Showing papers in "International Journal for Numerical Methods in Engineering in 2005"
TL;DR: A novel method for doing material optimization of general composite laminate shell structures is presented and its capabilities are illustrated with three examples.
Abstract: A novel method for doing material optimization of general composite laminate shell structures is presented and its capabilities are illustrated with three examples. The method is labelled Discrete Material Optimization (DMO) but uses gradient information combined with mathematical programming to solve a discrete optimization problem. The method can be used to solve the orientation problem of orthotropic materials and the material selection problem as well as problems involving both. The method relies on ideas from multiphase topology optimization to achieve a parametrization which is very general and reduces the risk of obtaining a local optimum solution for the tested configurations. The applicability of the DMO method is demonstrated for fibre angle optimization of a cantilever beam and combined fibre angle and material selection optimization of a four-point beam bending problem and a doubly curved laminated shell. Copyright © 2005 John Wiley & Sons, Ltd.
547 citations
TL;DR: In this article, the authors study the capabilities of Extended Finite Element Method (XFEM) to achieve accurate computations in non smooth situations such as crack problems, and show that the XFEM method ensures a weaker error than classical finite element methods, but the rate of convergence is not improved when the mesh parameter h is going to zero because of the presence of a singularity.
Abstract: The aim of the paper is to study the capabilities of the Extended Finite Element Method (XFEM) to achieve accurate computations in non smooth situations such as crack problems. Although the XFEM method ensures a weaker error than classical finite element methods, the rate of convergence is not improved when the mesh parameter h is going to zero because of the presence of a singularity. The difficulty can be overcome by modifying the enrichment of the finite element basis with the asymptotic crack tip displacement solutions as well as with the Heaviside function. Numerical simulations show that the modified XFEM method achieves an optimal rate of convergence (i.e. like in a standard finite element method for a smooth problem)
434 citations
TL;DR: The implementation of the X‐FEM method for stress analysis around cracks is improved in three ways: the enrichment strategy is revisited, a ‘geometrical’ enrichment in which a given domain size is enriched and the numerical integration scheme is dramatically improved for tip enrichment functions.
Abstract: Numerical crack propagation schemes were augmented in an elegant manner by the X-FEM method. The use of special tip enrichment functions, as well as a discontinuous function along the sides of the crack allows one to do a complete crack analysis virtually without modifying the underlying mesh, which is of industrial interest, especially when a numerical model for crack propagation is desired. This paper improves the implementation of the X-FEM method for stress analysis around cracks in three ways. First, the enrichment strategy is revisited. The conventional approach uses a 'topological' enrichment (only the elements touching the front are enriched). We suggest a 'geometrical' enrichment in which a given domain size is enriched. The improvements obtained with this enrichment are discussed. Second, the conditioning of the X-FEM both for topological and geometrical enrichments is studied. A preconditioner is introduced so that 'off the shelf' iterative solver packages can be used and perform as well on X-FEM matrices as on standard FEM matrices. The preconditioner uses a local (nodal) Cholesky based decomposition. Third, the numerical integration scheme to build the X-FEM stiffness matrix is dramatically improved for tip enrichment functions by the use of an ad hoc integration scheme. A 2D benchmark problem is designed to show the improvements and the robustness.
423 citations
TL;DR: By superposing and gluing models, the Arlequin method offers an extended modelling framework for the design of engineering structures as mentioned in this paper. But this method is not suitable for the modeling of complex structures.
Abstract: By superposing and gluing models, the Arlequin method offers an extended modelling framework for the design of engineering structures. This paper aims at developing the numerical aspects of the approach and at showing how it can be used with great flexibility and in a consistent manner to change locally a global mechanical model. The capabilities of the Arlequin method and the effectiveness of the implemented numerical tools are exemplified by 1-D, 2-D and 3-D numerical applications.
395 citations
TL;DR: In this paper, a quasi-static analysis of three-dimensional crack propagation in brittle and quasi-brittle solids is presented, where the extended finite element method (XFEM) is combined with linear tetrahedral elements.
Abstract: An Erratum has been published for this article in International Journal for Numerical Methods in Engineering 2005, 63(8): 1228.
We present a new formulation and a numerical procedure for the quasi-static analysis of three-dimensional crack propagation in brittle and quasi-brittle solids. The extended finite element method (XFEM) is combined with linear tetrahedral elements. A viscosity-regularized continuum damage constitutive model is used and coupled with the XFEM formulation resulting in a regularized ‘crack-band’ version of XFEM. The evolving discontinuity surface is discretized through a C0 surface formed by the union of the triangles and quadrilaterals that separate each cracked element in two. The element's properties allow a closed form integration and a particularly efficient implementation allowing large-scale 3D problems to be studied. Several examples of crack propagation are shown, illustrating the good results that can be achieved. Copyright © 2005 John Wiley & Sons, Ltd.
351 citations
TL;DR: In this article, a new generation of penetrometers, which have a much greater projected area than the cone shaft, and introduces a version of the strain path method based on classical upper bound solutions for the penetrationrometers.
Abstract: The problem of penetration resistance involves a continuously moving zone of plastic distortion in the soil medium. This has been explored for cone penetration and pile installation, where additional volume is intruded into the soil, using the strain path method with the flow field derived from classical fluid mechanics. This paper focuses on a new generation of penetrometers, which have a much greater projected area than the cone shaft, and introduces a version of the strain path method based on classical upper bound solutions for the penetrometers. The new approach is used to explore the effects of high strain rates, and gradual strength degradation, on the penetration resistance of cylindrical and spherical penetrometers. Copyright © 2005 John Wiley & Sons, Ltd.
349 citations
TL;DR: In this article, a new upper bound formulation of limit analysis of two and three-dimensional solids is presented, which is formulated in terms of stresses rather than velocities and plastic multipliers, and by means of duality theory it is shown that the formulation does indeed result in rigorous upper bound solutions.
Abstract: SUMMARY A new upper bound formulation of limit analysis of two- and three-dimensional solids is presented. In contrast to most discrete upper bound methods the present one is formulated in terms of stresses rather than velocities and plastic multipliers. However, by means of duality theory it is shown that the formulation does indeed result in rigorous upper bound solutions. Also, kinematically admissible discontinuities, which have previously been shown to be very efficient, are given an interpretation in terms of stresses. This allows for a much simpler implementation and, in contrast to existing formulations, extension to arbitrary yield criteria in two and three dimensions is straightforward. Finally, the capabilities of the new method are demonstrated through a number of examples. Copyright 2005 John Wiley & Sons, Ltd.
292 citations
TL;DR: In this article, a local tricubic interpolation scheme was proposed that is both C^1 and isotropic in three dimensions, which is based on a specific 64 × 64 matrix that gives the relationship between the derivatives at the corners of the elements and the coefficients of the tricubaic interpolant for this element.
Abstract: The purpose of this paper is to give a local tricubic interpolation scheme in three dimensions that is both C^1 and isotropic. The algorithm is based on a specific 64 × 64 matrix that gives the relationship between the derivatives at the corners of the elements and the coefficients of the tricubic interpolant for this element. In contrast with global interpolation where the interpolated function usually depends on the whole data set, our tricubic local interpolation only uses data in a neighbourhood of an element. We show that the resulting interpolated function and its three first derivatives are continuous if one uses cubic interpolants. The implementation of the interpolator can be downloaded as a static and dynamic library for most platforms. The major difference between this work and current local interpolation schemes is that we do not separate the problem into three one-dimensional problems. This allows for a much easier and accurate computation of higher derivatives of the extrapolated field. Applications to the computation of Lagrangian coherent structures in ocean data are briefly discussed.
289 citations
TL;DR: In this paper, the implementation of h-adaptivity for mesh-free particle methods within a structured framework is described, where the initial particle arrangement is structured along with a background mesh, and outside boundaries and interior interfaces are described by implicit functions.
Abstract: The implementation of h-adaptivity for meshfree particle methods within a structured framework is described In this framework, the initial particle arrangement is structured along with a background mesh, and outside boundaries and interior interfaces are described by implicit functions The advantage of meshfree approximations in this framework lies in the ease of implementing h-adaptivity and the simplicity of the data structures Particles can easily be added and removed without complications in the data structure, although there are some issues in the quadrature An a posteriori error estimation is used for the adaptive refinement An adaptive refinement strategy is applied to several linear elastic problems with high stress and strain gradients and singularities Several non-linear examples are also given Copyright © 2005 John Wiley & Sons, Ltd
254 citations
TL;DR: In this paper, a discrete damage-type constitutive model is applied to model cohesive cracks in quasi-brittle materials, whereby the discontinuity is not limited to interelement boundaries, but is allowed to propagate freely through the elements.
Abstract: The present contribution is concerned with the computational modelling of cohesive cracks in quasi-brittle materials, whereby the discontinuity is not limited to interelement boundaries, but is allowed to propagate freely through the elements. In the elements, which are intersected by the discontinuity, additional displacement degrees of freedom are introduced at the existing nodes. Therefore, two independent copies of the standard basis functions are used. One set is put to zero on one side of the discontinuity, while it takes its usual values on the opposite side, and vice versa for the other set. To model inelastic material behaviour, a discrete damage-type constitutive model is applied, formulated in terms of displacements and tractions at the surface. Some details on the numerical implementation are given, concerning the failure criterion, the determination of the direction of the discontinuity and the integration scheme. Finally, numerical examples show the performance of the method.
244 citations
TL;DR: A generalization of the eXtended finite element method (X-FEM) to model dynamic fracture and time-dependent problems from a more general point of view, and a proof of the stability of the numerical scheme in the linear case is given.
Abstract: This paper proposes a generalization of the eXtended finite element method (X-FEM) to model dynamic fracture and time-dependent problems from a more general point of view, and gives a proof of the stability of the numerical scheme in the linear case. First, we study the stability conditions of Newmark-type schemes for problems with evolving discretizations. We prove that the proposed enrichment strategy satisfies these conditions and also ensures energy conservation. Using this approach, as the crack propagates, the enrichment can evolve with no occurrence of instability or uncontrolled energy transfer. Then, we present a technique based on Lagrangian conservation for the estimation of dynamic stress intensity factors for arbitrary 2D cracks. The results presented for several applications are accurate for stationary or moving cracks. Copyright © 2005 John Wiley & Sons, Ltd.
TL;DR: In this paper, a so-called "sin 1 − 2" inequality is proved for any elasto-plastic material satisfying Mohr-Coulomb's yield criterion, and a robust numerical solution for the initial value problem is given in conjunction with the necessary and sufficient condition ensuring the convergence of solution.
Abstract: SUMMARY The paper deals with two essential and related closely processes involved in the finite element slope stability analysis in two-dimensional problems, i.e. computation of the factors of safety (FOS) and location of the critical slide surfaces. A so-called – inequality, sin 1 − 2 is proved for any elasto-plastic material satisfying Mohr–Coulomb’s yield criterion. In order to obtain an FOS of high precision with less calculation and a proper distribution of plastic zones in the critical equilibrium state, it is stated that the Poisson’s ratio should be adjusted according to the principle that the – inequality always holds as reducing the strength parameters c and . While locating the critical slide surface represented by the critical slide line (CSL) under the plane strain condition, an initial value problem of a system of ordinary differential equations defining the CSL is formulated. A robust numerical solution for the initial value problem based on the predictor–corrector method is given in conjunction with the necessary and sufficient condition ensuring the convergence of solution. A simple example, the kinematic solution of which is available, and a challenging example from a hydraulic project in construction are analysed to demonstrate the effectiveness of the proposed procedures. Copyright 2005 John Wiley & Sons, Ltd.
TL;DR: In this article, a mortar-based formulation for the solution of two-dimensional frictional contact problems involving finite deformation and large sliding is presented, with particular emphasis on key aspects of the linearization procedure and on the robust description of the friction kinematics.
Abstract: This paper presents a mortar-based formulation for the solution of two dimensional frictional contact problems involving finite deformation and large sliding. As is widely recognized, traditional node-to-surface contact formulations have several drawbacks in solution of deformable-to-deformable contact problems, including lack of general patch test passage, degradation of spatial convergence rates, and robustness issues associated with the faceted representation of contacting surfaces. The mortar finite element method, initially proposed as a technique to join dissimilarly meshed domains, has been shown to preserve optimal convergence rates in tied contact problems (see (Discretization Methods and Iterative Solvers Based on Domain Decomposition, Springer-Verlag, Heidelberg, 2001) for a recent review), and is examined here as an alternative spatial discretization method for large sliding contact. In particular, a novel description for frictional sliding conditions in large deformation mortar formulations is proposed in this work.
In recent years, the mortar element method has already been successfully implemented to solve frictional contact problems with linearized kinematics (see (Int. J. Numer. Meth. Engng 1993; 36: 3451)). However, in the presence of large deformations and finite sliding, one must face difficulties associated with the definition and linearization of contact virtual work in the case where the mortar projection has a direct dependence on the tangential relative motion along the interface. In this paper, such a formulation is presented, with particular emphasis on key aspects of the linearization procedure and on the robust description of the friction kinematics. Some novel techniques are proposed to treat the non-smoothness in the contact geometry and the searching required to define mortar segments. A number of numerical examples illustrate the performance and accuracy of the proposed formulation. Copyright © 2004 John Wiley & Sons, Ltd.
TL;DR: In this paper, the authors propose a new technique which allows the use of simplex finite elements (linear triangles in 2D and linear tetrahedra in 3D) in the large strain analysis of nearly incompressible solids.
Abstract: This paper proposes a new technique which allows the use of simplex finite elements (linear triangles in 2D and linear tetrahedra in 3D) in the large strain analysis of nearly incompressible solids. The new technique extends the F-bar method proposed by de Souza Neto et al. (Int. J. Solids and Struct. 1996; 33:3277-3296) and is conceptually very simple: It relies on the enforcement of (near-)incompressibility over a patch of simplex elements (rather than the point-wise enforcement of conventional displacement-based finite elements). Within the framework of the F-bar method, this is achieved by assuming, for each element of a mesh, a modified (F-bar) deformation gradient whose volumetric component is defined as the volume change ratio of a pre-defined patch of elements. The resulting constraint relaxation effectively overcomes volumetric locking and allows the successful use of simplex elements under finite strain near-incompressibility. As the original F-bar procedure, the present methodology preserves the displacement-based structure of the finite element equations as well as the strain-driven format of standard algorithms for numerical integration of path-dependent constitutive equations and can be used regardless of the constitutive model adopted. The new elements are implemented within an implicit quasi-static environment. In this context, a closed form expression for the exact tangent stiffness of the new elements is derived. This allows the use of the full Newton-Raphson scheme for equilibrium iterations. The performance of the proposed elements is assessed by means of a comprehensive set of benchmarking two- and three-dimensional numerical examples.
TL;DR: In this paper, a new formulation and numerical procedures are developed for the analysis of arbitrary crack propagation in shells using the extended finite element method, which is valid for completely non-linear problems.
Abstract: A new formulation and numerical procedures are developed for the analysis of arbitrary crack propagation in shells using the extended finite element method. The method is valid for completely non-linear problems. Through-the-thickness cracks in sandwich shells are considered. An exact shell kinematics is presented, and a new enrichment of the rotation field is proposed which satisfies the director inextensibility condition. To avoid locking, an enhanced strain formulation is proposed for the 4-node cracked shell element. A finite strain plane stress constitutive model based on the logarithmic corotational rate is employed. A cohesive zone model is introduced which embodies the special characteristics of the shell kinematics. Stress intensity factors are calculated for selected problems and crack propagation problems are solved. Copyright © 2004 John Wiley & Sons, Ltd.
TL;DR: In this paper, the anchor loss is computed using an absorbing boundary based on a perfectly matched layer (PML) which absorbs incoming waves over a wide frequency range for any nonzero angle of incidence.
Abstract: Electromechanical resonators and filters, such as quartz, ceramic, and surface-acoustic wave devices, are important signal-processing elements in communication systems. Over the past decade, there has been substantial progress in developing new types of miniaturized electromechanical resonators using microfabrication processes. For these micro-resonators to be viable they must have high and predictable quality factors (Q). Depending on scale and geometry, the energy losses that lower Q may come from material damping, thermoelastic damping, air damping, or radiation of elastic waves from an anchor. Of these factors, anchor losses are the least understood because such losses are due to a complex radiation phenomena in a semi-infinite elastic half-space. Here, we describe how anchor losses can be accurately computed using an absorbing boundary based on a perfectly matched layer (PML) which absorbs incoming waves over a wide frequency range for any non-zero angle of incidence. We exploit the interpretation of the PML as a complex-valued change of co-ordinates to illustrate how one can come to a simpler finite element implementation than was given in its original presentations. We also examine the convergence and accuracy of the method, and give guidelines for how to choose the parameters effectively. As an example application, we compute the anchor loss in a micro disk resonator and compare it to experimental data. Our analysis illustrates a surprising mode-mixing phenomenon which can substantially affect the quality of resonance.
TL;DR: In this paper, the constitutive law for the interface element has been extended by incorporating a modified version of a continuum fatigue damage model, which has been extensively applied to predict delamination growth due to static loading, has been modified to incorporate the effects of cyclic loading.
Abstract: This paper presents a computational technique for the prediction of fatigue-driven delamination growth in composite materials. The interface element, which has been extensively applied to predict delamination growth due to static loading, has been modified to incorporate the effects of cyclic loading. Using a damage mechanics formulation, the constitutive law for the interface element has been extended by incorporating a modified version of a continuum fatigue damage model. The paper presents details of the fatigue degradation strategy and examples of the predicted fatigue delamination growth in mode I, mode II and mixed mode I/II are presented to demonstrate that the numerical model mimics the Paris law behaviour usually observed in experimental testing. Copyright © 2005 John Wiley & Sons, Ltd.
TL;DR: In this article, a multiscale enrichment method based on the partition of unity (MEPU) method is presented, which is a synthesis of mathematical homogenization theory and the partition-of-unity method.
Abstract: A new multiscale enrichment method based on the partition of unity (MEPU) method is presented. It is a synthesis of mathematical homogenization theory and the partition of unity method. Its primary objective is to extend the range of applicability of mathematical homogenization theory to problems where scale separation may not be possible. MEPU is perfectly suited for enriching the coarse scale continuum descriptions (PDEs) with fine scale features and the quasi-continuum formulations with relevant atomistic data. Numerical results show that it provides a considerable improvement over classical mathematical homogenization theory and quasi-continuum formulations. Copyright © 2005 John Wiley & Sons, Ltd.
TL;DR: Wang et al. as mentioned in this paper presented an improved genetic algorithm (GA) to minimize the weight of truss with sizing, shape and topology variables, which completely considers the character of constrained optimization and proposed a new strategy of creating next population by competing between parent and offspring population based on constraint and fitness values.
Abstract: This paper presents an improved genetic algorithm (GA) to minimize weight of truss with sizing, shape and topology variables. Because of the nature of discrete and continuous variables, mixed coding schemes are proposed, including binary and float coding, integer and float coding. Surrogate function is applied to unify the constraints into single one; moreover surrogate reproduction is developed to select good individuals to mating pool on the basis of constraint and fitness values, which completely considers the character of constrained optimization. This paper proposes a new strategy of creating next population by competing between parent and offspring population based on constraint and fitness values; so that lifetime of excellent gene is prolonged. Because the initial population is created randomly and three operators of GA are also indeterminable, it is necessary to check whether the structural topology is desirable. An improved restart operator is proposed to introduce new gene and explore new space, so that the reliability of GA is enhanced. Selected examples are solved; the improved numerical results demonstrate that the enhanced GA scheme is feasible and effective. Copyright © 2005 John Wiley & Sons, Ltd.
TL;DR: In this article, the development of a computationally efficient finite element tool for the analysis of 3D steady state heat flow in geothermal heating systems is presented. But the authors focus on the development for vertical borehole heat exchangers and the surrounding soil layers.
Abstract: This paper presents the development of a computationally efficient finite element tool for the analysis of 3D steady state heat flow in geothermal heating systems. Emphasis is placed on the development of finite elements for vertical borehole heat exchangers and the surrounding soil layers. Three factors have contributed to the computational efficiency: the proposed mathematical model for the heat exchanger, the discretization of the spatial domain using the Petrov–Galerkin method and the sequential numerical algorithm for solving the resulting system of non-linear equations. These have contributed in reducing significantly the required number of finite elements necessary for describing the involved systems. Details of the mathematical derivations and some numerical examples are presented. Copyright © 2005 John Wiley & Sons, Ltd.
TL;DR: In this article, two immersed finite element (IFE) methods for solving the elliptic interface problem arising from electric field simulation in composite materials are presented, where the meshes used in these IFE methods can be independent of the interface geometry and position; therefore, if desired, a structured mesh such as a Cartesian mesh can be used in an IFE method to simulate 3D electric field in a domain with non-trivial interfaces separating different materials.
Abstract: This paper presents two immersed finite element (IFE) methods for solving the elliptic interface problem arising from electric field simulation in composite materials. The meshes used in these IFE methods can be independent of the interface geometry and position; therefore, if desired, a structured mesh such as a Cartesian mesh can be used in an IFE method to simulate 3-D electric field in a domain with non-trivial interfaces separating different materials. Numerical examples are provided to demonstrate that the accuracies of these IFE methods are comparable to the standard linear finite element method with unstructured body-fit mesh. Copyright © 2005 John Wiley & Sons, Ltd.
TL;DR: In this paper, a constitutive model for describing the stress-strain behavior of granular soils subjected to cyclic loading is presented, which is formulated using bounding surface theory within a critical state framework.
Abstract: A constitutive model for describing the stress–strain behaviour of granular soils subjected to cyclic loading is presented. The model is formulated using bounding surface theory within a critical state framework. A single set of material parameters is introduced for the complete characterization of the constitutive model. The shape of the bounding surface is based on experimental observations of undrained stress paths for loose samples. A mapping rule which passes through stress reversal points is introduced to depict the stress–strain behaviour during unloading and reloading. The effect of particle crushing is considered through a modified critical state line. Essential features of the model are validated using several experimental data from the literature. Both drained and undrained loading conditions are considered. The characteristic features of behaviour in granular soils subjected to cyclic loading are captured. Copyright © 2005 John Wiley & Sons, Ltd.
TL;DR: In this paper, finite element techniques are widely used for analysing non-linear mechanical processes, due to their inherent lack of convergence problems, and the energy content in the finite element is high.
Abstract: Due to their inherent lack of convergence problems explicit finite element techniques are widely used for analysing non-linear mechanical processes. In many such processes the energy content in the ...
TL;DR: In this paper, an anisotropic adaptive analysis procedure based on a discontinuous Galerkin finite element discretization and local mesh modification of simplex elements is presented for transient two-and three-dimensional problems governed by Euler's equation.
Abstract: An anisotropic adaptive analysis procedure based on a discontinuous Galerkin finite element discretization and local mesh modification of simplex elements is presented. The procedure is applied to transient two- and three-dimensional problems governed by Euler's equation. A smoothness indicator is used to isolate jump features where an aligned mesh metric field in specified. The mesh metric field in smooth portions of the domain is controlled by a Hessian matrix constructed using a variational procedure to calculate the second derivatives. The transient examples included demonstrate the ability of the mesh modification procedures to effectively track evolving interacting features of general shape as they move through a domain. Copyright (C) 2004 John Wiley Sons, Ltd.
TL;DR: In this article, the sinh function is used to calculate the position of the projection of the source point onto the boundary element, which is called the "nearly singular point".
Abstract: An implementation of the boundary element method requires the accurate evaluation of many integrals. When the source point is far from the boundary element under consideration, a straightforward application of Gaussian quadrature suffices to evaluate such integrals. When the source point is on the element, the integrand becomes singular and accurate evaluation can be obtained using the same Gaussian points transformed under a polynomial transformation which has zero Jacobian at the singular point. A class of integrals which lies between these two extremes is that of 'nearly singular' integrals. Here, the source point is close to, but not on, the element and the integrand remains finite at all points. However, instead of remaining flat, the integrand develops a sharp peak as the source point moves closer to the element, thus rendering accurate evaluation of the integral difficult. This paper presents a transformation, based on the sinh function, which automatically takes into account the position of the projection of the source point onto the element, which we call the 'nearly singular point', and the distance from the source point to the element. The transformation again clusters the points towards the nearly singular point, but does not have a zero Jacobian. Implementation of the transformation is straightforward and could easily be included in existing boundary element method software. It is shown that, for the two-dimensional boundary element method, several orders of magnitude improvement in relative error can be obtained using this transformation compared to a conventional implementation of Gaussian quadrature. Asymptotic estimates for the truncation errors are also quoted. Copyright © 2004 John Wiley & Sons, Ltd.
TL;DR: In this article, a non-linear quadrilateral shell element for the analysis of thin structures is presented, which is based on a Hu-Washizu functional with independent displacement, stress and strain fields.
Abstract: In the paper a non-linear quadrilateral shell element for the analysis of thin structures is presented. The variational formulation is based on a Hu–Washizu functional with independent displacement, stress and strain fields. The interpolation matrices for the mid-surface displacements and rotations as well as for the stress resultants and strains are specified. Restrictions on the interpolation functions concerning fulfillment of the patch test and stability are derived. The developed mixed hybrid shell element possesses the correct rank and fulfills the in-plane and bending patch test. Using Newton's method the finite element approximation of the stationary condition is iteratively solved. Our formulation can accommodate arbitrary non-linear material models for finite deformations. In the examples we present results for isotropic plasticity at finite rotations and small strains as well as bifurcation problems and post-buckling response. The essential feature of the new element is the robustness in the equilibrium iterations. It allows very large load steps in comparison to other element formulations. Copyright © 2005 John Wiley & Sons, Ltd.
TL;DR: In this article, an approach to emulate non-reflecting boundary conditions in atomistic simulations of crystalline solids is proposed, where the outer, non-simulated, region is accurately represented by a memory function, related to the lattice dynamics Green's function.
Abstract: Computer simulations of atomic scale processes in solids are often associated with the issue of spurious reflection of elastic waves at the boundaries of a molecular dynamics domain. In this paper, we propose an approach to emulate non-reflecting boundary conditions in atomistic simulations of crystalline solids. Harmonic response of the outer, non-simulated, region is accurately represented by a memory function, related to the lattice dynamics Green's function. The outward wave flow is cancelled due to work done by the corresponding response forces. Performance of method, dependent on a series of method parameters, is illustrated on a benchmark problem. Copyright © 2004 John Wiley & Sons, Ltd.
TL;DR: The goal of this paper is to compare a number of algorithms for computing a large number of eigenvectors of the generalized symmetric eigenvalue problem arising from a modal analysis of elastic structures by considering the use of preconditioned iterative methods.
Abstract: The goal of our paper is to compare a number of algorithms for computing a large number of eigenvectors of the generalized symmetric eigenvalue problem arising from a modal analysis of elastic structures. The shift-invert Lanczos algorithm has emerged as the workhorse for the solution of this generalized eigenvalue problem; however, a sparse direct factorization is required for the resulting set of linear equations. Instead, our paper considers the use of preconditioned iterative methods. We present a brief review of available preconditioned eigensolvers followed by a numerical comparison on three problems using a scalable algebraic multigrid (AMG) preconditioner.
TL;DR: In this paper, the DSC-Ritz method is proposed for vibration analysis of Mindlin plates, where two basis functions are constructed by using DSC delta sequence kernels of the positive type.
Abstract: This paper introduces a novel method for the free vibration analysis of Mindlin plates. The proposed method takes the advantage of both the local bases of the discrete singular convolution (DSC) algorithm and the pb-2 Ritz boundary functions to arrive at a new approach, called DSC-Ritz method. Two basis functions are constructed by using DSC delta sequence kernels of the positive type. The energy functional of the Mindlin plate is represented by the newly constructed basis functions and is minimized under the Ritz variational principle. Extensive numerical experiments are considered by different combinations of boundary conditions of Mindlin plates of rectangular and triangular shapes. The performance of the proposed method is carefully validated by convergence analysis. The frequency parameters agree very well with those in the literature. Numerical experiments indicate that the proposed DSC-Ritz method is a very promising new method for vibration analysis of Mindlin plates. Copyright © 2004 John Wiley & Sons, Ltd.
TL;DR: In this article, an adaptive remeshing procedure for lower bound limit analysis with application to soil mechanics is presented. But the authors do not consider the effect of stress singularities in the boundary conditions.
Abstract: The objective of this work is to present an adaptive remeshing procedure for lower bound limit analysis with application to soil mechanics. Unlike conventional finite element meshes, a lower bound grid incorporates statically admissible stress discontinuities between adjacent elements. These discontinuities permit large stress jumps over an infinitesimal distance and reduce the number of elements needed to predict the collapse load accurately. In general, the role of the discontinuities is crucial as their arrangement and distribution has a dramatic influence on the accuracy of the lower bound solution (Limit Analysis and Soil Plasticity, 1975). To ensure that the discontinuities are positioned in an optimal manner requires an error estimator and mesh adaptation strategy which accounts for the presence of stress singularities in the computed stress field.
Recently, Borges et al. (Int. J. Solids Struct. 2001; 38:1707–1720) presented an anisotropic mesh adaptation strategy for a mixed limit analysis formulation which used a directional error estimator. In the present work, this strategy has been tailored to suit a discontinuous lower bound formulation which employs the stresses and body forces as primary unknowns. The adapted mesh has a maximum density of discontinuities in the direction of the maximum rate of change in the stress field. For problems involving strong stress singularities in the boundary conditions (e.g. a strip footing), the automatic generation of discontinuity fans, centred on the singular points, has been implemented.
The efficiency of the proposed technique is demonstrated by analysis of two classical soil mechanics problems; namely the bearing capacity of a rigid strip footing and the collapse of a vertical cut. Copyright © 2005 John Wiley & Sons, Ltd.