An Error Analysis of Various Finite Element Patterns

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Although the finite element method has come into wide use in the field of structural and continuum mechanics, its error characteristics are not well known. This paper discusses the error characteristics of the finite element method in the case of triangular elements with a linear shape function generally used in plane stress analysis. The paper analyzes the discretization errors of finite element method using the technique proposed by Walz et al., with some generalizations. Here approximations included in the calculations of finite element method are discussed with various element patterns in comparison with the equilibrium equations of the field. The analysis reveals that the approximations in finite element method do not converge to the field equations in almost all the element patterns checked here as the element size is made infinitesimal. From this point of view, it interprets what kind of element patterns should be applied. Errors caused by the approximate strain-displacement relation are also discussed by a similar technique.

収録刊行物

  • Bulletin of JSME

    Bulletin of JSME 16 (102), 1803-1813, 1973

    一般社団法人 日本機械学会

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