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The linear elasticity problem has important applications in structural analysis and engineering design. It is shown that the classical Crouzeix–Raviart finite element method is unstable to solve the linear elasticity eigenvalue problem with the pure traction boundary condition. In this paper, first we propose a new scheme with the stabilization terms. Then we prove the a priori error estimates for approximate eigenpairs. Finally, we carry out numerical experiments using the stabilized scheme. Theoretical analysis and numerical results show that this scheme is locking free and efficient. [ABSTRACT FROM AUTHOR]

In this paper we analyze a mixed displacement‐pseudostress formulation for the elasticity eigenvalue problem. We propose a finite element method to approximate the pseudostress tensor with Raviart–Thomas elements and the displacement with piecewise polynomials. With the aid of the classic theory for compact operators, we prove that our method is convergent and does not introduce spurious modes. Error estimates for the proposed method are derived. Finally, we report some numerical tests supporting the theoretical results. [ABSTRACT FROM AUTHOR]

The paper presents the features of solutions to nonlocal elasticity problems in domains with stepped transitions and elliptical notches. A comparative analysis of the solutions obtained in the classical and nonlocal elasticity theories was carried out, as well as an analysis of the influence of the main parameters of the model on the final results. The presented solutions for the region with a step transition are in qualitative agreement with the experimental data and have similar portraits of deformations and resultant stresses along the loading axis. In regions with elliptical notches, similar effects are observed. In addition to qualitative agreement with experiments, solutions in the nonlocal formulation have lower stress values in the concentrators and exhibit edge effects, which are characterized by sharp stress and strain gradients at the domain boundaries. The solutions were carried out numerically by the finite element method. [ABSTRACT FROM AUTHOR]

For the first time, this paper proposes a multiscale computational approach to investigate mixed‐mode I/II fracture in two‐dimensional lattices containing material anisotropies which find their applications in additive manufacturing of cellular structures. The layer‐by‐layer fabrication of lattices produced by the additive manufacturing techniques causes material anisotropies corresponding to the build orientation. Such material anisotropies, together with the cell topology, affect the fracture behavior of lattice components under various mechanical loading. The effective macroscopic elastic properties of periodic lattices obtained via numerical homogenization are fed into a continuum‐based fracture criterion to obtain crack path and onset of fracture under mixed‐mode I/II conditions. Different cell topologies are considered, and the predictions are compared with the results obtained directly by the finite element analysis. The results of this work can pave the way toward further understanding, and eventually, optimizing fracture toughness of additively manufactured lattices against various loading profiles. [ABSTRACT FROM AUTHOR]

Multiscale finite element analysis based on the asymptotic homogenization theory was carried out for short fiber reinforced plastics (FRP), and the effects of fiber morphologies on mechanical properties were systematically organized. Cellulose microfibers were used as the reinforcing fibers and polypropylene was used as the matrix. In order to quantify the enhancement effect of intrinsic fibers on the mechanical properties, a new indicator based on strain energy, contribution proportion of fiber (CPf) was proposed. In this paper, as the first demonstration of introducing the CPf, unidirectionally oriented short FRP was focused and elastic properties were analyzed for fundamental fiber morphologies. In terms of the fluctuation rate based on the elastic modulus of the matrix, when the volume content of fiber is 3.0 vol%, the elastic modulus of composites varied by 106%, 105%, 97.6%, and 35.1%, respectively, depending on the fiber orientation, fiber aspect ratio, fiber/matrix interface and fiber‐to‐fiber distance. Based on the CPf, fiber morphologies could be divided into two. The first factors are fiber orientation angle and fiber content, which determine the rate of change in mechanical properties with respect to the CPf. The second factors are fiber aspect ratio, fiber/matrix interface, and fiber‐to‐fiber distance, which affect the mechanical properties according to the rate of change determined by the first factors. The complicated influence of the fiber morphologies on the mechanical properties could be unified by introducing the CPf. These computations show that CPf is effective for systematic analysis and design of fiber morphologies. [ABSTRACT FROM AUTHOR]

This paper presents an analysis on the elastic characteristics of luffa and palm natural fiber composites (NFC) with epoxy and ecopoxy matrixes, taking into account the impact of fiber volume fractions. Furthermore, longitudinal modulus, transverse modulus, shear modulus, and Poisson's ratio were predicted using representative volume elements (RVEs) with chopped random and unidirectional fiber arrangements. However, analytical approaches such as rule of mixture, Chamis, Halpin–Tsai, and Nielsen were considered for validating and comparing the findings of finite element analyses. Hence, it was found that increasing fiber volume fraction increased the elastic properties of palm/epoxy, palm/ecopoxy, and luffa/epoxy NFCs, but decreased that of luffa/ecopoxy NFC. Addition of palm fibers in ecopoxy and epoxy had stronger effect than luffa on enhancing the elastic properties of the final structure. However, greatest elastic characteristics observed through analytical and numerical models were obtained for ecopoxy matrix with 0.5 palm fibers. A strong agreement was observed between the results obtained from analytical approaches and RVE unidirectional model. Chamis model exhibited higher outcomes compared to the considered analytical techniques, while Halpin–Tsai model showed the least values. [ABSTRACT FROM AUTHOR]

In this paper, we present the numerical analysis on high order dual parametric finite element methods for the cavitation computation problems in nonlinear elasticity, which leads to a meshing strategy assuring high efficiency on numerical approximations to cavity deformations. Furthermore, to cope with the high order approximation of the finite element methods, properly chosen weighted Gaussian type numerical quadrature is applied to the singular part of the elastic energy. Our numerical experiments show that the high order dual parametric finite element methods work well when coupled with properly designed weighted Gaussian type numerical quadratures for the singular part of the elastic energy, and the convergence rates of the numerical cavity solutions are shown to be significantly improved as expected. [ABSTRACT FROM AUTHOR]

This paper presents a numerical formulation of a three dimensional embedded beam element for the modeling of piles, which incorporates an explicit interaction surface between soil and pile. The formulation is herein implemented for lateral loading of piles but is able to represent soil-pile interaction phenomena in a general manner for different types of loading conditions or ground movements. The model assumes perfect adherence between beam and soil along the interaction surface. The paper presents a comparison of the results obtained by means of the present formulation and by means of a previously formulated embedded pile element without interaction surface, as well as reference semi-analytical solutions and a fully 3D finite element (FE) model. It is seen that the proposed embedded element provides a better convergence behavior than a previously formulated embedded element and is able to reproduce key features of a full 3D FE model. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm and a fully coupled hydromechanical-fracture formulation for the simulation of three-dimensional nonplanar hydraulic fracture propagation. The propagation algorithm automatically estimates the magnitude of time steps such that a regularized form of Irwin's criterion is satisfied along the predicted 3-D fracture front at every fracture propagation step. A generalized finite element method is used for the discretization of elasticity equations governing the deformation of the rock, and a finite element method is adopted for the solution of the fluid flow equation on the basis of Poiseuille's cubic law. Adaptive mesh refinement is used for discretization error control, leading to significantly fewer degrees of freedom than available nonadaptive methods. An efficient computational scheme to handle nonlinear time-dependent problems with adaptive mesh refinement is presented. Explicit fracture surface representations are used to avoid mapping of 3-D solutions between generalized finite element method meshes. Examples demonstrating the accuracy, robustness, and computational efficiency of the proposed formulation, regularized Irwin's criterion, and propagation algorithm are presented. [ABSTRACT FROM AUTHOR]

In this paper, a novel three-dimensional (3D) cellular structure with negative Poisson's ratio was designed by alternating cuboid surface indents on the vertical ribs of the unit cells. The Poisson's ratio and Young's modulus of structures with different geometric parameters were determined using the finite element method (FEM) as a function of these parameters. Samples with identical geometric variables were fabricated via 3D printing, and their through-thickness direction Poisson's ratios were measured and compared with simulation results. Results showed that the Poisson's ratio of the 3D cellular structures can be tuned from positive to negative and can reach a minimal value of −0.958. Good agreement was found between the experimental results and the simulation. This lattice structure is considerably stiffer than re-entrant negative Poisson's ratio foam with the same solid phase. The design concept developed here can be optimized for specific applications via geometric parameters manipulation. [ABSTRACT FROM AUTHOR]

We propose in this paper analytical and numerical models that describe the in-plane uniaxial elastic properties (Young's moduli and Poisson's ratios) of a honeycomb structure with curved walls. We perform a parametric analysis of the mechanical performance of this honeycomb also by taking into account the different types of deformations acting inside the cell walls. The curved wall honeycomb possesses higher magnitudes of the Poisson's ratio ν12 in the auxetic configuration compared to classical center symmetric configuration with straight cell wall. The presence of the curvature also allows creating configurations with positive Poisson's ratio even for negative internal cell angles, and makes this honeycomb design attractive for mechanical tailoring. [ABSTRACT FROM AUTHOR]

An improvement to the workflow used in modeling boundary-value problems in complex materials, which allows for reducing computational time by the factor of 5 while maintaining comparable quality of the solution is proposed in this paper. After formulating the main goals of the paper, a review of the state-of-the-art techniques used for generating a digital material representation is presented. This is followed by a description of the procedure for solving boundary-value problems and finding a representation of a given microstructure in a desired functional base. Finally, we showcase how to combine these techniques to obtain mentioned significant calculation speedup. Developed approach is validated during investigation of a selected case study, which is modeling of a linear elastic deformation of a dual phase ferritic-martensitic steel under thermal loading conditions. [ABSTRACT FROM AUTHOR]

Analyses of I-II mixed mode central cracked plate by finite element method are performed in this paper, and some different phenomena are found. First for I-II mixed mode crack, the distribution of J integral along crack tip thickness depends on biaxiality factors because of the existence of vertex (corner) singularity, which is unlike that for mode I or mode II crack. Then J integrals at middle layer keep constant for any cracked plates with different inclined angles β when the biaxiality ratio is equal to 1 or −1, which implies that the inclined angle or the extent of I-II mixed mode has no effect on the J integral for positive or negative equal axial loading conditions. And the decreasing trend of J integral with the inclined angle β for biaxiality ratio λ being between−1 and 1 is just opposite with that for biaxiality ratio λ being larger than 1 and smaller than −1. Finally, proposed h1 ( a/ W, n, λ, β) of cracked plate with different inclined angles under different biaxial loading are calculated. [ABSTRACT FROM AUTHOR]

Elastic interactions between pores and cracks reflect how they are organized or spatially distributed in porous rocks. The principle goal of this paper is to understand and characterize the effect of elastic interactions on the effective elastic properties. We perform finite element modelling to quantitatively study how the spatial arrangement of inclusions affects stress distribution and the resulting overall elasticity. It is found that the stress field can be significantly altered by elastic interactions. Compared with a non-interacting situation, stress shielding considerably stiffens the effective media, while stress amplification appreciably reduces the effective elasticity. We also demonstrate that the T-matrix approach, which takes into account the ellipsoid distribution of pores or cracks, can successfully characterize the competing effects between stress shielding and stress amplification. Numerical results suggest that, when the concentrations of cracks increase beyond the dilute limit, the single parameter crack density is not sufficient to characterize the contribution of the cracks to the effective elasticity. In order to obtain more reliable and accurate predictions for the effective elastic responses and seismic anisotropies, the spatial distribution of pores and cracks should be included. Additionally, such elastic interaction effects are also dependent on both the pore shapes and the fluid infill. [ABSTRACT FROM AUTHOR]

This paper describes a method for determination of elastic parameters (elastic moduli and Poisson's ratio) of orthotropic composite plate-type structural elements using the results of natural frequency measurements. The identification of parameter values is provided by minimization of weighted squared difference (discrepancy) between physically measured frequencies and natural frequencies calculated by Finite Element Method. The metamodels for the frequency dependence on the elastic parameters and other geometrical and physical parameters of test specimens, including parameters with uncertainty ('noisy constants') are built using experimental designs optimized according to the Mean Squared Error space filling criterion and third-order polynomial approximations. The minimum of weighted squared difference between measured and calculated frequencies is found using the multistart random search method. The expressions for standard deviations of identified parameters depending on deviations of 'noisy constants' are derived using linearized metamodels. The expressions for identification errors allow the statement of the identification task as a robust minimization problem by simultaneous minimization of the discrepancy function and standard deviations of the identified values by varying the values of unknown elastic parameters and weighting coefficients for different frequencies. The partial scaling of natural frequencies is used for the reduction of the uncertainty impact on the identification error. This allows reducing the identification error of elastic moduli about two times and Poisson's ratio about 20 times in comparison with the results obtained by using dimensioned frequencies. [ABSTRACT FROM AUTHOR]

The virtual contact loading method (VCLM), a highly efficient numerical method to solve elastic contact problems, is proposed in this paper. Having applied virtual loads on the possible contact region (PCR) of a structure system, we carried out the usual finite-element calculations only once and made a local iteration analysis in PCR then the contact region (shape and size), contact state (stick, slide or mixed), contact normal and shear stress distributions, and the stress and displacement fields in contact bodies were all obtained simultaneously. This method is very simple and easy to use. The elastic contact problems for cylinder-cylinder are solved in this paper and the results agree well with those in previous work. [ABSTRACT FROM AUTHOR]

This paper presents materials and core/shell architectures that provide optimized mechanical properties in packages for stretchable electronic systems. Detailed experimental and theoretical studies quantitatively connect the geometries and elastic properties of the constituent materials to the overall mechanical responses of the integrated systems, with a focus on interfacial stresses, effective modulus, and maximum extent of elongation. Specific results include core/shell designs that lead to peak values of the shear and normal stresses on the skin that remain less than 10 kPa even for applied strains of up to 20%, thereby inducing minimal somatosensory perception of the device on the human skin. Additional, strain-limiting mesh structures embedded in the shell improve mechanical robustness by protecting the active components from strains that would otherwise exceed the fracture point. Demonstrations in precommercial stretchable electronic systems illustrate the utility of these concepts. [ABSTRACT FROM AUTHOR]

The paper deals with a 3D multi-parametric stress field representation ahead of notches in plates of finite thickness under different loading conditions. Under certain hypotheses, the 3D governing equations of elasticity can be reduced to a system where a bi-harmonic equation and a harmonic equation have to be simultaneously satisfied. The former provides the solution of the corresponding plane notch problem, and the latter provides the solution of the corresponding out-of-plane shear notch problem. The solution is valid close the notch edge, through the plate thickness, with exclusion of a very limited zone close to the free surface of the plates. Also, under elastic-plastic conditions there are circumstances where it is possible to separate the in-plane problem from the out-of-plane problem. A new analytical frame is proposed, and the results are compared with those obtained from 3D finite element models of a plate with a square notch. In the presence of remote applied tensile stress, the slope of the induced, out-of-plane, shear stress component matches that of the mode III plastic problem. [ABSTRACT FROM AUTHOR]

SUMMARY This work proposes an iterative procedure to analyze dynamic linear/nonlinear fully saturated porous media considering time-domain finite element discretization. In this iterative approach, each phase of the coupled problem is treated separately, uncoupling the governing equations of the model. Thus, simpler, smaller, and better conditioned systems of equations are obtained, rendering more attractive techniques. A relaxation parameter is introduced in order to improve the efficiency and robustness of the iterative solution, and an expression to compute optimal values for the relaxation parameter is discussed. At the end of the paper, numerical examples are presented, illustrating the effectiveness and potentialities of the proposed methodology. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the mechanical behavior of the Scarf Lap Joints (SLJs) bonded with adhesive under a tensile load was analyzed. The effects of adherend thickness at the interface stress-strain distributions of SLJs were examined. The stress-strain analyses were performed by Finite Element Method (3D-FEM). The 3D-FEM code was employed with Ansys (Ver.12.0.1). Experimental results were compared with the 3D-FEM results and were found quite reasonable. It was concluded that both experimental and 3D-FEM failure loads were increased with increased adherend thickness. The results indicated that the maximum failure loads were determined at t=8 mm in all joints. The analysis of the SLJs under tensile load showed that the stress and strain concentrations occurred around the edges of the joints. [ABSTRACT FROM AUTHOR]

SUMMARY Arterial walls in the healthy physiological regime are characterized by quasi-incompressible, anisotropic, hyperelastic material behavior. Polyconvex material functions representing such materials typically incorporate a penalty function to account for the incompressibility. Unfortunately, the penalty will affect the conditioning of the stiffness matrices. For high penalty parameters, the performance of iterative solvers will degrade, and when direct solvers are used, the quality of the solutions will deteriorate. In this paper, an augmented Lagrange approach is used to cope with the quasi-incompressibility condition. Here, the penalty parameter can be chosen much smaller, and as a consequence, the arising linear systems of equations have better properties. An improved convergence is then observed for the finite element tearing and interconnecting-dual primal domain decomposition method, which is used as an iterative solver. Numerical results for an arterial geometry obtained from ultrasound imaging are presented. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Based on the auxiliary space method, a preconditioner is studied in this paper for linear systems of equations arising from higher order finite element (FEM) discretizations of linear elasticity equations. The main idea, which is proposed by Xu ( Computing 1996; 56:215-235) for the scalar PDE, is to construct the preconditioner as a combination of a smoother and a coarse level solver, where the systems of equations arising from lower order FEM discretizations are used in the coarse level solver. It is theoretically shown that the condition number of the preconditioned systems is uniformly bounded with respect to both the problem size and moderate Poisson's ratio. When the Poisson's ratio is near the limit of 0.5, we have presented some numerical tests for the case of fourth-order FEM discretization in a combination with quadratic conforming FEM as a coarse space. The results are almost robust when Poisson's ratio is near the limit of 0.5. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Most of the electromagnetic devices, especially electrical machines, have the disadvantage to be exposed to high vibrations caused by magnetic forces. The aim of this study is to propose a methodology to optimize the cylindrical stators generally used in electrical machines regarding the vibration phenomena. Techniques for vibration reduction require knowledge of the proper frequencies, which depend on mechanical shapes and dimensions as well as material properties such as mass density, Young's modulus and Poisson's ratio. This paper proposes a new approach which is based on the identification of mass density (lamination stacking factor) and Young's modulus in the goal to minimize the vibratory behavior of electrical machines. In this goal, we have used artificial intelligent and finite element method (FEM) analysis to solve the magneto-mechanical inverse problem (IP). In the proposed approach, a Multilayer Perceptron Neural Network (MLPNN) is used as a forward model in order to decrease the FEM time consuming. Thus, a Genetic Algorithm (GA) is used to solve the IP in a reasonable time of running. An example study of an induction machine proves that the developed approach may be applied in both design and identification applications. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An over-deterministic method has been employed for calculating the stress intensity factors (SIFs) as well as the coefficients of the higher-order terms in the Williams series expansions in cracked bodies, using the conventional finite element analysis. For a large number of nodes around the crack tip, an over-determined set of simultaneous linear equations is obtained, and using the fundamental concepts of the least-squares method, the coefficients of the Williams expansion can be calculated for pure mode I, pure mode II and mixed mode I/II conditions. A convergence study has been conducted to examine the effects of the number of nodes used, the number of terms in Williams expansion and the distance of the selected nodes from the crack tip, on the accuracy of the results. It is shown that the simple method presented in this paper, yields accurate results even for coarse finite element meshes or in the absence of singular elements. The accuracy of SIFs and the coefficients of higher-order terms are validated by using the available results in the literature. [ABSTRACT FROM AUTHOR]

Whilst the periodontal ligament (PDL) acts as an attachment tissue between bone and tooth, hypotheses regarding the role of the PDL as a hydrodynamic damping mechanism during intraoral food processing have highlighted its potential importance in finite element (FE) analysis. Although experimental and constitutive models have correlated the mechanical function of the PDL tissue with its anisotropic, heterogeneous, viscoelastic and non-linear elastic nature, in many FE simulations the PDL is either present or absent, and when present is variably modelled. In addition, the small space the PDL occupies and the inability to visualize the PDL tissue using μCT scans poses issues during FE model construction and so protocols for the PDL thickness also vary. In this paper we initially test and validate the sensitivity of an FE model of a macaque mandible to variations in the Young's modulus and the thickness of the PDL tissue. We then tested the validity of the FE models by carrying out experimental strain measurements on the same mandible in the laboratory using laser speckle interferometry. These strain measurements matched the FE predictions very closely, providing confidence that material properties and PDL thickness were suitably defined. The FE strain results across the mandible are generally insensitive to the absence and variably modelled PDL tissue. Differences are only found in the alveolar region adjacent to the socket of the loaded tooth. The results indicate that the effect of the PDL on strain distribution and/or absorption is restricted locally to the alveolar bone surrounding the teeth and does not affect other regions of the mandible. [ABSTRACT FROM AUTHOR]

This paper reports the use of polynomial wavelets as approximation functions in hybrid-mixed stress finite element models applied to the solution of plane elasticity problems. The stress and displacement fields in the domain and the displacements on the static boundary are independently approximated. The kinematic boundary conditions are locally satisfied. All remaining equations are enforced in a weighted residual form so designed as to ensure that the discrete model embodies the relevant properties of continuum systems, namely the static-kinematic duality and elastic reciprocity. A set of numerical applications is presented to illustrate the use of the hybrid-mixed model and to assess its efficiency and accuracy. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we will discuss the geometric-based algebraic multigrid (AMG) method for two-dimensional linear elasticity problems discretized using quadratic and cubic elements. First, a two-level method is proposed by analyzing the relationship between the linear finite element space and higher-order finite element space. And then a geometric-based AMG method is obtained with the existing solver used as a solver on the first coarse level. The resulting AMG method is applied to some typical elasticity problems including the plane strain problem with jumps in Young's modulus. The results of various numerical experiments show that the proposed AMG method is much more robust and efficient than a classical AMG solver that is applied directly to the high-order systems alone. Moreover, we present the corresponding theoretical analysis for the convergence of the proposed AMG algorithms. These theoretical results are also confirmed by some numerical tests. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Currently, there is major interest within the biomedical community in developing accurate non-invasive means for analyzing bone micro-structure. This paper presents a new approach for a multi-scale finite element (FE) analysis of a trabecular structure. Two domain decomposition approaches are investigated as a basis for computational analysis at the micro-scale level, which is then applied for solving a 2D elasticity FE problem. In addition, a homogenization procedure from micro- to macro-scale level is presented. The proposed new multi-scale FE method has the potential to provide new insights into bone structure and behavior. Moreover, it is expected that the outcomes of this research will develop into a computerized virtual biopsy system. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Background/purpose: Various analyses have been performed to identify the mechanical properties of the human skin tissue in vivo. They generally use different approaches and hypotheses (behavior laws as well as mechanical tests) and the obtained results are consequently difficult to analyze and compare. In this paper, an inverse method that can be adapted to any kind of mechanical tests and behavior laws is presented. Method: A suction deformation performed on the volar aspect of the forearm of a subject is considered. This test is modeled with the finite element method to compare the experimental and simulated curves using an inverse method that allows the skin mechanical parameters identification. This process is based on two optimization algorithms, Kalman's filter and Gauss–Newton's methods. To account for the nonlinear behavior of the skin, a specific nonlinear elastic law, which is then compared with standard linear elastic and neo-Hookean's mechanical behaviors, was developed. Results: The obtained results first prove that neither linear elasticity nor neo-Hookean's laws can be used to model the skin. On the contrary, the nonlinear elastic model presents a relevant fit of the experimental curves. The skin thickness is also proved to be another key point to be taken into consideration. Conclusions: The obtained results are successfully compared with literature and the reliability of the proposed method is underlined with the identification of 300 additional experimental curves. The different works we are currently focusing on are finally introduced. [ABSTRACT FROM AUTHOR]

The paper presents an expression useful to estimate the notch stress intensity factor (NSIF) from finite element analyses carried out by using a mesh pattern with a constant element size. The evaluation of the NSIF from a numerical analysis of the local stress field usually requires very refined meshes and then large computational effort. The usefulness of the presented expression is that (i) only the elastic peak stress numerically evaluated at the V-notch tip is needed and no longer the whole stress–distance set of data; (ii) the adopted meshes are rather coarse if compared to those necessary for the evaluation of the whole local stress field. The proposed expression needs the evaluation of a virtual V-notch tip radius, i.e. the radius which would produce the same elastic peak stress than that calculated by FEM at the sharp V-notch tip by means of a given mesh pattern. Once such a radius has been theoretically determined for a given geometry, the expression can be applied in a wide range of notch depths and opening angles. [ABSTRACT FROM AUTHOR]

On the basis of detailed three-dimensional (3D) elastic finite element (FE) analyses, this paper provides tractable approximations for elastic T stress solutions for circumferential inner-surface cracks in cylinders. Internal pressure and global bending moment were considered. The FE model and analysis procedure employed in the analysis were verified using existing solutions for both elastic stress intensity factor and T stress. To cover a practical range, three different values of the ratio of the mean radius of cylinder to the thickness, Rm/ t, were selected; furthermore, four different values of the ratio of the crack depth to the thickness, a/ t, ranging from 0.1 to 0.75 and three different values of θ/π ranging from 0.1 to 0.4 were selected. On the basis of FE analyses results, polynomial approximations were proposed at three different locations: surface point, middle point and deepest point. On the basis of the detailed 3D elastic FE analysis, the solutions presented are believed to be the most accurate, and thus provide valuable information for structural integrity assessment considering a crack-tip constraint. [ABSTRACT FROM AUTHOR]

The interest in using fibre-reinforced composites in structural components is increasing. Some of these structural composites, such as wind turbine blades, aircraft components and torsion shafts are subject to fatigue loadings. It is widely accepted that fully reversed cyclic loading is the most adverse loading for fibre-reinforced composites, but the modelling of the material behaviour under this loading condition is very difficult. In this paper, a damage model is presented for woven glass fibre-reinforced composites subject to fully reversed cyclic loading. First fatigue experiments have been conducted in displacement-controlled fully reversed bending and the stiffness degradation and damage patterns have been observed. Based on these experimental data, a damage model has been developed, which includes the in-plane stress components and the degradation of the in-plane elastic properties. The model has been implemented in a commercial finite-element code and simulation of the successive stages in the fatigue life has been performed. The model has been validated for a plain woven glass fabric reinforced composite and simulated stiffness degradation, damage growth and damage distribution have been compared with experimental data. [ABSTRACT FROM AUTHOR]

In this paper, the Crouzeix–Velte decomposition is generalized with respect to boundary conditions and boundary value problems, moreover, in the discrete case, the gap between the first-order staggered grid approximation and the high-order Scott–Vogelius elements (which was the only finite element family until now for which such a decomposition was known) is filled by proving that the (second-order) Fortin–Soulie elements also admit such a decomposition—which is of advantage when iteratively solving the corresponding boundary value problems (Stokes, linear elasticity) and for long-term calculations. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Dynamic problems of active optimal vibration control of elastic structures are solved by applying ‘static’ beam elements from standard structural FEM software. The approach uses an analogy between the optimality equations for the vibration control problem and the equations for the static bending of certain beams. The computer implementation of the analogy, which was presented in Part I of the paper, is discussed here in detail. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the ‘second-order’ incomplete triangular factorization (Kaporin, 1998) is considered as a preconditioner for the CG method. Some refinements of the original algorithm are proposed and investigated, which give rise to a more efficient modified incomplete Cholesky 2nd-order (MIC2) type preconditionings. Numerical results are given for a set of real-life large-scale SPD linear systems arising in the finite element modelling of linear elasticity problems which clearly indicate the superiority of the MIC2 preconditionings. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The constant γ in the strengthened Cauchy-Buniakowski-Schwarc (CBS) inequality plays a key role in the convergence analysis of the multilevel iterative methods. We consider in this paper the approximation of the two-dimensional elasticity problem by bilinear rectangle finite elements. Two semi-coarsening refinement procedures are studied. We prove for both cases new estimates of the constant γ, uniformly on the Poisson ratio. As a result of the presented analysis we obtain an optimal order algebraic multiLevel iteration (AMLI) method for the case of balanced semi-coarsening mesh refinement. The total computational complexity of the algorithm is proportional to the size of the discrete problem with a proportionality constant independent of the Poisson ratio, that is, the algorithm is of optimal order for almost incompressible elasticity problems. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper discusses an iterative scheme for solving large-scale three-dimensional linear elasticity problems, discretized on a tensor product of two-dimensional and one-dimensional meshes. A framework is chosen of the additive AMLI method to develop a preconditioner of a ‘black-box’ type which is robust with respect to discontinuities of the problem coefficients and imposes only weak (and acceptable in practice) restrictions on the choice of the meshing procedure. The preconditioner works on a hierarchical sequence of nested finite element spaces to solve the problem with arithmetic cost, nearly proportional to the number of degrees of freedom on the finest mesh. It is particularly well suited for the case when the solution is known to be strongly varying in certain subregions of the domain and the mesh is locally prerefined there to reduce the discretization error. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This is a presentation of a quadrilateral finite element for wrinkled curved elastic membranes. A modified form of the deformation gradient enables us to avoid the spurious compressive stresses generated by a classical model. It results in non-linear relations for the eigeneomponents of the Cauchy stres.'; tensor. which are solved by means of a secant method. The application of the element to sail design is presented in this paper. [ABSTRACT FROM AUTHOR]

The paper deals with the symbolic integration of a 4-noded isoparametric finite element for plane elasticity. An efficient approach to generate explicit formulas for computing the elementary stiffness matrix is discussed. The procedure is based on the use of the Derive symbolic manipulation code as well as in a posteriori manipulation of the expressions obtained. The accuracy of the results is tested in extremely distorted and geometrically ill-conditioned elements. Three practical engineering models are presented and the accuracy of the results is discussed. A computer time comparison between both numerical and symbolic integration approaches is also included, showing that relevant CPU savings are obtained when applying symbolic integration. [ABSTRACT FROM AUTHOR]

The paper investigates the convergence of the h-, p- and hp-versions of a variational symmetric boundary element method (BEM) in plane elasticity by numerical experiments. The study discusses mixed boundary value problems on polygonal domains, i.e. problems for which the exact solution is analytic except in a finite number of points. The convergence of the error in energy norm is displayed for all versions of the BEM. All results are also compared with those obtained by the corresponding finite element methods. The theoretically predicted asymptotic convergence rates for all versions of the method can be observed in the numerical experiments. A comparison of computer times is given as well. [ABSTRACT FROM AUTHOR]

An essential requirement for a satisfactory curved shell finite element is a capability for exact representation of rigid body movements: otherwise serious difficulties can occur, as is well known from early developments in shell finite element analysis. It is shown in this paper that appropriate assumed displacement fields for a particular shallow curved shell finite element with 18 degrees of freedom can be obtained in a very simple, yet apparently novel, way which permits the exact recovery of all rigid body movements. The shallow curved shell finite element considered here is constructed on a triangular flat facet approximation to a general thin elastic shell; it has quadratic middle surface geometry to allow for accurate modeling of arbitrary curvatures. [ABSTRACT FROM AUTHOR]

Mindlin-type plate and shell finite elements are the most widely used ones in the analysis of laminated composite structures. In the commercially available finite element programs, the transverse shear correction factors for these elements are usually the same as for structures made of isotropic materials. In the paper the shear correction factors are determined using energy principles for general laminates in cylindrical bending. Results for various materials and laminates are presented. [ABSTRACT FROM AUTHOR]

The paper reports some numerical experiments on the effectivity of the Zienkiewicz-Zhu error estimate (1987) and comparisons of two adaptive mesh generators: ADMESH, developed by Jin and Wiberg (1990) and MAD2D by Peraire et al. (1987) and Zhu et al. (1990-91). From the experiments we observe that: (1) without any empirical correction, the effectivity of the error estimate for linear triangular elements is good if post-processed continuous stresses are obtained by adequately using an iterative stress recovery procedure (Zienkiewicz et al., 1985), and is also acceptable by using a simple `averaging' procedure; (2) these two mesh generators are basically comparable. [ABSTRACT FROM AUTHOR]

In this paper, the discontinuous Galerkin (dG) method is introduced and applied for a problem of nearly incompressible material behavior, where the standard finite element method, namely the conventional continuous Galerkin (cG) method faces the well-known problem of volumetric locking. The highlight of the work lies in the reduced integration scheme for the boundary terms of the dG method. Two different reduced and mixed integration schemes are presented and applied to reduce the calculation time. The dG method converges much faster than standard cG method with respect to the number of the elements, provided that the penalty value is sufficiently large. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In order to consider growing expectations on vibro-acoustic performance of products within the design process, reliable simulation tools are necessary. In this paper, we present a approach for the simulation of laminated shells composed of elastic and poroelastic layers. We assume that the shell is given by a parametrization, which allows us to work witn the exact geometry. The three-dimensional problem is reduced to a two-dimensional one, by choosing a set of through-the-thickness functions for each quantity and through-the-thickness integration. The implemented high order finite element approach for the reduced problem on the reference surface relays on hierarchical shape functions. In a numerical example, we show the influence of poroelastic materials attached to a aluminium shell. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Summary: The Neumann problem of linear elasticity is singular with a kernel formed by the rigid motions of the body. There are several tricks that are commonly used to obtain a nonsingular linear system. However, they often cause reduced accuracy or lead to poor convergence of the iterative solvers. In this paper, different well‐posed formulations of the problem are studied through discretization by the finite element method, and preconditioning strategies based on operator preconditioning are discussed. For each formulation, we derive preconditioners that are independent of the discretization parameter. Preconditioners that are robust with respect to the first Lamé constant are constructed for the pure displacement formulations, whereas a preconditioner that is robust in both Lamé constants is constructed for the mixed formulation. It is shown that, for convergence in the first Sobolev norm, it is crucial to respect the orthogonality constraint derived from the continuous problem. On the basis of this observation, a modification to the conjugate gradient method is proposed, which achieves optimal error convergence of the computed solution. [ABSTRACT FROM AUTHOR]

This paper communicates a new algorithmic concept, how higher-order Runge-Kutta (RK) methods for time integration of viscoelastic constitutive laws can be introduced into nonlinear finite element methods in order (i) to obtain the full nominal order p in time integration, (ii) to ensure that global equilibrium is only required at the end of time intervals Δ t but not in the interior at RK-stages, and (iii) to obtain -based on (i) and (ii)- a considerable speed-up compared with Backward-Euler. The condition to realize (i)-(iii) is, that the approximation of total strain in time must be of the same order as the time-integration method, which is a completion of the concept of algorithmic consistency in computational inelasticity. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]