Showing papers on "Smoothed finite element method published in 2002"
Book•
29 Jul 2002TL;DR: In this paper, Galerkin et al. defined mesh-free methods for shape function construction, including the use of mesh-less local Petrov-Galerkin methods.
Abstract: Preliminaries Physical Problems in Engineering Solid Mechanics: A Fundamental Engineering Problem Numerical Techniques: Practical Solution Tools Defining Meshfree Methods Need for Meshfree Methods The Ideas of Meshfree Methods Basic Techniques for Meshfree Methods Outline of the Book Some Notations and Default Conventions Remarks Meshfree Shape Function Construction Basic Issues for Shape Function Construction Smoothed Particle Hydrodynamics Approach Reproducing Kernel Particle Method Moving Least Squares Approximation Point Interpolation Method Radial PIM Radial PIM with Polynomial Reproduction Weighted Least Square (WLS) Approximation Polynomial PIM with Rotational Coordinate Transformation Comparison Study via Examples Compatibility Issues: An Analysis Other Methods Function Spaces for Meshfree Methods Function Spaces Useful Spaces in Weak Formulation G Spaces: Definition G1h Spaces: Basic Properties Error Estimation Concluding Remarks Strain Field Construction Why Construct Strain Field? Historical Notes How to Construct? Admissible Conditions for Constructed Strain Fields Strain Construction Techniques Concluding Remarks Weak and Weakened Weak Formulations Introduction to Strong and Weak Forms Weighted Residual Method A Weak Formulation: Galerkin A Weakened Weak Formulation: GS-Galerkin The Hu-Washizu Principle The Hellinger-Reissner Principle The Modified Hellinger-Reissner Principle Single-Field Hellinger-Reissner Principle The Principle of Minimum Complementary Energy The Principle of Minimum Potential Energy Hamilton's Principle Hamilton's Principle with Constraints Galerkin Weak Form Galerkin Weak Form with Constraints A Weakened Weak Formulation: SC-Galerkin Parameterized Mixed Weak Form Concluding Remarks Element Free Galerkin Method EFG Formulation with Lagrange Multipliers EFG with Penalty Method Summary Meshless Local Petrov-Galerkin Method MLPG Formulation MLPG for Dynamic Problems Concluding Remarks Point Interpolation Methods Node-Based Smoothed Point Interpolation Method (NS-PIM) NS-PIM Using Radial Basis Functions (NS-RPIM) Upper Bound Properties of NS-PIM and NS-RPIM Edge-Based Smoothed Point Interpolation Methods (ES-PIMs) A Combined ES/NS Point Interpolation Methods (ES/NS-PIM) Strain-Constructed Point Interpolation Method (SC-PIM) A Comparison Study Summary Meshfree Methods for Fluid Dynamics Problem Introduction Navier-Stokes Equations Smoothed Particle Hydrodynamics Method Gradient Smoothing Method (GSM) Adaptive Gradient Smoothing Method (A-GSM) A Discussion on GSM for Incompressible Flows Other Improvements on GSM Meshfree Methods for Beams PIM Shape Function for Thin Beams Strong Form Equations Weak Formulation: Galerkin Formulation A Weakened Weak Formulation: GS-Galerkin Three Models Formulation for NS-PIM for Thin Beams Formulation for Dynamic Problems Numerical Examples for Static Analysis Numerical Examples: Upper Bound Solution Numerical Examples for Free Vibration Analysis Concluding Remarks Meshfree Methods for Plates Mechanics for Plates EFG Method for Thin Plates EFG Method for Thin Composite Laminates EFG Method for Thick Plates ES-PIM for Plates Meshfree Methods for Shells EFG Method for Spatial Thin Shells EFG Method for Thick Shells ES-PIM for Thick Shells Summary Boundary Meshfree Methods RPIM Using Polynomial Basis RPIM Using Radial Function Basis Remarks Meshfree Methods Coupled with Other Methods Coupled EFG/BEM Coupled EFG and Hybrid BEM Remarks Meshfree Methods for Adaptive Analysis Triangular Mesh and Integration Cells Node Numbering: A Simple Approach Bucket Algorithm for Node Searching Relay Model for Domains with Irregular Boundaries Techniques for Adaptive Analysis Concluding Remarks MFree2D(c) Overview Techniques Used in MFree2D Preprocessing in MFree2D Postprocessing in MFree2D Index References appear at the end of each chapter.
1,768 citations
TL;DR: A survey of mesh-free and particle methods and their applications in applied mechanics can be found in this article, where the emphasis is placed on simulations of finite deformations, fracture, strain localization of solids; incompressible as well as compressible flows; and applications of multiscale methods and nano-scale mechanics.
Abstract: Recent developments of meshfree and particle methods and their applications in applied mechanics are surveyed. Three major methodologies have been reviewed. First, smoothed particle hydrodynamics ~SPH! is discussed as a representative of a non-local kernel, strong form collocation approach. Second, mesh-free Galerkin methods, which have been an active research area in recent years, are reviewed. Third, some applications of molecular dynamics ~MD! in applied mechanics are discussed. The emphases of this survey are placed on simulations of finite deformations, fracture, strain localization of solids; incompressible as well as compressible flows; and applications of multiscale methods and nano-scale mechanics. This review article includes 397 references. @DOI: 10.1115/1.1431547#
833 citations
TL;DR: In this article, an enriched finite element method for the multi-dimensional Stefan problems is presented, where the standard finite element basis is enriched with a discontinuity in the derivative of the temperature normal to the interface.
Abstract: An enriched finite element method for the multi-dimensional Stefan problems is presented. In this method the standard finite element basis is enriched with a discontinuity in the derivative of the temperature normal to the interface. The approximation can then represent the phase interface and the associated discontinuity in the temperature gradient within an element. The phase interface can be evolved without re-meshing or the use of artificial heat capacity techniques. The interface is described by a level set function that is updated by a stabilized finite element scheme. Several examples are solved by the proposed method to demonstrate the accuracy and robustness of the method. Copyright © 2001 John Wiley & Sons, Ltd.
312 citations
TL;DR: In this article, the implicit surfaces are defined by radial basis functions and internal features such as material interfaces, sliding interfaces and cracks are treated by enrichment techniques developed in the extended finite element method.
Abstract: A paradigm is developed for generating structured finite element models from solid models by means of implicit surface definitions. The implicit surfaces are defined by radial basis functions. Internal features, such as material interfaces, sliding interfaces and cracks are treated by enrichment techniques developed in the extended finite element method. Methods for integrating the weak form for such models are proposed. These methods simplify the generation of finite element models. Results presented for several examples show that the accuracy of this method is comparable to standard unstructured finite element methods.
255 citations
TL;DR: In this paper, a 3D co-rotational beam element for the analysis of frame structures is proposed for the buckling and post-buckling analysis of the frame structures.
186 citations
145 citations
TL;DR: In this article, an object-oriented finite element approach to microstructure-based modeling is provided with two examples: SiC particle-reinforced Al matrix composites and double-cemented WC particle-resinforced Co-matrix composites.
118 citations
TL;DR: In this paper, a displacement and rotation based finite element method for the solution of boundary value problems in linear isotropic Cosserat elasticity is proposed, and the field equations for the problem of plane strain are derived from the three-dimensional theory and expressed in oblique rectilinear coordinates.
101 citations
TL;DR: In this paper, a new finite element procedure for the solution of the incompressible Navier-Stokes equations is presented, where the velocities are interpolated using the flow conditions over the elements and the pressure is interpolated to satisfy the infsup condition for incompressibility analysis.
86 citations
TL;DR: In this article, the authors compared several methods used to predict the elastic properties of woven fabric composite materials and presented a new one, which is a simplified version of the method of cells for woven composites.
75 citations
TL;DR: In this article, a model for the calculation of S/N-curves is presented, which takes into account the stress gradient to define the local stress limit, the number of cycles at the fatigue limit and the slope.
TL;DR: Least-squares spectral element methods are based on two important and successful numerical methods: spectral/hp element methods and least squares finite element methods as mentioned in this paper, which combine the generality of finite element method with the accuracy of the spectral methods and also have the theoretical and computational advantages of the least square methods, making them a competitive candidate for the solution of large-scale problems arising in scientific computing.
TL;DR: In this paper, a micro-structural mechanics approach is adopted to model the development of fracture in concrete, where the continuum is assumed to have an underlying micro-structure of lattice type, which has been demonstrated as a useful description for concrete fracture.
TL;DR: In this paper, an eight-node brick element is proposed to adjust to the physical situation automatically in the sense that the stabilizing forces are chosen to be proportional to the mean tangent modulus of the material across the thickness.
TL;DR: In this article, a numerical method for continuum-based shape design sensitivity analysis and optimization using the mesh-free method is proposed, where the reproducing kernel particle method is used for domain discretization in conjunction with the Gauss integration method.
Abstract: A numerical method for continuum-based shape design sensitivity analysis and optimization using the meshfree method is proposed. The reproducing kernel particle method is used for domain discretization in conjunction with the Gauss integration method. Special features of the meshfree method from a sensitivity analysis viewpoint are discussed, including the treatment of essential boundary conditions, and the dependence of the shape function on the design variation. It is shown that the mesh distortion that exists in the finite element–based design approach is effectively resolved for large shape changing design problems through 2-D and 3-D numerical examples. The number of design iterations is reduced because of the accurate sensitivity information.
TL;DR: A new mathematical and computational framework for boundary value problems described by self-adjoint differential operators is presented and a new criterion is proposed for establishing the minimally conforming spaces which is more in agreement with the physics and mathematics of the BVP.
Abstract: In this paper a new mathematical and computational framework for boundary value problems described by self-adjoint differential operators is presented. In this framework, numerically computed solutions, when converged, possess the same degree of global smoothness in terms of differentiability up to any desired order as the theoretical solutions. This is accomplished using spaces Ĥk,p that contain basis functions of degree p and order k - 1 (or the order of the space k). It is shown that the order of space k is an intrinsically important independent parameter in all finite element computational processes in addition to the discretization characteristic length h and the degree of basis functions p when the theoretical solutions are analytic. Thus, in all finite element computations, all quantities of interest (e.g., quadratic functional, error or residual functional, norms and seminorms, error norms, etc.) are dependent on h, p as well as k. Therefore, for fixed h and p, convergence of the finite element process can also be investigated by changing k, hence k-convergence and thus the k-version of finite element method. With h, p, and k as three independent parameters influencing all finite element processes, we now have k, hk, pk, and hpk versions of finite element methods. The issue of minimally conforming finite element spaces is reexamined and it is demonstrated that the definition of currently believed minimally conforming space which permit weak convergence of the highest-order derivatives of the dependent variables appearing in the bilinear form is not justifiable mathematically or from physics view point. A new criterion is proposed for establishing the minimally conforming spaces which is more in agreement with the physics and mathematics of the BVP. Significant features and merits of the proposed mathematical and computational framework are presented, discussed, illustrated, and substantiated mathematically as well as numerically with the Galerkin and least-squares finite element formulations for self-adjoint boundary-value problems.
TL;DR: A novel procedure for implementing the essential boundary condition using the hierarchical enrichment method is presented, which produces results that more closely match experimental and analytical results for a flow past a cylinder problem than does either the finite-element method or other meshfree methods that require matrix inversion for the application of essential boundary conditions.
TL;DR: In this paper, a hybrid method based on the combination of conventional finite element method and scaled boundary finite element (SBFEM) method is proposed for railway structural components taking the unbounded media into account.
Book•
12 Mar 2002
TL;DR: The basic Equations of Non-Newtonian Fluid Mechanics are presented, with examples of models based on Simplified Domain Geometry, and some Tensor Calculus Relations are described.
Abstract: 1. The Basic Equations of Non-Newtonian Fluid Mechanics. 1.1 Governing Equations of Non-Newtonian Fluid Mechanics 1.2 Classification of Inelastic Time-Independent Fluids 1.3 Inelatic Time-Dependent Fluids 1.4 Viscoelastic Fluids 2. Weighted Residual Finite Element Methods - An Outline. 2.1 Finite Element Approximation 2.2 Numerical Solutions of Differential Equations by the Weighted Residual Method 3. Finite Element Modelling of Polymeric Flow Processes. 3.1 Solution of the Equations of Continuity and Motion 3.2 Modelling of Viscoelastic Flow 3.3 Solution of the Energy Equation 3.4 Imposition of Boundary Conditions in Polymeric Processing Models 3.5 Free Surface and Moving Boundary Problems 4. Working Equations of the Finite Element Schemes. 4.1 Modelling of Steady State Stokes Flow of a Generalized Newtonian Fluid 4.2 Variations of Viscosity 4.3 Modelling of Steady State Viscometric Flow - Working Equations of the Continuous Penalty Scheme in Cartesian Coordinate Systems 4.4 Modelling of Thermal Energy Balance 4.5 Modelling of Transient Stokes Flow of Generalized Newtonian and Non-Newtonian Fluids 5. Rational Approximations and Illustrative Examples. 5.1 Models based on Simplified Domain Geometry 5.2 Models based on Simplified Governing Equations 5.3 Models representing Selected Segments of a Large Domain 5.4 Models based on Decoupled Flow Equations - Simulation of the Flow inside a Cone-and-Plate Rheometer 5.5 Models based on Thin Layer Approximation 5.6 Stiffness Analysis of Solid Polymeric Materials 6. Finite Element Software - Main Components. 6.1 General Consideration to Finite Element Mesh Generation 6.2 Main Components of Finite Element Processor Programs 6.3 Numerical Solution of the Global Systems of Algebraic Equations 6.4 Solutions Algorithms based on the Gaussian Elimination Method 6.5 Computation Errors 7. Computer Simulations - Finite Element Program. 7.1 Program Structure and Algorithm 7.2 Program Specifications 7.3 Input Data File 7.4 Extension of PPVN.f to Axisymmetric Problems 7.5 Circulatory Flow in a Rectangular Domain 7.6 Source Code of PPVN.f References 8. Appendix - Summary of Vector and Tensor Analysis. 8.1 Vector Algebra 8.2 Some Vector Calculua Relations 8.3 Tensor Algebra 8.4 Some Tensor Calculus Relations Author Index. Subject Index.
Book•
01 Jan 2002
TL;DR: In this article, a finite element analysis of scalar field problems is described, and a patch test solution of linear systems of equations is proposed. But the patch test is based on a linear system of equations, not on the integration of finite elements.
Abstract: Governing equations and their approximate solution computer storage and manipulation of numbers the finite difference method the method of weighted residuals variational methods introduction to the finite element method development of finite element equations steps in performing finite element analysis element interpolation functions element mapping finite element analysis of scalar field problems finite element analysis in linear elastostatics implementation, modelling, and related issues. Appendices: mathematical potpourri matrices and linear algebra some notes on heat flow local and natural coordinate systems the patch test solution of linear systems of equations notes on integration of finite elements.
TL;DR: In this paper, a composite tetrahedral element consisting of an ensemble of 12 four-node linear Tetrahedral elements, coupled with a linear assumed deformation defined over the entire domain of the composite element is designed to have well-defined lumped masses and contact tractions in dynamic contact problems.
Abstract: We develop and analyse a composite ‘CT3D’ tetrahedral element consisting of an ensemble of 12 four-node linear tetrahedral elements, coupled to a linear assumed deformation defined over the entire domain of the composite element. The element is designed to have well-defined lumped masses and contact tractions in dynamic contact problems while at the same time, minimizing the number of volume constraints per element. The relation between displacements and deformations is enforced weakly by recourse to the Hu–Washizu principle. The element arrays are formulated in accordance with the ‘assumed-strain’ prescription. The formulation of the element accounts for fully non-linear kinematics. Integrals over the domain of the element are computed by a five-point quadrature rule. The element passes the patch test in arbitrarily distorted configurations. Our numerical tests demonstrate that CT element has been found to possess a convergence rate comparable to those of linear simplicial elements, and that these convergence rates are maintained as the near-incompressible limit is approached. We have also verified that the element satisfies the Babuska–Brezzi condition for a regular mesh configuration. These tests suggest that the CT3D element can indeed be used reliably in calculations involving near-incompressible behaviour which arises, e.g., in the presence of unconfined plastic flow.
TL;DR: In this article, a new transition element for modeling solid-to-beam and plate-tobeam connections is presented, which is based upon the hybrid stress method and the resulting transition element is hypostatic.
01 Jan 2002
TL;DR: A 2-D elasticity problem with curved boundary is used to clearly illustrate the influence of the mesh shape geometric approximation order and shape representation method on the accuracy of finite element solution in a p-version analysis.
Abstract: Higher order (p-version) finite element methods have been shown to be clearly superior to low order finite element methods when properly applied. However, realization of the full benefits of p-version finite elements for general 3-D geometries requires the careful construction and control of the mesh. A 2-D elasticity problem with curved boundary is used to clearly illustrate the influence of the mesh shape geometric approximation order and shape representation method on the accuracy of finite element solution in a p-version analysis. Consideration is then given to a new approach for the representation of mesh geometry for p-version meshes and to the automatic generation of p-version meshes.
TL;DR: The convergence analysis of the multiscale finite element method is presented, designed to efficiently capture the large scale behavior of the solution without resolving all small scale features, and is naturally adapted to massively parallel computers.
Abstract: In this paper, we study a multiscale finite element method for solving a class of elliptic problems with finite number of well separated scales. The method is designed to efficiently capture the large scale behavior of the solution without resolving all small scale features. This is accomplished by constructing the multiscale finite element base functions that are adaptive to the local property of the differential operator. The construction of the base functions is fully decoupled from element to element; thus the method is perfectly parallel and is naturally adapted to massively parallel computers. We present the convergence analysis of the method along with the results of our numerical experiments. Some generalizations of the multiscale finite element method are also discussed.
TL;DR: In this article, a semi-analytical finite element method was proposed for elastic shells conveying fluids, where the structural equations are based on the shell element proposed by Ramasamy and Ganesan [Comput Struct 70 (1998) 363] while the fluid model is based on velocity potential.
TL;DR: In this article, a new numerical technique combining the finite element method and strip element method is presented to study the scattering of elastic waves by a crack and/or inclusion in an anisotropic laminate.
Abstract: A new numerical technique combining the finite element method and strip element method is presented to study the scattering of elastic waves by a crack and/or inclusion in an anisotropic laminate. Two-dimensional problems in the frequency domain are studied. The interior part of the plate containing cracks or inclusions is modeled by the conventional finite element method. The exterior parts of the plate are modeled by the strip element method that can deal problems of infinite domain in a rigorous and efficient manner. Numerical examples are presented to validate the proposed technique and demonstrate the efficiency of the proposed method. It is found that, by combining the finite element method and the strip element method, the shortcomings of both methods are avoided and their advantages are maintained. This technique is efficient for wave scattering in anisotropic laminates containing inclusions and/or cracks of arbitrary shape.
TL;DR: In this article, the fundamental concepts behind the moving particle finite element method, which combines salient features of finite element and mesh-free methods, are presented and illustrated via two-dimensional linear elastic problems.
Abstract: This paper presents the fundamental concepts behind the moving particle finite element method, which combines salient features of finite element and meshfree methods. The proposed method alleviates certain problems that plague meshfree techniques, such as essential boundary condition enforcement and the use of a separate background mesh to integrate the weak form. The method is illustrated via two-dimensional linear elastic problems. Numerical examples are provided to show the capability of the method in benchmark problems. Copyright © 2001 John Wiley & Sons, Ltd.
TL;DR: In this article, a new class of solution methods based on a short-characteristics approach embedded in the finite element framework for the solution of the radiation transport equation is developed and tested.
TL;DR: In this paper, a combined experimental and numerical investigation is described for powder compaction processes, which utilises material properties derived from experimental work as input for inelastic analysis of a finite element model.