boundary integral equations. The discretization of the boundary surface uses one-dimensional boundary elements. It also adopts the infinite boundary element to take into account the influence of a far-field region on the boundary surface. Numerical verifications of displacements and stresses for three benchmark problems are conducted, which gives the excellent agreement with previously published results. Case studies are presented to numerically illustrate the influences of both vertically non-homogeneous elastic material properties and spherical cavity on the elastic fields induced by uniform tractions on the boundary surface. These numerical results show that this new BEM is a fast and simple numerical algorithm for accurately computing the axisymmetric elastic fields in vertically non-homogeneous solids with or without cavity induced by normal tractions. [ABSTRACT FROM AUTHOR]

In this paper, a new term is proposed – through a novel technique – to the ACI equation for checking punching in order to account for the effects of warping. New punching parameters γ vw and J w are hence presented and evaluated/calibrated to include the effects of warping on punching and moment transfer analysis. The method is based on elastic analysis of the entire slab using principles of the theory of elasticity via the boundary element method (BEM) and the shear deformable plates. For verification purposes, the adopted model is first used to compute the classic punching design parameters γ v and γ f due to unit moment. Curves for the aforementioned punching parameters due to warping, namely, γ vw and J w , are hence generated for rectangular columns to be conveniently and efficiently used for design purposes. Then, through applying the proposed method to some real-world examples, it has been shown that punching checks shall be carried out considering warping effects in order to avoid un-conservative results from a design perspective, i.e., to avoid underestimation of the actual (maximum) punching-shear stress demand. [ABSTRACT FROM AUTHOR]

Based on the modified couple-stress theory, the size-dependent behavior of the functionally graded anisotropic elastic composites is analytically investigated when the load is applied on the top surface of the composite plate. The functionally graded material is assumed to be exponential in the thickness direction of the plate. By expanding the solutions of the displacements in terms of the two-dimensional Fourier series, the final governing equations are reduced to an eigenvalue and eigenvector problem. The exact solutions of the elastic fields with the modified couple-stress effect are derived under two kinds of boundary conditions. The classical elastic solutions are reduced from the present solutions as a special case. Numerical examples show the effect of the functional gradient factor and the material length-scale on the elastic fields along the thickness direction of the plate. Some important features observed in this paper could be useful in designing the functionally graded laminated composites with size-dependency. [ABSTRACT FROM AUTHOR]

The objective of this paper is to develop a new unified theoretical structure for modeling interstitial growth and muscle activation in soft tissues. The model assumes a simple continuum with a single velocity field. In contrast with many other formulations, evolution equations are proposed directly for a scalar measure of elastic dilatation and a tensorial measure of elastic distortional deformation. The evolution equation for elastic dilatation includes a rate of mass supply or removal that controls volumetric growth and causes the elastic dilatation to evolve towards its homeostatic value. Similarly, the evolution equation for elastic distortional deformation includes a rate of growth that causes the elastic distortional deformation tensor to evolve towards its homeostatic value. Specific forms for these inelastic rates of growth and the associated homeostatic values have been considered for volumetric, area and fiber growth processes, as well as for muscle activation. Since the rate of growth appears in the evolution equations and not a growth tensor it is possible to model the combined effects of multiple growth and muscle activation mechanisms simultaneously. Also, robust, strongly objective, numerical algorithms have been developed to integrate the evolution equations. [ABSTRACT FROM AUTHOR]

Abstract: A load moving on the surface of an elastic halfspace forms a basic problem that is related to different fields of engineering, such as the subsoil response due to vehicle motion or the ultrasound field due to an angle beam transducer. Many numerical techniques have been developed to solve this problem, but these do not provide the fundamental physical insights that are offered by closed form solutions, which are very rare in comparison. This paper describes the development and analysis of the closed form space–time domain solution for a knife-edge load, i.e. a line segment of normal traction, moving at a constant speed on the surface of an elastic halfspace. The various contributions making up the exact solution, obtained with the Cagniard–De Hoop method, produce all the complicated wave patterns from this distributed type of loading. Examples are the transient wave field at the starting position of the load, angled conical and plane waves propagating into the solid, Rayleigh waves propagating along the surface, and head waves spreading and attenuating in specific directions from the loading path. The influence of the load speed on the wave field is investigated by considering the singularities in the relevant complex domains, for each sonic range relative to the bulk wave velocities. The characteristic wave fronts and wave patterns as exhibited by the particle displacements are evaluated for subsonic, transonic and supersonic load speeds. [Copyright &y& Elsevier]

Abstract: The Ritz variational method is applied to problems of a crack (a cut) in the middle half-plane of a three-dimensional elastic wedge. The faces of the elastic wedge are either stress-free (Problem A) or are under conditions of sliding or rigid clamping (Problems B and C respectively). The crack is open and is under a specified normal load. Each of the problems reduces to an operator integrodifferential equation in relation to the jump in normal displacement in the crack area. The method selected makes it possible to calculate the stress intensity factor at a relatively small distance from the edge of the wedge to the cut area. Numerical and asymptotic solutions [Pozharskii DA. An elliptical crack in an elastic three-dimensional wedge. Izv. Ross Akad. Nauk. MTT 1993;(6):105–12] for an elliptical crack are compared. In the second part of the paper the case of a cut reaching the edge of the wedge at one point is considered. This models a V-shaped crack whose apex has reached the edge of the wedge, giving a new singular point in the solution of boundary-value problems for equations of elastic equilibrium. The asymptotic form of the normal displacements and stress in the vicinity of the crack tip is investigated. Here, the method employed in [Babeshko VA, Glushkov YeV, Zinchenko ZhF. The dynamics of Inhomogeneous Linearly Elastic Media. Moscow: Nauka; 1989] and [Glushkov YeV, Glushkova NV. Singularities of the elastic stress field in the vicinity of the tip of a V-shaped three-dimensional crack. Izv. Ross Akad. Nauk. MTT 1992;(4):82–6] to find the operator spectrum is refined. The new basis function system selected enables the elements of an infinite-dimensional matrix to be expressed as converging series. The asymptotic form of the normal stress outside a V-shaped cut, which is identical with the asymptotic form of the contact pressure in the contact problem for an elastic wedge of half the aperture angle, is determined, when the contact area supplements the cut area up to the face of the wedge. [Copyright &y& Elsevier]

Abstract: This paper presents a crack growth prediction analysis based on the numerical Green''s function (NGF) procedure and on the minimum strain energy density criterion for crack extension, also known as S-criterion. In the NGF procedure, the hypersingular boundary integral equation is used to numerically obtain the Green''s function which automatically includes the crack into the fundamental infinite medium. When solving a linear elastic fracture mechanisms (LEFM) problem, once the NGF is obtained, the classical boundary element method can be used to determine the external boundary unknowns and, consequently, the stress intensity factors needed to predict the direction and increment of crack growth. With the change in crack geometry, another numerical analysis is carried out without need to rebuilding the entire element discretization, since only the crack built in the NGF needs update. Numerical examples, contemplating crack extensions for two-dimensional LEFM problems, are presented to illustrate the procedure. [Copyright &y& Elsevier]

In this paper, a boundary element method for three-dimensional elasto-plastic stress analysis of frictional contact problems in the framework of small strains and small displacements is presented. The contact conditions are used to unite the different system of equations for each body in contact. Several types of contact interface conditions are covered including infinite friction, frictionless and Coulomb friction. In order to include plastic deformation, the initial strain formulation and von Mises yield criterion are employed. The proposed algorithm is applied to the elasto-plastic analysis of the frictionless rigid punch, a large plate with a rigid, circular, cylindrical inclusion under the increasing load and the ceramic femoral head frictional contact problem. [Copyright &y& Elsevier]

The computer simulation is replacing mechanical experiments in many cases due to its cost-effectiveness and improved accuracy. Nevertheless, its application fields are still limited to elastic analysis, as there exists a significant amount of model error in present inelastic material models. In this paper, we first propose a material model using neural networks, which has the ability to describe plasticity and cyclic plasticity. The proposed model was first created with the material data of 2 1/4Cr-1 Mo steel, and the results show that the model can represent the actual cyclic plastic material behavior within a 2% error. The model is then implemented in a commercially available finite element analysis package and the cyclic plastic deformation behavior of a test specimen of the material is predicted within a 3% error. [Copyright &y& Elsevier]

This paper examines the axisymmetric elastostatic problem related to the unilateral receding contact at a pre-compressed smooth bimaterial elastic interface. The separation at the interface is caused by the action of axisymmetric stress fields of unequal magnitude, which are applied at any location of the separate halfspace regions. The analysis of the problem focuses on the determination of the zone of separation as a function of the pre-compression, the magnitudes and locations of the axisymmetric stress fields inducing the separation, and the elasticity characteristics of the halfspace regions. It is found that the radius of the separation zone can be evaluated in explicit form. In the particular instance when the loadings applied at the surface of the halfspace regions are equal in magnitude and distribution, the analysis reveals that the radius of the separation zone is independent of the elasticity properties of the halfspace regions and can be evaluated in exact closed form. [Copyright &y& Elsevier]

Variation of critical loads due to initial imperfections at the hilltop bifurcation point is described by elastic stability theory. We derive a system of bifurcation equations for a potential system expressing local behavior at this bifurcation point, which is a double critical point occurring as a coincidence of a simple pitchfork bifurcation point and a limit point. The piecewise linear law of imperfection sensitivity of critical loads in Thompson and Schorrock [J. Mech. Phys. Solids 23 (1975) 21] is revised by extending initial imperfections to be considered in the bifurcation equations. Based on this sensitivity law, a procedure to determine the most influential (worst or optimum) initial imperfection is formulated. As the most essential development of this paper, under the assumption that initial imperfections are subject to a multi-variate normal distribution, we derive the probability density function of critical loads that follows a Weibull-like distribution. The validity of theoretical developments is assessed through its application to elastic truss structures. [Copyright &y& Elsevier]

In this paper a theoretical analysis of the internal bone remodeling process induced by a medullary pin is presented. Bone is treated as a poroelastic material using Biot''s formulation. Based on the theory of small-strain adaptive elasticity, a new theoretical approach for internal remodeling is proposed. Our results show that the rate of internal remodeling decreases as the porosity of the bone increases. [Copyright &y& Elsevier]

• Theory of gradient-elastic membranes at finite strains is developed. • The internal energy density involves first and second deformation gradient tensors. • Simple constitutive laws for isotropic and anisotropic materials are introduced. • An FE formulation for the numerical analysis of gradient-elastic membranes is presented. • The theory can predict maximum amplitude of wrinkles in stretched thin sheets. In this paper, a gradient theory for large deformation analysis of elastic membranes is developed. Thin membranes are modelled as material surfaces, and the formulation starts with an internal energy density function, which is assumed to be dependent upon the first as well as the second spatial derivatives of deformation field. Governing equilibrium equations and boundary conditions are derived in a variational framework. General forms of constitutive equations for the developed model are discussed. In particular, constitutive laws incorporating two material length-scale parameters and suitable for isotropic as well as anisotropic materials are introduced. Since the strong form of the governing differential equations is highly nonlinear, a finite element formulation for numerical solution of initially flat gradient-elastic membranes is developed. As an application of the introduced theory, wrinkling phenomenon in a thin elastic membrane under uniaxial stretching is studied. Numerical simulations show that by proper selection of the material length-scale parameters in the proposed constitutive law, the theory is capable of capturing the detailed wrinkling patterns in stretched membranes. Notably, the maximum wrinkling amplitude obtained by the present formulation has good agreement to the experimental data reported in the literature. Applicability of the developed formulation to predict the deformation of anisotropic materials is also investigated. In particular, it is also shown that the formulation is able to successfully capture the buckling of pantographic lattice as well as wrinkling of engineering fabrics. [ABSTRACT FROM AUTHOR]