Showing papers on "Smoothed finite element method published in 1995"
Book•
26 Jun 1995
TL;DR: The Finite Element Method as mentioned in this paper is a method for linear analysis in solid and structural mechanics, and it has been used in many applications, such as heat transfer, field problems, and Incompressible Fluid Flows.
Abstract: 1. An Introduction to the Use of Finite Element Procedures. 2. Vectors, Matrices and Tensors. 3. Some Basic Concepts of Engineering Analysis and an Introduction to the Finite Element Methods. 4. Formulation of the Finite Element Method -- Linear Analysis in Solid and Structural Mechanics. 5. Formulation and Calculation of Isoparametric Finite Element Matrices. 6. Finite Element Nonlinear Analysis in Solid and Structural Mechanics. 7. Finite Element Analysis of Heat Transfer, Field Problems, and Incompressible Fluid Flows. 8. Solution of Equilibrium Equations in State Analysis. 9. Solution of Equilibrium Equations in Dynamic Analysis. 10. Preliminaries to the Solution of Eigenproblems. 11. Solution Methods for Eigenproblems. 12. Implementation of the Finite Element Method. References. Index.
8,068 citations
DOI•
01 Jun 1995
TL;DR: In this paper, a new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved, which can therefore be more efficient than the usual finite element methods.
Abstract: : A new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved. This new method can therefore be more efficient than the usual finite element methods. An additional feature of the partition-of-unity finite element method is that finite element spaces of any desired regularity can be constructed very easily. Moreover the method is of "meshless" type. This paper includes a convergence proof of this method and illustrates its efficiency by an application to the Helmholtz equation for high wave numbers. The basic estimates for a-posteriori error estimation for this new method are also proved. (AN)
369 citations
TL;DR: In this article, the authors developed a two-dimensional elastic-absorption finite element model of isotropic elastic porous noise control materials and investigated the effect of edge constraints on the surface normal impedance of a foam sample in a standing-wave tube.
Abstract: In this paper the development of a two‐dimensional elastic‐absorption finite element model of isotropic elastic porous noise control materials is described. A method for coupling elastic‐absorption finite elements with conventional acoustic finite elements is also presented for the cases when the interface between the adjacent air space and the foam is either unfaced or sealed by a membrane. The accuracy of the acoustic/elastic‐absorption model has been verified by comparing its predictions with analytical solutions for the case of wave propagation in a foam‐filled waveguide. Further, the finite element model has been used to investigate the effect of edge constraints on the surface normal impedance of a foam sample in a standing‐wave tube. As expected, edge constraints were found to stiffen the foam acoustically at low frequencies.
138 citations
TL;DR: In this article, a new formulation based on a three-field discretization using displacements, pressure and a "vorticity moment" as variables with an appropriate treatment of the boundary conditions was proposed.
120 citations
TL;DR: A survey of variational principles which form the basis for computational methods in both continuum mechanics and multi-rigid body dynamics is presented in this article, with the distinguishing feature of making an explicit use of the finite rotation tensor.
Abstract: A survey of variational principles, which form the basis for computational methods in both continuum mechanics and multi-rigid body dynamics is presented: all of them have the distinguishing feature of making an explicit use of the finite rotation tensor. A coherent unified treatment is therefore given, ranging from finite elasticity to incremental updated Lagrangean formulations that are suitable for accomodating mechanical nonlinearities of an almost general type, to time-finite elements for dynamic analyses. Selected numerical examples are provided to show the performances of computational techniques relying on these formulations. Throughout the paper, an attempt is made to keep the mathematical abstraction to a minimum, and to retain conceptual clarity at the expense of brevity. It is hoped that the article is self-contained and easily readable by nonspecialists. While a part of the article rediscusses some previously published work, many parts of it deal with new results, documented here for the first time.
111 citations
TL;DR: A brief review of multifield variational principles for the formulation of finite element methods in solid mechanics and an account of the evolution of hybrid/mixed finite element method are presented in this article.
109 citations
TL;DR: In this article, a geometric nonlinear finite element method is used to analyze fabric deformation characterized by large displacements and rotations, but small strains, using shell/plate elements.
Abstract: Fabric deformation characterized by large displacements and rotations but small strains is analyzed using a geometric nonlinear finite element method. The fabrics are modeled by shell/plate elements. Special considerations for applying the finite element method to fabric analysis are discussed and several examples of fabric deformation presented. The results from the finite element model are compared with experimental data and are in good agreement.
84 citations
TL;DR: A new method for numerically solving the equations of the hydrodynamic model for semiconductor devices in two space dimensions is introduced, which combines a standard mixed finite element method with the so-called Runge-Kutta Discontinuous Galerkin (RKDG) method.
Abstract: In this paper we introduce a new method for numerically solving the equations of the hydrodynamic model for semiconductor devices in two space dimensions. The method combines a standard mixed finite element method, used to obtain directly an approximation to the electric field, with the so-called Runge-Kutta Discontinuous Galerkin (RKDG) method, originally devised for numerically solving multi-dimensional hyperbolic systems of conservation laws, which is applied here to the convective part of the equations. Numerical simulations showing the performance of the new method are displayed, and the results compared with those obtained by using Essentially Nonoscillatory (ENO) finite difference schemes. From the perspective of device modeling, these methods are robust, since they are capable of encompassing broad parameter ranges, including those for which shock formation is possible. The simulations presented here are for Gallium Arsenide at room temperature, but we have tested them much more generally with considerable success.
61 citations
TL;DR: Improved first-order approximations of displacements, stresses, and forces are presented to preserve the ease of implementation and the efficiency and to improve significantly the quality of the results, such that the method can be used in problems with very large changes in the design variables, including geometric changes and elimination of members.
Abstract: Improved first-order approximations of displacements, stresses, and forces are presented The main objectives in developing the method presented are 1) to preserve the ease of implementation and the efficiency of the common first-order approximations and 2) to improve significantly the quality of the results, such that the method can be used in problems with very large changes in the design variables, including geometrical changes and elimination of members The method is based on results of a single exact analysis and can be used with a general finite element system It is suitable for different types of design variables and structures Results obtained by the proposed method are compared with various first-order approximations for modifications in the cross section as well as the geometry and the topology of the structure It is shown that the proposed approximations are most effective in terms of the accuracy, the efficiency, and the ease of implementation
47 citations
01 Jan 1995
TL;DR: Numerical solutions of transonic flows are presented which illustrate the versatility and the accuracy of the proposed method and show by numerical testing that, in the presence of curved boundaries, a high order approximation requires a corresponding high-order approximation of the geometry of the domain.
Abstract: This work describes a high order accurate discontinuous finite element method for the numerical solution of the equations governing compressible inviscid flows. Our investigation has focused on the problem of correctly prescribing the boundary conditions along curved boundaries. “Ale show by numerical testing that, in the presence of curved boundaries, a high order approximation of the solution requires a corresponding high-order approximation of the geometry of the domain. Numerical solutions of transonic flows are presented which illustrate the versatility and the accuracy of the proposed method.
43 citations
TL;DR: In this article, a new finite element is proposed for use in the three-dimensional simulation of transient physical processes with sharply varying solutions, intended to function in adaptive h-refinement schemes as a versatile transition between regions of different refinement levels.
Abstract: A new finite element, viable for use in the three-dimensional simulation of transient physical processes with sharply varying solutions, is presented The element is intended to function in adaptive h-refinement schemes as a versatile transition between regions of different refinement levels, ensuring interelement continuity by constructing a piecewise linear solution at the element boundaries, and retaining all degrees of freedom in the solution phase Construction of the element shape functions is described, and a numerical example is presented which illustrates the advantages of using such an element in an adaptive refinement problem The new element can be used in moving-front problems, such as those found in reservoir engineering and groundwater flow applications
01 Jan 1995
TL;DR: The fundamentals of stochastic computational mechanics and its application to the analysis of uncertain structural systems are summarized and recapitulated in a book by Liu and Belytschko (1989).
Abstract: It is becoming increasingly evident that traditional deterministic methods will not be sufficient to properly design advanced structures or structural components subjected to a variety of complex loading conditions Because of uncertainty in loading conditions, material behavior, geometric configuration, and supports, the stochastic computational mechanics, which accounts for all these uncertain aspects, must be applied to provide rational reliability analysis and to describe the behavior of the structure The fundamentals of stochastic computational mechanics and its application to the analysis of uncertain structural systems are summarized and recapitulated in a book by Liu and Belytschko (1989)
TL;DR: The problem of obtaining an incompressible wind field that adjusts to an experimental one is solved by two different adaptive finite element methods, using linear interpolation of a potential function and a mixed finite element method.
01 Jan 1995
TL;DR: The finite element method has become established as the universally accepted analysis method in structural design as discussed by the authors, which leads to the construction of a discrete system of matrix equations to represent the mass and stiffness effects of a continuous structure.
Abstract: In modern times the finite element method has become established as the universally accepted analysis method in structural design. The method leads to the construction of a discrete system of matrix equations to represent the mass and stiffness effects of a continuous structure. The matrices are usually banded and symmetric. No restriction is placed upon the geometrical complexity of the structure because the mass and stiffness matrices are assembled from the contributions of the individual finite elements with simple shapes. Thus, each finite element possesses a mathematical formula which is associated with a simple geometrical description, irrespective of the overall geometry of the structure. Accordingly, the structure is divided into discrete areas or volumes known as elements. Element boundaries are defined when nodal points are connected by a unique polynomial curve or surface. In the most popular (isoparametric, displacement type) elements, the same polynomial description is used to relate the internal, element displacements to the displacements of the nodes. This process is generally known as shape function interpolation. Since the boundary nodes are shared between neighbouring elements, the displacement field is usually continuous across the element boundaries. Figure 2.1 illustrates the geometric assembly of finite elements to form part of the mesh of a modelled structure.
TL;DR: It is shown that all element quadrature may be done in closed form, yielding a set of algebraic equations, and can be used to determine switching structures and initial guesses for a shooting code.
Abstract: This paper presents an extension of a finite element formulation based on a weak form of the necessary conditions to solve optimal control problems. First, a general formulation for handling internal boundary conditions and discontinuities in the state equations is presented. Then, the general formulation is modified for optimal control problems subject to state-variable inequality constraints. Solutions with touch points and solutions with stateconstrained arcs are considered. After the formulations are developed, suitable shape and test functions are chosen for a finite element discretization. It is shown that all element quadrature (equivalent to one-point Gaussian quadrature over each element) may be done in closed form, yielding a set of algebraic equations. To demonstrate and analyze the accuracy of the finite element method, a simple state-constrained problem is solved. Then, for a more practical application of the use of this method, a launch vehicle ascent problem subject to a dynamic pressure constraint is solved. The paper also demonstrates that the finite element results can be used to determine switching structures and initial guesses for a shooting code.
TL;DR: In this article, a frequency analysis is applied to determine the phase velocity of semi-implicit linear, quadratic and cubic basis one-dimensional finite element methods and several comparative finite difference/ finite volume algorithms.
Abstract: SUMMARY ATaylor series augmentation of a weak statement (a ‘Taylor weak statement’ or ‘Taylor-Galerkin’ method) is used to systematically reduce the dispersion error in a finite element approximation of the one-dimensional transient advection equation. A frequency analysis is applied to determine the phase velocity of semi-implicit linear, quadratic and cubic basis one-dimensional finite element methods and of several comparative finite difference/ finite volume algorithms. The finite element methods analysed include both GaIerkin and Taylor weak statements. The frequency analysis is used to obtain an improved linear basis Taylor weak statement finite element algorithm. Solutions are reported for verification problems in one and two dimensions and are compared with finite volume solutions. The improved finite element algorithms have sufficient phase accuracy to achieve highly accurate linear transient solutions with little or no artificial diffusion. Application of the Galerkm finite element method (FEM) to parabolic and hyperbolic differential equations has presented difficulties with the control of dispersion error. Dispersion error results fiom shorter-wavelength solution components travelling at the wrong speed, usually too slowly. Waves travelling at the wrong speed eventually appear in the wrong place as extraneous short waves and can lead to instability in a non-linear problem statement. The ‘upwind’ finite volume method has been extensively applied either to reduce dispersion error or to artificially &&se the resulting short waves. The interpolation is biased for greater contribution fiom the direction of the velocity. It originated with the donor cell method of Courant et af. in 1952 and was applied to the FEM in the 1970s as the Petrov-Galerkin methods of Christie et ~1.~9 and Heinrich et ~1.~3~ Early Petrov-Galerkin methods suffered from excess diffusion of the solution and later work has been oriented towards reducing the excess diffusion, including the SUPG method of Brooks and Hughes6 in 1980 and the methods of Dick7 in 1983, Westerink and Sheas in 1989, Bouloutas and Celia9 in 199 1 and Konda et al. lo in 1992. Similar work in the finite volume method is typified by the QUICK methods of Leonard” in 1979 and Leonard and Mokhtari12 in 1992. Many upwind methods still cause excess diffusion and some also cause an undesirable increase in the width of the matrix stencil, thus increasing the computational effort. An alternative approach which avoids these problems originated for the finite volume method with Lax and WendroP3 in 1960. The
TL;DR: The capabilities that are provided by pre- and post-processors are reviewed and enhancements and new features that will likely be developed in the near future are suggested.
Abstract: The vector absorbing boundary condition (ABC) is an effective way of truncating the infinite domain of a 3-D scattering problem, and thereby permitting its solution with a finite element method. One of the terms of the ABC is a surface divergence term. It is shown that due to its presence, the normal continuity of the field must be enforced on the surface where the ABC is applied. Numerical analysis of scattering by a conducting sphere demonstrates that if normal continuity is not enforced, the maximum error in the near held may more than double. A similar error occurs if the surface divergence term is omitted from the formulation. >
TL;DR: This paper presents an application of the rigid finite element method to modeling of flexible links of spatial systems and takes into account large deflections of the link and an influence of centrifugal forces on deflections and deformations.
Abstract: This paper presents an application of the rigid finite element method to modeling of flexible links of spatial systems. It is assumed that the movement of the base, with which the flexible system is connected, is known. The model presented takes into account large deflections of the link and an influence of centrifugal forces on deflections and deformations. Methods applied in dynamic analysis of manipulators with rigid links are used to derive the equations of motion. The results of numerical calculations are compared with those obtained by other authors who used the finite element approach.
TL;DR: In this article, an expression for the potential energy of a shell of general shape, including thickness shear deformation and without neglecting z R in comparison with unity, is derived.
01 Jan 1995
TL;DR: The use of finite elements in neutron transport gives deterministic treatments a geometrical capability with a flexibility comparable to that achievable by the stochastic Monte Carlo method.
TL;DR: In this article, the authors give an abstract stability result for finite element methods for a given norm once it is established with respect to another norm, which is useful for the convergence analysis of multigrid methods for the solution of discrete problems.
Abstract: We give an abstract stability result for finite element methods. It provides a general guideline for establishing the stability of finite element methods for a given norm once it is established with respect to another norm. The abstract result yields stability estimates of natural norms for finite element methods, which have recently been developed to stabilize effects like dominant convection, incompressibility constraints, or boundary conditions. These stability results simplify the error analysis of the discretizations and are helpful fin the convergence analysis of multigrid methods for the solution of the corresponding discrete problems. © 1995 John Wiley & Sons, Inc.
TL;DR: An element-by-element iterative finite element algorithm for linear elasticity problems that is constructed in a manner very similar to the Static Relaxation algorithm used in the Discrete Element Method, thus facilitating the development of a unified FEM/DEM analysis.
TL;DR: In this article, a theoretical basis for a finite element iterative algorithm for load-displacement analysis of elasticity problems in which the elastic body fractures under load is established, and convergence of the algorithm to a physically meaningful solution is proved, and illustrated by results for a cantilever-type problem.
TL;DR: In this article, a new computational model of the edge plasma in axisymmetric magnetic fusion devices has been developed based on finite element methods, where Braginskii-type plasma fluid equations and a one-energy group neutral particle diffusion equation are spatially discretized on a two-dimensional domain using Galerkin, modified artificial diffusion, and anisotropic streamline-upwind/Petrov-Galerkin finite element method.
TL;DR: A general finite element formulation using cubic Hermitian interpolation for dynamic analysis of pipes conveying fluid is presented in this paper, where both the effects of shearing deformations and rotary inertia are considered.
Abstract: A general finite element formulation using cubic Hermitian interpolation for dynamic analysis of pipes conveying fluid is presented. Both the effects of shearing deformations and rotary inertia are considered. The development retains the use of the classical four degrees-of-freedom for a two-node element. The effect of moving fluid is treated as external distributed forces on the support pipe and the fluid finite element matrices are derived from the virtual work done due to the fluid inertia forces. Finite element matrices for both the support pipe and moving fluid are derived and given explicitly. A numerical example is given to demonstrate the validity of the model.