Showing papers on "Smoothed finite element method published in 1971"

The finite element method in engineering science

Abstract: Thank you very much for downloading the finite element method in engineering science. Maybe you have knowledge that, people have search numerous times for their favorite books like this the finite element method in engineering science, but end up in malicious downloads. Rather than enjoying a good book with a cup of tea in the afternoon, instead they cope with some infectious bugs inside their computer.

Electromagnetic and electrical modeling by the finite element method

Abstract: Application of the finite element method to the solution of physical problems is based on minimization of energy; in the present case electromagnetic energy is minimized. Representation of a volume of space by a number of finite elements and description of field or potential distribution by a finite set of unknown values make it possible to replace the energy variational equation by matrix equations. It is shown that a solution for secondary rather than total field quantities can be obtained directly. Such a procedure has several advantages.Approximations are involved in using non-infinitesimal elements and finite meshes of elements. It is usually necessary to pay more attention to mesh size than texture (element size).Examples of induced polarization anomalies over two-dimensional models illustrate effects of topography and of a highly conducting layer above bodies of polarizable material. Computed electromagnetic anomalies of two-dimensional structures, with line source excitation, include the effects of adjacent conductors and magnetic conductors set in a less conductive half-space.

Computer implementation of the finite element method

Abstract: : A detailed study of the implementation of finite element methods for solving two-dimensional elliptic partial differential equations is presented. Generation and storage schemes for triangular meshes are considered, and the use of irregular meshes for finite element methods is shown to be relatively inexpensive in terms of storage. The report demonstrates that much of the manipulation of the basis functions necessary in the derivation of the approximation equations can be done semi-symbolically rather than numerically as is usually done. Ordering algorithms, compact storage schemes, and efficient implementation of elimination methods are studied in connection with sparse systems of finite element equations. A Fortran code is included for the finite element solution of a class of elliptic boundary value problems, and numerical solutions of several problems are presented. Comparisons among different finite element methods, and between finite element methods and their competitors are included.

Global‐local finite element

Abstract: Finite element procedures usually require more degrees of freedom for a specified accuracy than does a classical Ritz procedure if suitable coordinate functions are available. This paper develops a combined global and local dependent variable representation which couples the conventional and finite element Ritz methods. This hybrid method preserves much of the flexibility of the finite element method while increasing the solution accuracy for a specified system order. The method is illustrated by examination of a beam and a plate vibration problem.

Large Strain, Elasto-Plastic Finite Element Analysis

Abstract: Two dimensional structures large strain elastoplastic analysis by finite element method, using variational principles to derive equilibrium equations

On Solutions of Plane Strain Consolidation Problems by Finite Element Methods

Abstract: The formulation is presented of the equations governing the solution of true three-dimensional consolidation problems by means of finite element methods. The numerical procedure for handling the re...

Finite element method applied to the problem of stability of a non‐conservative system

Abstract: The finite element method is applied to the stability analysis of structural systems subject to non-conservative forces. The development of the method is general, but the specific application considered here is the stability of thin-walled members subject to follower forces. The method predicts the type of instability, whether it be buckling or flutter. Example problems, for which exact solutions are known, illustrate the accuracy and convergence characteristic of the finite element formulation.

Use of finite element computer programs in fracture mechanics

Abstract: Since the theoretical stresses and strains at the tip of a V-notched crack in an elastic continuum are infinite, the question arises as to the accuracy of strain energy as calculated from finite element computer programs for systems containing such a crack. Two geometries for which analytical solutions are available were analyzed using a plane stress finite element computer program. Results show that accuracy in both cases depended upon proper selection of a grid network. Several methods of calculating stress intensity factors are discussed. Application of the finite element computer program in the analysis of fracture in solid propellant rocket motor cartridge or grain is included.

A powerful hybrid method in finite element analysis

Abstract: An important limitation of finite element analysis, namely, the need for a large number of small elements in regions of finite or infinite stress concentrations and the difficulties of convergence in such cases, is well known. Rao1 suggested a possibility of overcoming this by developing hybrid techniques combining continuum and finite element concepts. In such techniques, each region of stress concentration is covered by one large primary element whose description includes term(s) identifying the type and order of concentration, while the remaining structure is split into a few secondary elements which are conventional finite elements. In this paper a procedure incorporating this concept is developed and its effectiveness is clearly demonstrated by successful application to two important examples, one of them with stress singularities. The concept, in fact, can be applied equally well to other two- and three-dimensional problems of continua with discontinuities and concentrations.

Analysis of finite deformations of elastic solids by the finite element method.

Abstract: Finite element applications, particularly to analyses of finite deformations in elastic solids, are reviewed, along with the difficulties encountered in the formulation of certain problems and in their numerical solution. Various approaches are discussed for overcoming these and other difficulties. A computer program designed for finite elasticity problems is described, and several numerical examples are presented.

The finite element method for elliptic differential equations

Abstract: Publisher Summary This chapter explores the finite element method for elliptic differential equations. The finite element method is a special method for the numerical solution of partial differential equations. The name was coined by engineers who used the method in structural mechanics. The finite element method became a very widely used method in practice. The theoretical investigation of different aspects began a few years ago. Nevertheless, many fundamental results are known at present. There is a variety of methods called the finite element method. The chapter presents one special approach aimed especially at solving elliptical equations. To avoid incidental technical difficulties, the chapter presents the results and numerical experiments for simple model problems. The chapter discusses approximation theory, which plays a very important role in the investigation of the finite element method.