Showing papers in "International Journal for Numerical Methods in Engineering in 2001"
TL;DR: In this paper, a strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integrations, where an integration constraint is introduced as a necessary condition for a linear exactness in the mesh-free Galerkin approximation.
Abstract: Domain integration by Gauss quadrature in the Galerkin mesh-free methods adds considerable complexity to solution procedures. Direct nodal integration, on the other hand, leads to a numerical instability due to under integration and vanishing derivatives of shape functions at the nodes. A strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integration. For convergence, an integration constraint (IC) is introduced as a necessary condition for a linear exactness in the mesh-free Galerkin approximation. The gradient matrix of strain smoothing is shown to satisfy IC using a divergence theorem. No numerical control parameter is involved in the proposed strain smoothing stabilization. The numerical results show that the accuracy and convergent rates in the mesh-free method with a direct nodal integration are improved considerably by the proposed stabilized conforming nodal integration method. It is also demonstrated that the Gauss integration method fails to meet IC in mesh-free discretization. For this reason the proposed method provides even better accuracy than Gauss integration for Galerkin mesh-free method as presented in several numerical examples. Copyright © 2001 John Wiley & Sons, Ltd.
1,209 citations
TL;DR: In this paper, a finite element analysis of delamination in laminated composites is addressed using interface elements and an interface damage law, where the principles of linear elastic fracture mechanics are indirectly used by equating the area underneath the traction/relative displacement curve to the critical energy release rate of the mode under examination.
Abstract: The finite element analysis of delamination in laminated composites is addressed using interface elements and an interface damage law. The principles of linear elastic fracture mechanics are indirectly used by equating, in the case of single-mode delamination, the area underneath the traction/relative displacement curve to the critical energy release rate of the mode under examination. For mixed-mode delamination an interaction model is used which can fulfil various fracture criteria proposed in the literature. It is then shown that the model can be recast in the framework of a more general damage mechanics theory. Numerical results are presented for the analyses of a double cantilever beam specimen and for a problem involving multiple delamination for which comparisons are made with experimental results. Issues related with the numerical solution of the non-linear problem of the delamination are discussed, such as the influence of the interface strength on the convergence properties and the final results, the optimal choice of the iterative matrix in the predictor and the number of integration points in the interface elements. Copyright © 2001 John Wiley & Sons, Ltd.
1,169 citations
TL;DR: In this article, a technique for modeling arbitrary discontinuities in finite elements is presented, in which both the signed distance function and its derivatives are considered, and a standard displacement Galerkin method is used for developing the discrete equations.
Abstract: A technique for modelling arbitrary discontinuities in finite elements is presented. Both discontinuities in the function and its derivatives are considered. Methods for intersecting and branching discontinuities are given. In all cases, the discontinuous approximation is constructed in terms of a signed distance functions, so level sets can be used to update the position of the discontinuities. A standard displacement Galerkin method is used for developing the discrete equations. Examples of the following applications are given: crack growth, a journal bearing, a non-bonded circular inclusion and a jointed rock mass. Copyright © 2001 John Wiley & Sons, Ltd.
1,091 citations
TL;DR: In this paper, a modified version of the minimum compliance topology optimization problem is studied, where the direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field by the mean of a convolution operator.
Abstract: In this article, a modified (‘filtered’) version of the minimum compliance topology optimization problem is studied. The direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field by the mean of a convolution operator. In this setting it is possible to establish the existence of solutions. Moreover, convergence of an approximation by means of finite elements can be obtained. This is illustrated through some numerical experiments. The ‘filtering’ technique is also shown to cope with two important numerical problems in topology optimization, checkerboards and mesh dependent designs. Copyright © 2001 John Wiley & Sons, Ltd.
920 citations
TL;DR: In this paper, a model which allows the introduction of displacements jumps to conventional finite elements is developed, where the path of the discontinuity is completely independent of the mesh structure.
Abstract: A model which allows the introduction of displacements jumps to conventional finite elements is developed. The path of the discontinuity is completely independent of the mesh structure. Unlike so-called ‘embedded discontinuity’ models, which are based on incompatible strain modes, there is no restriction on the type of underlying solid finite element that can be used and displacement jumps are continuous across element boundaries. Using finite element shape functions as partitions of unity, the displacement jump across a crack is represented by extra degrees of freedom at existing nodes. To model fracture in quasi-brittle heterogeneous materials, a cohesive crack model is used. Numerical simulations illustrate the ability of the method to objectively simulate fracture with unstructured meshes. Copyright © 2001 John Wiley & Sons, Ltd.
914 citations
TL;DR: An algorithm which couples the level set method (LSM) with the extended finite element method (X‐FEM) to model crack growth is described, which requires no remeshing as the crack progresses, making the algorithm very efficient.
Abstract: SUMMARYAn algorithm which couples the level set method (LSM) with the extended!nite element method(X-FEM) to model crack growth is described. The level set method is used to represent the cracklocation, including the location of crack tips. The extended!nite element method is used to computethe stress and displacement!elds necessary for determining the rate of crack growth. This combinedmethod requires no remeshing as the crack progresses, making the algorithm very e#cient. Thecombination of these methods has a tremendous potential for a wide range of applications. Numericalexamples are presented to demonstrate the accuracy of the combined methods. Copyright ? 2001John Wiley & Sons, Ltd. KEY WORDS : extended!nite elements method; level set method; crack growth 1. INTRODUCTIONIn this paper, we describe an algorithm where the level set method (LSM) is coupled withthe extended!nite element method (X-FEM) [1–3] to model crack growth. The LSM isa numerical scheme developed by Osher and Sethian [4] to model the motion of interfaces.In the LSM the interface is represented as the zero level set of a function of one higherdimension. The current formulation of the LSM has no provision for modelling free movingendpoints on curves or free moving edges on surfaces. A similar level set representation wasused in Reference [5] to model the evolution of a curve segment. However, unlike the methodpresented here, in Reference [5] the endpoints of the evolving curve segment remain!xed.We present an extension of the LSM for modelling the evolution of an open curve segmentand use this extension to model the growth of a fatigue crack.
747 citations
TL;DR: In this article, a point interpolation method (PIM) is presented for stress analysis for two-dimensional solids, where the problem domain is represented by properly scattered points.
Abstract: A point interpolation method (PIM) is presented for stress analysis for two-dimensional solids. In the PIM, the problem domain is represented by properly scattered points. A technique is proposed to construct polynomial interpolants with delta function property based only on a group of arbitrarily distributed points. The PIM equations are then derived using variational principles. In the PIM, the essential boundary conditions can be implemented with ease as in the conventional finite element methods. The present PIM has been coded in FORTRAN. The validity and efficiency of the present PIM formulation are demonstrated through example problems. It is found that the present PIM is very easy to implement, and very flexible for obtained displacements and stresses of desired accuracy in solids. As the elements are not used for meshing the problem domain, the present PIM opens new avenues to develop adaptive analysis codes for stress analysis in solids and structures. Copyright © 2001 John Wiley & Sons, Ltd.
669 citations
TL;DR: This paper presents a dual–primal formulation of the FETI‐2 concept that eliminates the need for that second set of Lagrange multipliers, and unifies all previously developed one‐level and two‐level FETi algorithms into a single dual‐primal FetI‐DP method.
Abstract: The FETI method and its two-level extension (FETI-2) are two numerically scalable domain decomposition methods with Lagrange multipliers for the iterative solution of second-order solid mechanics and fourth-order beam, plate and shell structural problems, respectively.The FETI-2 method distinguishes itself from the basic or one-level FETI method by a second set of Lagrange multipliers that are introduced at the subdomain cross-points to enforce at each iteration the exact continuity of a subset of the displacement field at these specific locations. In this paper, we present a dual–primal formulation of the FETI-2 concept that eliminates the need for that second set of Lagrange multipliers, and unifies all previously developed one-level and two-level FETI algorithms into a single dual–primal FETI-DP method. We show that this new FETI-DP method is numerically scalable for both second-order and fourth-order problems. We also show that it is more robust and more computationally efficient than existing FETI solvers, particularly when the number of subdomains and/or processors is very large. Copyright © 2001 John Wiley & Sons, Ltd.
628 citations
TL;DR: In this article, the use of topology optimization as a synthesis tool for the design of large-displacement compliant mechanisms is described, and an objective function for the synthesis of large displacement mechanisms is proposed together with a formulation for synthesis of path-generating compliant mechanisms.
Abstract: This paper describes the use of topology optimization as a synthesis tool for the design of large-displacement compliant mechanisms. An objective function for the synthesis of large-displacement mechanisms is proposed together with a formulation for synthesis of path-generating compliant mechanisms. The responses of the compliant mechanisms are modelled using a total Lagrangian finite element formulation, the sensitivity analysis is performed using the adjoint method and the optimization problem is solved using the method of moving asymptotes. Procedures to circumvent some numerical problems are discussed. Copyright © 2001 John Wiley & Sons, Ltd.
429 citations
TL;DR: In this paper, two modified fast Fourier transform methods were proposed to handle composites with high contrast (typically above 104) or infinite contrast (those containing voids or rigid inclusions or highly non-linear materials).
Abstract: A numerical method making use of fast Fourier transforms has been proposed in Moulinec and Suquet (1994, 1998) to investigate the effective properties of linear and non-linear composites. This method is based on an iterative scheme the rate of convergence of which is proportional to the contrast between the phases. Composites with high contrast (typically above 104) or infinite contrast (those containing voids or rigid inclusions or highly non-linear materials) cannot be handled by the method. This paper presents two modified schemes. The first one is an accelerated scheme for composites with high contrast which extends to elasticity a scheme initially proposed in Eyre and Milton (1999). Its rate of convergence varies as the square root of the contrast. The second scheme, adequate for composites with infinite contrast, is based on an augmented Lagrangian method. The resulting saddle-point problem involves three steps. The first step consists of solving a linear elastic problem, using the fast Fourier transform method. In the second step, a non-linear problem is solved at each individual point in the volume element. The third step consists of updating the Lagrange multiplier. Applications of this scheme to rigidly reinforced and to voided composites are shown. Copyright © 2001 John Wiley & Sons, Ltd.
398 citations
TL;DR: In this article, the convergence and accuracy of the K-L expansion are investigated by comparing the second-order statistics of the simulated random process with that of the target process, and it is shown that the factors affecting convergence are: (a) ratio of the length of the process over correlation parameter, (b) form of the covariance function, and (c) method of solving for the eigen-solutions of the function.
Abstract: A random process can be represented as a series expansion involving a complete set of deterministic functions with corresponding random coefficients Karhunen–Loeve (K–L) series expansion is based on the eigen-decomposition of the covariance function Its applicability as a simulation tool for both stationary and non-stationary Gaussian random processes is examined numerically in this paper The study is based on five common covariance models The convergence and accuracy of the K–L expansion are investigated by comparing the second-order statistics of the simulated random process with that of the target process It is shown that the factors affecting convergence are: (a) ratio of the length of the process over correlation parameter, (b) form of the covariance function, and (c) method of solving for the eigen-solutions of the covariance function (namely, analytical or numerical) Comparison with the established and commonly used spectral representation method is made K–L expansion has an edge over the spectral method for highly correlated processes For long stationary processes, the spectral method is generally more efficient as the K–L expansion method requires substantial computational effort to solve the integral equation The main advantage of the K–L expansion method is that it can be easily generalized to simulate non-stationary processes with little additional effort Copyright © 2001 John Wiley & Sons, Ltd
TL;DR: In this article, a non-Sibsonian interpolation scheme based on natural neighbours was proposed and its performance in a Galerkin method for the solution of elliptic partial dierential equations that arise in linear elasticity is studied.
Abstract: SUMMARY Natural neighbour co-ordinates (Sibson co-ordinates) is a well-known interpolation scheme for multivariate data tting and smoothing. The numerical implementation of natural neighbour co-ordinates in a Galerkin method is known as the natural element method (NEM). In the natural element method, natural neighbour co-ordinates are used to construct the trial and test functions. Recent studies on NEM have shown that natural neighbour co-ordinates, which are based on the Voronoi tessellation of a set of nodes, are an appealing choice to construct meshless interpolants for the solution of partial dierential equations. In Belikov et al. (Computational Mathematics and Mathematical Physics 1997; 37(1):9{15), a new interpolation scheme (non-Sibsonian interpolation) based on natural neighbours was proposed. In the present paper, the nonSibsonian interpolation scheme is reviewed and its performance in a Galerkin method for the solution of elliptic partial dierential equations that arise in linear elasticity is studied. A methodology to couple nite elements to NEM is also described. Two signicant advantages of the non-Sibson interpolant over the Sibson interpolant are revealed and numerically veried: the computational eciency of the non-Sibson algorithm in 2-dimensions, which is expected to carry over to 3-dimensions, and the ability to exactly impose essential boundary conditions on the boundaries of convex and non-convex domains. Copyright ? 2001 John Wiley & Sons, Ltd.
TL;DR: A general approach to the dimensional reduction of non‐linear finite element models of solid dynamics is presented, and it is shown how the problem can be formulated in an approximation (Ritz) basis of much smaller dimension.
Abstract: A general approach to the dimensional reduction of non-linear finite element models of solid dynamics is presented. For the Newmark implicit time-discretization, the computationally most expensive phase is the repeated solution of the system of linear equations for displacement increments. To deal with this, it is shown how the problem can be formulated in an approximation (Ritz) basis of much smaller dimension. Similarly, the explicit Newmark algorithm can be also written in a reduced-dimension basis, and the computation time savings in that case follow from an increase in the stable time step length.
In addition, the empirical eigenvectors are proposed as the basis in which to expand the incremental problem. This basis achieves approximation optimality by using computational data for the response of the full model in time to construct a reduced basis which reproduces the full system in a statistical sense. Because of this ‘global’ time viewpoint, the basis need not be updated as with reduced bases computed from a linearization of the full finite element model.
If the dynamics of a finite element model is expressed in terms of a small number of basis vectors, the asymptotic cost of the solution with the reduced model is lowered and optimal scalability of the computational algorithm with the size of the model is achieved. At the same time, numerical experiments indicate that by using reduced models, substantial savings can be achieved even in the pre-asymptotic range. Furthermore, the algorithm parallelizes very efficiently.
The method we present is expected to become a useful tool in applications requiring a large number of repeated non-linear solid dynamics simulations, such as convergence studies, design optimization, and design of controllers of mechanical systems.
TL;DR: It is shown that, within the framework of the Newmark family of numeric schemes, continuity of velocities at the interfaces enables the definition of an algorithm which is stable for all cases envisaged, and proposes to extend this to non-linear situations in the following cases.
Abstract: We present a method with domain decomposition to solve time-dependent non-linear problems. This method enables arbitrary numeric schemes of the Newmark family to be coupled with different time steps in each subdomain: this coupling is achieved by prescribing continuity of velocities at the interface. We are more specifically interested in the coupling of implicit/explicit numeric schemes taking into account material and geometric non-linearities. The interfaces are modelled using a dual Schur formulation where the Lagrange multipliers represent the interfacial forces. Unlike the continuous formulation, the discretized formulation of the dynamic problem is unable to verify simultaneously the continuity of displacements, velocities and accelerations at the interfaces. We show that, within the framework of the Newmark family of numeric schemes, continuity of velocities at the interfaces enables the definition of an algorithm which is stable for all cases envisaged. To prove this stability, we use an energy method, i.e. a global method over the whole time interval, in order to verify the algorithms properties. Then, we propose to extend this to non-linear situations in the following cases: implicit linear/explicit non-linear, explicit non-linear/explicit non-linear and implicit non-linear/explicit non-linear. Finally, we present some examples showing the feasibility of the method. Copyright © 2001 John Wiley & Sons, Ltd.
TL;DR: In this article, the subdivision shell elements of Cirak et al. were extended to the finite-deformation range, allowing for finite membrane and thickness stretching, as well as for large deflections and bending strains.
Abstract: We have extended the subdivision shell elements of Cirak et al. [18] to the finite-deformation range. The assumed finite-deformation kinematics allows for finite membrane and thickness stretching, as well as for large deflections and bending strains. The interpolation of the undeformed and deformed surfaces of the shell is accomplished through the use of subdivision surfaces. The resulting ‘subdivision elements’ are strictly C1-conforming, contain three nodes and one single quadrature point per element, and carry displacements at the nodes only. The versatility and good performance of the subdivision elements is demonstrated with the aid of a number of test cases, including the stretching of a tension strip; the inflation of a spherical shell under internal pressure; the bending and inflation of a circular plate under the action of uniform pressure; and the inflation of square and circular airbags. In particular, the airbag solutions, while exhibiting intricate folding patterns, appear to converge in certain salient features of the solution, which attests to the robustness of the method.
TL;DR: In this paper, a 2.5D finite/infinite element procedure for dealing with ground vibrations induced by moving loads is proposed, where the profile of the half-space is divided into a near field and a semi-infinite far field, and the near field containing loads and irregular structures is simulated by finite elements, while the far field covering the soils extending to infinity by the infinite elements with due account taken of the radiation effects for moving loads.
Abstract: The objective of this study is to propose a 2.5D finite/infinite element procedure for dealing with the ground vibrations induced by moving loads. Besides the two in-plane degrees of freedom (DOFs) per node conventionally used for plane strain elements, an extra DOF is introduced to account for the out-of-plane wave transmission. The profile of the half-space is divided into a near field and a semi-infinite far field. The near field containing loads and irregular structures is simulated by the finite elements, while the far field covering the soils extending to infinity by the infinite elements with due account taken of the radiation effects for moving loads. Enhanced by the automated mesh expansion procedure proposed previously by the writers, the far field impedances for all the lower frequencies are generated repetitively from the mesh created for the highest frequency considered. Finally, the accuracy of the proposed method is verified through comparison with a number of analytical solutions. Copyright © 2001 John Wiley & Sons, Ltd.
TL;DR: In this article, a cohesive formulation of fracture is taken as a basis for the simulation of processes of combined tension-shear damage and mixed-mode fracture in specimens subjected to dynamic loading, and the model accurately captures the experimentally observed fracture patterns and displacement fields, as well as crack paths and cracktip velocities, as a function of pre-crack geometry and loading conditions.
Abstract: A cohesive formulation of fracture is taken as a basis for the simulation of processes of combined tension-shear damage and mixed-mode fracture in specimens subjected to dynamic loading. Our three-dimensional finite-element calculations account explicitly for crack nucleation, microcracking, the development of macroscopic cracks and inertia. In particular, a tension-shear damage coupling arises as a direct consequence of slanted microcrack formation in the process zone. We validate the model against the three-point-bend concrete beam experiments of Guo et al. (International Journal of Solids and Structures 1995; 32(17/18):2951–2607), John (PhD Thesis, Northwestern University, 1988), and John and Shah (Journal of Structural Engineering 1990; 116(3):585–602) in which a pre-crack is shifted from the central cross-section, leading to asymmetric loading conditions and the development of a mixed-mode process zone. The model accurately captures the experimentally observed fracture patterns and displacement fields, as well as crack paths and crack-tip velocities, as a function of pre-crack geometry and loading conditions. In particular, it correctly accounts for the competition between crack-growth and nucleation mechanisms.
TL;DR: In this article, a finite point method, least square collocation meshless method, is proposed, where the equilibrium conditions are satisfied not only at the collocation points but also at the auxiliary points in a least square sense.
Abstract: A finite point method, least-squares collocation meshless method, is proposed. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted. Unlike the direct collocation method, the equilibrium conditions are satisfied not only at the collocation points but also at the auxiliary points in a least-squares sense. The moving least-squares interpolant is used to construct the trial functions. The computational effort required for the present method is in the same order as that required for the direct collocation, while the present method improves the accuracy of solution significantly. The proposed method does not require any mesh so that it is a truly meshless method. Three numerical examples are studied in detail, which show that the proposed method possesses high accuracy with low computational effort. Copyright © 2001 John Wiley & Sons, Ltd.
TL;DR: In this article, a microstructural model for the mechanical behavior of quasi-brittle materials is developed and verified for concrete and bone specimens, based on interface elements equipped with a constitutive law representing non-linear fracture, while continuum elements remain linear elastic.
Abstract: A microstructural model for the mechanical behaviour of quasi-brittle materials is developed and verified for concrete and bone specimens. The model is based on interface elements equipped with a constitutive law representing non-linear fracture, while continuum elements remain linear elastic. The interface constitutive model is implemented with a sub-stepping scheme. Non-linear geometric effects due to large displacements are included in the model by means of an incremental Lagrangian formulation, although strains in the continuum and relative displacements in the interfaces are assumed to remain small. An arc-length procedure is used to ensure convergence during the highly non-linear behaviour in the post-peak regime. Concrete and bone specimens are idealized as two-phase particle composites and are discretized into finite elements, including interface elements along the main potential crack paths. The numerical results in tension and compression are described and compared with experimental observations. The need of considering non-linear geometric effects in this type of calculations is also discussed. Copyright © 2001 John Wiley & Sons, Ltd.
TL;DR: A traction-based version of the micro-macro strategy is described and the influence of the numerical parameters as well as the performance of the approach are discussed.
Abstract: SUMMARY A new micro-macro computational strategy is proposed for the analysis of structures which are described up to the micro level, such as composite structures. The description of micro and macro quantities is performed on the interface arising from the decomposition of the structure into an assembly of substructures and interfaces. A traction-based version of the micro-macro strategy is described and the influence of the numerical parameters as well as the performance of the approach are discussed. Copyright c 2000 John Wiley & Sons, Ltd.
TL;DR: In this article, a 3D p-version with anisotropic Ansatz spaces is proposed to predict the structural behavior of 3D plates and shells with approximately the same amount of degrees of freedom as in the 2D case, but significantly more accurate due to the 3D model.
Abstract: In this paper we present an implementation of a three-dimensional p-version for structural problems of solids with almost arbitrarily curved surfaces. Applying the blending function method, complex structures can often be modelled by a few p-elements, being the basis for a higher order approximation. Numerical examples will demonstrate, that the p-version with anisotropic Ansatz spaces allows to predict the structural behaviour of three-dimensional plates and shells with approximately the same amount of degrees of freedom as in the two-dimensional case, yet significantly more accurate due to the three-dimensional model. Furthermore, it is advantageous to compute complex structures exclusively with three-dimensional discretizations as no special elements are needed to model the transition from dimensionally reduced formulations like plates or shells to fully three-dimensional solid elements. Using the p-version with anisotropic Ansatz spaces the whole structure can be efficiently discretized with solid elements, even if the aspect ratio of the elements becomes very large. Copyright © 2001 John Wiley Sons, Ltd.
TL;DR: This paper shows that the exact fast static structural reanalysis techniques introduced by researchers mostly for truss structures and some for frames and plate structures are variants of the well-known Sherman–Morrison and Woodbury (SMW) formulas for the update of the inverse of a matrix.
Abstract: Several exact fast static structural reanalysis techniques, introduced by researchers mostly for truss structures and some for frames and plate structures, are reviewed. Most utilize the property that the solution of a system of linear equations can be updated inexpensively when the matrix is changed by a low-rank increment. This paper shows that these methods are variants of the well-known Sherman–Morrison and Woodbury (SMW) formulas for the update of the inverse of a matrix. In addition, the paper extends the low-cost linear reanalysis in the spirit of the SMW formulas to some non-linear reanalysis problems. For a linear reanalysis, the extension reduces to the SMW formulas. Copyright © 2001 John Wiley & Sons, Ltd.
TL;DR: In this article, a finite cloud method combining collocation with a fixed kernel technique is presented as a true meshless technique for the numerical solution of partial differential equations, including elasticity, heat conduction, thermoelasticity, Stokes flow and piezoelectricity.
Abstract: We introduce fixed, moving and multiple fixed kernel techniques for the construction of interpolation functions over a scattered set of points. We show that for a particular choice of nodal volumes, the fixed, moving and multiple fixed kernel approaches are identical to the fixed, moving and multiple fixed least squares approaches. A finite cloud method, which combines collocation with a fixed kernel technique for the construction of interpolation functions, is presented as a true meshless technique for the numerical solution of partial differential equations. Numerical results are presented for several one-and two-dimensional problems, including examples from elasticity, heat conduction, thermoelasticity, Stokes flow and piezoelectricity. Copyright © 2001 John Wiley & Sons, Ltd.
TL;DR: In this paper, a 3D surface triangulation representing the vessel walls is generated using a direct tessellation of the boundary voxels, which is then smoothed and the quality of the resulting surface is improved.
Abstract: The successful application of computational modelling of blood ow for the planning of surgical and interventional procedures to treat cardiovascular diseases strongly depends on the rapid construction of anatomical models. The large individual variability of the human vasculature and the strong dependence of blood ow characteristics on the vessel geometry require modelling on a patient-speci c basis. Various image processing and geometrical modelling techniques are integrated for the rapid construction of geometrical surface models of arteries starting from medical images. These discretely de ned surfaces are then used to generate anatomically accurate nite element grids for hemodynamic simulations. The proposed methodology operates directly in 3D and consists of three stages. In the rst stage, the images are ltered to reduce noise and segmented using a region-growing algorithm in order to obtain a properly de ned boundary of the arterial lumen walls. In the second stage, a surface triangulation representing the vessel walls is generated using a direct tessellation of the boundary voxels. This surface is then smoothed and the quality of the resulting triangulation is improved. Finally, in the third stage, the triangulation is subdivided into so-called discrete surface patches for surface gridding, the desired element size distribution is de ned and the nite element grid generated. Copyright ? 2001 John Wiley & Sons, Ltd.
TL;DR: In this article, a framework for modeling an elastic continuum using a grillage of beam-like structural elements derived from discrete element concepts is described, and the beam element properties are derived in detail and implemented in a structural analysis code for validation against classical two-dimensional plane elasticity solutions.
Abstract: A framework is described for modelling an elastic continuum using a grillage of beam-like structural elements derived from discrete element concepts. The beam element properties are derived in detail and implemented in a structural analysis code for validation against classical two-dimensional plane elasticity solutions. The framework offers the possibility of modelling the onset and propagation of fracture in materials that are initially continuous, without the need for specialized elements or remeshing in the context of traditional finite elements. Copyright © 2001 John Wiley & Sons, Ltd.
TL;DR: In this article, a new method for the simulation of particulate flows, based on the extended finite element method (X-FEM), is described, where particle surfaces need not conform to the finite element boundaries, so that moving particles can be simulated without remeshing.
Abstract: A new method for the simulation of particulate flows, based on the extended finite element method (X-FEM), is described. In this method, the particle surfaces need not conform to the finite element boundaries, so that moving particles can be simulated without remeshing. The near field form of the fluid flow about each particle is built into the finite element basis using a partition of unity enrichment, allowing the simple enforcement of boundary conditions and improved accuracy over other methods on a coarse mesh. We present a weak form of the equations of motion useful for the simulation of freely moving particles, and solve example problems for particles with prescribed and unknown velocities. Copyright © 2001 John Wiley & Sons, Ltd.
TL;DR: In this paper, the authors investigate the behavior of finite elements with embedded displacement discontinuities that represent cracks and propose a new concept of a model with transition from a smeared to an embedded (discrete) crack.
Abstract: The paper investigates the behaviour of finite elements with embedded displacement discontinuities that represent cracks. Examples of fracture simulations show that an incorrect separation of nodes due to a locally mispredicted crack direction leads to a severe stress locking, which produces spurious secondary cracking. As a possible remedy the paper advocates a new concept of a model with transition from a smeared to an embedded (discrete) crack. An additional improvement is achieved by reformulating the smeared part as non-local. Various criteria for placing the discontinuity are compared, and the optimal technique is identified. Remarkable insensitivity of the resulting model to mesh-induced directional bias is demonstrated. It is shown that the transition to an explicit description of a widely opening crack as a displacement discontinuity improves the behaviour of the combined model and remedies certain pathologies exhibited by regularized continuum models. Copyright © 2001 John Wiley & Sons, Ltd.
TL;DR: In this paper, the authors describe a triangular element with an embedded displacement discontinuity that represents a crack, and the constitutive model is formulated within the framework of damage theory, with crack closure effects and friction on the crack faces taken into account.
Abstract: The recently emerged idea of enriching standard finite element interpolations by strain or displacement discontinuities has triggered the development of powerful techniques that allow efficient modelling of regions with highly localized strains, e.g. of fracture zones in concrete, or shear bands in metals or soils. The present paper describes a triangular element with an embedded displacement discontinuity that represents a crack. The constitutive model is formulated within the framework of damage theory, with crack closure effects and friction on the crack faces taken into account. Numerical aspects of the implementation are discussed. In a companion paper, the embedded crack approach is combined with the more traditional smeared crack approach. Copyright © 2001 John Wiley & Sons, Ltd.
TL;DR: In this paper, one-step implicit integration algorithms for non-linear elastodynamics are developed, where the discretization process rests on Galerkin methods in space and time.
Abstract: In the present paper one-step implicit integration algorithms for non-linear elastodynamics are developed. The discretization process rests on Galerkin methods in space and time. In particular, the continuous Galerkin method applied to the Hamiltonian formulation of semidiscrete non-linear elastodynamics lies at the heart of the time-stepping schemes. Algorithmic conservation of energy and angular momentum are shown to be closely related to quadrature formulas that are required for the calculation of time integrals. We newly introduce the ‘assumed strain method in time’ which enables the design of energy–momentum conserving schemes and which can be interpreted as temporal counterpart of the well-established assumed strain method for finite elements in space. The numerical examples deal with quasi-rigid motion as well as large-strain motion. Copyright © 2001 John Wiley & Sons, Ltd.