Object-oriented finite elements I. Principles of symbolic derivations and automatic programming

doi:10.1016/0045-7825(96)01040-7

Computer Methods in Applied Mechanics and Engineering

Volume 132, Issues 3–4, 1 June 1996, Pages 259-276

https://doi.org/10.1016/0045-7825(96)01040-7 Get rights and content

Abstract

The development of a numerical finite element model for a given initial-boundary-value problem goes essentially through the derivation of a weak form, its discretization and finally the derivation of the matrix forms. These steps can, to a large extent, be automated, except for the ones which require intelligence or some form of decision making from the developer.

The article outlines the essential steps of an interactive quasi-automatic approach and illustrates it in the example of a linear uniaxial bar formulation for dynamics. The implementation is done in SmalltalkV. A detailed description of the proposed environment is described in a companion article.

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They used dynamic techniques for code linking and class inheritance and proposed a flexible and easy-to-use input-file format. The research works of [18–20] are an ingenious attempt to automatically derive FE equations. They presented an interactive symbolic OO environment for the derivation of the weak form, its discretization, and the matrix forms of a given initial-boundary-value problem.
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By modularizing the solver, it becomes easier to solve different physical phenomena with the same numerical code. One application of modularity is the research of Eyheramendy and Zimmerman [2–4] who have developed a toolkit for semi-automatic symbolic derivation of linear finite-element models of initial-boundary-value problems. In more recent work [5], non-linear problems are also supported.
Numerical simulations of partial different equations are used in a variety of domains, allowing complete testing and simulation of a product or process even before it is created. However, numerical solvers are not used in all the domains where such equations arise due to the lack of available software or knowledge of numerical methods by scientists. The difficulty of writing a numerical solver is even greater for multiphysics problems, which combine distinct but coupled physical phenomena into a single simulation.
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Object-oriented programming in FEM and BEM: A bibliography (1990-2003)
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This paper gives a bibliographical review of the object-oriented programming applied to the finite element method as well as to the boundary element method. The bibliography at the end of the paper contains references to papers, conference proceedings and theses/dissertations on the subject that were published between 1990 and 2003. The following topics are included: finite element method—object-oriented programming philosophy, mesh modelling, distributed/parallel processing, toolkits and libraries, object-oriented specific applications (aerospace, civil engineering/geomechanics, coupled problems, dynamical systems, electromagnetics, fracture mechanics and contact problems, material simulations/manufacturing, mechanical engineering, nonlinear structural simulations, optimization, others); boundary element method. Totally 408 references are listed.

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Object-oriented finite elements I. Principles of symbolic derivations and automatic programming

Abstract

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

Comput. Struct.

Comput. Methods Appl. Mech. Engrg.

Comput. Struct.

Comput. Struct.