Showing papers on "Finite element method published in 1992"
TL;DR: The diffuse element method (DEM) as discussed by the authors is a generalization of the finite element approximation (FEM) method, which is used for generating smooth approximations of functions known at given sets of points and for accurately estimating their derivatives.
Abstract: This paper describes the new “diffuse approximation” method, which may be presented as a generalization of the widely used “finite element approximation” method. It removes some of the limitations of the finite element approximation related to the regularity of approximated functions, and to mesh generation requirements. The diffuse approximation method may be used for generating smooth approximations of functions known at given sets of points and for accurately estimating their derivatives. It is useful as well for solving partial differential equations, leading to the so called “diffuse element method” (DEM), which presents several advantages compared to the “finite element method” (FEM), specially for evaluating the derivatives of the unknown functions.
1,951 citations
TL;DR: The basic explicit finite element and finite difference methods that are currently used to solve transient, large deformation problems in solid mechanics are reviewed.
Abstract: Explicit finite element and finite difference methods are used to solve a wide variety of transient problems in industry and academia. Unfortunately, explicit methods are rarely discussed in detail in finite element text books. This paper reviews the basic explicit finite element and finite difference methods that are currently used to solve transient, large deformation problems in solid mechanics. A special emphasis has been placed on documenting methods that have not been previously published in journals.
1,218 citations
TL;DR: In this paper, a finite element formulation based on stabilized bilinear and linear equal-order-interpolation velocity-pressure elements is presented for computation of steady and unsteady incompressible flows.
Abstract: Finite element formulations based on stabilized bilinear and linear equal-order-interpolation velocity-pressure elements are presented for computation of steady and unsteady incompressible flows. The stabilization procedure involves a slightly modified Galerkin/least-squares formulation of the steady-state equations. The pressure field is interpolated by continuous functions for both the quadrilateral and triangular elements used. These elements are employed in conjunction with the one-step and multi-step time integration of the Navier-Stokes equations. The three test cases chosen for the performance evaluation of these formulations are the standing vortex problem, the lid-driven cavity flow at Reynolds number 400, and flow past a cylinder at Reynolds number 100.
838 citations
TL;DR: In this paper, a new strategy based on the stabilized space-time finite element formulation is proposed for computations involving moving boundaries and interfaces, where the deformation of the spatial domain with respect to time is taken into account automatically.
Abstract: A new strategy based on the stabilized space-time finite element formulation is proposed for computations involving moving boundaries and interfaces. In the deforming-spatial-domain/space-time (DSD/ST) procedure the variational formulation of a problem is written over its space-time domain, and therefore the deformation of the spatial domain with respect to time is taken into account automatically. Because the space-time mesh is generated over the space-time domain of the problem, within each time step, the boundary (or interface) nodes move with the boundary (or interface). Whether the motion of the boundary is specified or not, the strategy is nearly the same. If the motion of the boundary is unknown, then the boundary nodes move as defined by the other unknowns at the boundary (such as the velocity or the displacement). At the end of each time step a new spatial mesh covers the new spatial domain. For computational feasibility, the finite element interpolation functions are chosen to be discontinuous in time, and the fully discretized equations are solved one space-time slab at a time.
833 citations
TL;DR: In this paper, a framework is presented within which the augmented Lagrangians is readily applied to problems involving contact with friction, which is well-suited to finite element implementation, and a set of numerical examples is presented in which the utility of the method is demonstrated even in the presence of finite deformations and inelasticity.
828 citations
TL;DR: In this paper, a class of assumed strain mixed finite element methods for fully nonlinear problems in solid mechanics is presented which, when restricted to geometrically linear problems, encompasses the classical method of incompatible modes as a particular case.
Abstract: A class of ‘assumed strain’ mixed finite element methods for fully non-linear problems in solid mechanics is presented which, when restricted to geometrically linear problems, encompasses the classical method of incompatible modes as a particular case. The method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part, formulated in the context of a three-field variational formulation. The resulting class of mixed methods provides a possible extension to the non-linear regime of well-known incompatible mode formulations. In addition, this class of methods includes non-linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements. The good performance of the proposed methodology is illustrated in a number of simulations including 2-D, 3-D and axisymmetric finite deformation problems in elasticity and elastoplasticity. Remarkably, these methods appear to be specially well suited for problems involving localization of the deformation, as illustrated in several numerical examples.
763 citations
TL;DR: Stabilized methods are proposed and analyzed for a linearized form of the incompressible Navier-Stokes equations, allowing any combination of velocity and continuous pressure interpolations and generalizing previous works restricted to low-order interpolations.
Abstract: Stabilized methods are proposed and analyzed for a linearized form of the incompressible Navier-Stokes equations. The methods are extended and tested for the nonlinear model. The methods combine the good features of stabilized methods already proposed for the Stokes flow and for advective-diffusive flows. These methods also generalize previous works restricted to low-order interpolations, thus allowing any combination of velocity and continuous pressure interpolations. A careful design of the stability parameters is suggested which considerably simplifies these generalizations.
732 citations
TL;DR: In this paper, the deforming spatial-domain/spacetime (DSD/ST) approach is used for finite element computational strategies for free-surface flows, two-liquid flows, and flows with drifting cylinders.
Abstract: New finite element computational strategies for free-surface flows, two-liquid flows, and flows with drifting cylinders are presented. These strategies are based on the deforming spatial-domain/spacetime (DSD/ST) procedure. In the DSD/ST approach, the stabilized variational formulations for these types of flow problem are written over their space-time domains. One of the important features of the approach is that it enables one to circumvent the difficulty involved in remeshing every time step and thus reduces the projection errors introduced by such frequent remeshings. Computations are performed for various test problems mainly for the purpose of demonstrating the computational capability developed for this class of problems. In some of the test cases, such as the liquid drop problem, surface tension is taken into account. For flows involving drifting cylinders, the mesh moving and remeshing schemes proposed are convenient and reduce the frequency of remeshing.
648 citations
TL;DR: In this article, a review of stabilized finite element methods for the Navier-Stokes problem is presented, and a global convergence analysis is presented and numerical experiments are performed, and the design of the stability parameter is confirmed to be a crucial ingredient for simulating the advective-diffusive model, and improved possibilities are suggested.
Abstract: Some stabilized finite element methods for the Stokes problem are reviewed. The Douglas-Wang approach confirms better stability features for high order interpolations. Next, the advective-diffusive model is approximated in the light of various stabilized methods, a global convergence analysis is presented and numerical experiments are performed. Biquadratic elements produce better numerical results under all stabilized methods examined. The design of the stability parameter is confirmed to be a crucial ingredient for simulating the advective-diffusive model, and some improved possibilities are suggested. Combinations of these methodologies are given in the conclusions and will be examined in detail in the sequel to this paper applied to the incompressible Navier-Stokes equations.
644 citations
TL;DR: In this paper, a complete formulation of a model of coupled associative thermoplasticity at finite strains is presented, addressing in detail the numerical analysis aspects involved in its finite element implementation, and assessing the performance of the proposed mechanical and finite element models in a comprehensive set of numerical simulations.
Abstract: This paper presents a complete formulation of a model of coupled associative thermoplasticity at finite strains, addresses in detail the numerical analysis aspects involved in its finite element implementation, and assesses the performance of the proposed mechanical and finite element models in a comprehensive set of numerical simulations. On the thermomechanical side, novel aspects of the proposed model of thermoplasticity are (1) the explicit characterization of the plastic (configurational) entropy as an independent internal variable, (2) a thermomechanical extension of the principle of maximum dissipation consistent with the multiplicative decomposition of the deformation gradient, and (3) the exploitation of this extended principle in the formulation of an associative flow which characterizes the evolution of the plastic entropy in terms of the change of the flow criterion with respect to temperature. On the numerical analysis side, salient features of the proposed approach are (4) a new global product formula algorithm constructed via an operator split of the nonlinear initial value problem, which leads to a two-step solution procedure, (5) a unified class of local return mapping algorithms which preserves exactly the incompressibility constraint on the plastic flow and reduces to the classical radial return method for isothermal J 2 - flow theory, and (6) the formulation of a mixed finite element method in terms of the elastic entropy and the temperature field which circumvents well-known difficulties associated with the incompressibility constraint on the plastic flow. The exact linearization of both the product formula algorithm and an alternative simulataneous solution scheme for the coupled thermomechanical problem is given in two appendices.
630 citations
Book•
01 Aug 1992
TL;DR: The DtN method for time-harmonic wave problems was proposed in this paper, where it was applied to beam and shell problems, as well as to time dependent problems.
Abstract: 1. Introduction and overview. 2. Boundary integral and boundary element methods. 3. Artificial boundary conditions and NRBCs. 4. Local non-reflecting boundary conditions. 5. Nonlocal non-reflecting boundary conditions. 6. Special numerical procedures for unbounded and large domains. Part II. 7. The DtN method. 8. Computational aspects of the DtN method. 9. Application of the DtN method to beam and shell problems. 10. The DtN method for time-harmonic waves. 11. The DtN method for time dependent problems. Appendix: The finite element method. References. Index.
TL;DR: In this article, a finite element formulation is presented for modeling the dynamic as well as static response of laminated composites containing distributed piezoelectric ceramics subjected to both mechanical and electrical loadings.
Abstract: A finite element formulation is presented for modeling the dynamic as well as static response of laminated composites containing distributed piezoelectric ceramics subjected to both mechanical and electrical loadings. The formulation was derived from the variational principle with consideration for both the total potential energy of the structures and the electrical potential energy of the piezoceramics. An eight-node three-dimensional composite brick element was implemented for the analysis, and three-dimensional incompatible modes were introduced to take into account the global bending behavior resulting from the local deformations of the piezoceramics. Experiments were also conducted to verify the analysis and the computer simulations. Overall, the comparisons between the predictions and the data agreed fairly well. Numerical examples were also generated by coupling the analysis with simple control algorithms to control actively the response of the integrated structures in a closed loop.
TL;DR: In this article, the authors compare homogenization and standard mechanics RVE-based analyses for periodic porous composites with finite ν, and conclude that homogenisation is preferable over standard mechanics of materials approaches for periodic composites even when the material is only locally periodic and ν is finite.
Abstract: Composite material elastic behavior has been studied using many approaches, all of which are based on the concept of a Representative Volume Element (RVE). Most methods accurately estimate effective elastic properties when the ratio of the RVE size to the global structural dimensions, denoted here as ν, goes to zero. However, many composites are locally periodic with finite ν. The purpose of this paper was to compare homogenization and standard mechanics RVE based analyses for periodic porous composites with finite ν. Both methods were implemented using a displacement based finite element formulation. For one-dimensional analyses of composite bars the two methods were equivalent. Howver, for two- and three-dimensional analyses the methods were quite different due to the fact that the local RVE stress and strain state was not determined uniquely by the applied boundary conditions. For two-dimensional analyses of porous periodic composites the effective material properties predicted by standard mechanics approaches using multiple cell RVEs converged to the homogenization predictions using one cell. In addition, homogenization estimates of local strain energy density were within 30% of direct analyses while standard mechanics approaches generally differed from direct analyses by more than 70%. These results suggest that homogenization theory is preferable over standard mechanics of materials approaches for periodic composites even when the material is only locally periodic and ν is finite.
TL;DR: In this paper, the elastic contact problem of a rigid cylindrical punch indenting a multi-layered linear elastic half space is studied and then used to model the unloading phase of a microindentation test of thin fims deposited on a substrate.
TL;DR: First some well-known features of superconducting materials are reviewed and then various results concerning the model, the resultant differential equations, and their solution on bounded domains are derived.
Abstract: The authors consider the Ginzburg–Landau model for superconductivity. First some well-known features of superconducting materials are reviewed and then various results concerning the model, the resultant differential equations, and their solution on bounded domains are derived. Then, finite element approximations of the solutions of the Ginzburg–Landau equations are considered and error estimates of optimal order are derived.
TL;DR: In this article, a relation between stabilized finite element methods and the Galerkin method employing interpolations with bubble functions is established for the advective-diffusive model and for the linearized compressible Navier-Stokes equations.
TL;DR: In this article, a computational procedure is developed to solve the problems of coupled motion of a rigid body and a viscous incompressible fluid; the former is mounted on elastic springs, and the latter is surrounding the rigid body.
Abstract: A computational procedure is developed to solve the problems of coupled motion of a rigid body and a viscous incompressible fluid; the former is mounted on elastic springs, and the latter is surrounding the rigid body. The arbitrary Lagrangian-Eulerian method is employed to incorporate the interface conditions between the body and the fluid. The streamline upwind/Petrov-Galerkin finite element method is used for the spatial discretization of the fluid domain, and the predictor-corrector method is used for the time integration. The method is applied to evaluate the added mass and the added damping of a circular cylinder as well as to simulate the vibration of a circular cylinder induced by vortex sheddings.
Book•
30 Sep 1992TL;DR: The finite element method is the most effective method for the solution of composite laminates as discussed by the authors, but it is limited to simple geometries because of the difficulty in constructing the approximation functions for complicated geometrie.
Abstract: The partial differential equations governing composite laminates (see Section 2.4) of arbitrary geometries and boundary conditions cannot be solved in closed form. Analytical solutions of plate theories are available (see Reddy [1–5]) mostly for rectangular plates with all edges simply supported (i.e., the Navier solutions) or with two opposite edges simply supported and the remaining edges having arbitrary boundary conditions (i.e., the Levy solutions). The Rayleigh-Ritz and Galerkin methods can also be used to determine approximate analytical solutions, but they too are limited to simple geometries because of the difficulty in constructing the approximation functions for complicated geometries. The use of numerical methods facilitates the solution of these equations for problems of practical importance. Among the numerical methods available for the solution of differential equations defined over arbitrary domains, the finite element method is the most effective method. A brief introduction to the finite element method is presented in Section 3.2.
TL;DR: In this article, a general approach to adaptivity for finite element methods is presented and applications to linear elasticity, non-linear elasto-plasticity and nonlinear conservation laws, including numerical results.
TL;DR: In this article, a methodology to improve the quality of the finite element calculations in the regions of unacceptable errors has been developed, where the superimposed regions can be of arbitrary shape, unlimited by the problem geometry, boundary conditions and the underlying mesh topography.
01 Jul 1992
TL;DR: The results indicate that the twin goals of realistic computer animation and valid biomechanical simulation of muscle can be met using these methods, providing a principled foundation both for animators wishing to create anatomically based characters and biomechanicals engineers interested in studying muscle function.
Abstract: Muscle is the fundamental “motor” that drives all animal motion. We propose that changes in shape of moving human and animal figures will be accurately reproduced by simulating the muscle action and resulting forces that propel these figures. To test this hypothesis, we developed a novel computational model of skeletal muscle. The geometry and underlying material properties of muscle are captured using the finite element method (FEM). A biomechanical model of muscle action is used to apply non-linear forces to the finite element mesh nodes. We have tried to validate the FEM model by simulating well known muscle experiments and plotting out key quantities. Our results indicate that the twin goals of realistic computer animation and valid biomechanical simulation of muscle can be met using these methods, providing a principled foundation both for animators wishing to create anatomically based characters and biomechanical engineers interested in studying muscle function. CR Categories: 1.3.7 [Computer Graphics]: ThreeDimensional Graphics and Realism—Animation. Additional
TL;DR: The introduction to finite element vibration analysis second is universally compatible with any devices to read and available in the book collection an online access to it is set as public so you can get it instantly.
Abstract: introduction to finite element vibration analysis second is available in our book collection an online access to it is set as public so you can get it instantly. Our digital library hosts in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Merely said, the introduction to finite element vibration analysis second is universally compatible with any devices to read
TL;DR: In this article, the authors review several existing models for describing the deformation behavior of a circular thin film in a bulge test, and then analyze these models in light of the finite element results.
Abstract: Since its first application to thin films in the 1950's the bulge test has become a standard technique for measuring thin film mechanical properties. While the apparatus required for the test is simple, interpretation of the data is not. Failure to recognize this fact has led to inconsistencies in the reported values of properties obtained using the bulge test. For this reason we have used the finite element method to model the deformation behavior of a thin film in a bulge test for a variety of initial conditions and material properties. In this paper we will review several of the existing models for describing the deformation behavior of a circular thin film in a bulge test, and then analyze these models in light of the finite element results. The product of this work is a set of equations and procedures for analyzing bulge test data that will improve the accuracy and reliability of this technique.
Book•
30 Jan 1992
TL;DR: This textbook concentrates on mesh generation, an essential prerequisite for the numerical analysis of engineering problems, through the use of computational geometry, and provides a detailed survey of existing methods and highlights the increasing need for automatic techniques.
Abstract: This textbook concentrates on mesh generation, an essential prerequisite for the numerical analysis of engineering problems, through the use of computational geometry. The author provides a detailed survey of existing methods and highlights the increasing need for automatic techniques. Traditional structured grids are considered alongside the unstructured meshes of triangles and tetrahedra. The text contains information on the algorithms for the creation of two-and three-dimensional cases, and details tools for the modification and exploitation of meshes.
TL;DR: Three-dimensional finite element models of a partially edentulated human mandible were generated to calculate the mechanical response to simulated isometric biting and mastication loads and showed that a model with over 30,000 degrees of freedom was required to obtain analysis accuracy.
Book•
01 Oct 1992
TL;DR: In this paper, the authors present guidelines for Element Meshes and Global Nodal Numbering, as well as a selection of approximate functions for the FE-method - Scalar Problems and Weight Function - Weighted Residual Methods.
Abstract: * Introduction. * Matrix Algebra. * Direct Approach. * Strong and Weak Formulations - One-dimensional Heat Flow. * Gradient - Gauss' Divergence Theorem - Green Theorem. * Strong and Weak Forms - Two-and Three-Dimensional Heat Flow. * Choice of Approximating Functions for the FE-method - Scalar Problems. * Choice of Weight Function - Weighted Residual Methods. * FE-formulation of One-Dimensional Heat Flow. * FE-formulation of Two-and-Three Dimensional Heat Flow. * Guidelines for Element Meshes and Global Nodal Numbering. * Stresses and Strains. * Linear Elasticity. * FE-formulation of Torsion and Non-circular Shafts. * Approximating Functions for the FE-method - Vector Problems. * FE-formulation of Three-and-Two Dimensional Elasticity. * FE-formulation of Beams. * FE-formulation of Plates. * Isoparametric Finite Elements. * Numerical Integration.
TL;DR: In this paper, a method for automatically extending small-strain state-update algorithms and their corresponding consistent tangents into the finite deformation range within the framework of multiplicative plasticity is presented.
Abstract: We provide a method for automatically extending small‐strain state‐update algorithms and their correspondent consistent tangents into the finite deformation range within the framework of multiplicative plasticity. The procedure, when it applies, operates at the level of kinematics and, hence, can be implemented once and for all independently of the material‐specific details of the constitutive model. The versatility of the method is demonstrated by a numerical example.
TL;DR: This paper uses a variational approach and a finite element method to actually express the surface in a discrete basis of continuous functions, which leads to a reduced computational complexity and a better numerical stability.
Abstract: In this paper, we generalize the deformable model [4, 7] to a 3-D model, which evolves in 3-D images, under the action of internal forces (describing some elasticity properties of the surface), and external forces attracting the surface toward some detected edgels. Our formalism leads to the minimization of an energy which is expressed as a functional. We use a variational approach and a finite element method to actually express the surface in a discrete basis of continuous functions. This leads to a reduced computational complexity and a better numerical stability.
TL;DR: In this paper, the Galerkin/least-squares method with DtN boundary conditions is designed to exhibit superior behavior for problems of acoustics, providing accurate solutions with relatively low mesh resolution and allowing numerical damping of unresolved waves.
Abstract: Finite element methods are constructed for the reduced wave equation in unbounded domains. Exterior boundary conditions for a computational problem are derived from an exact relation between the solution and its derivatives on an artificial boundary by the DtN method, precluding singular behavior in finite element models. Galerkin and Galerkin/least-squares finite element methods are presented. Model problems of radiation with inhomogeneous Neumann boundary conditions in plane and spherical configurations are employed to design and evaluate the numerical methods in the entire range of propagation and decay. The Galerkin/least-squares method with DtN boundary conditions is designed to exhibit superior behavior for problems of acoustics, providing accurate solutions with relatively low mesh resolution and allowing numerical damping of unresolved waves. General convergence results guarantee the good performance of Galerkin/least-squares methods on all configurations of practical interest. Numerical tests validate these conclusions.