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The method of auxiliary mapping for the finite element solutions of elasticity problems containing singularities. (English) Zbl 0833.73061

Summary: We have introduced a new approach called the method of auxiliary mapping to deal with elliptic boundary value problems with singularities. In this paper this method is extended so that it can handle the plane elasticity problems containing singularities. In order to show the effectiveness, this method is compared with the conventional approach in the framework of the \(p\)-version of the finite element method. Moreover, it is demonstrated that this method yields a better solution for those elasticity problems containing strong singularities than does the \(h - p\) version of the finite element method.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74B99 Elastic materials
74H99 Dynamical problems in solid mechanics
74B05 Classical linear elasticity
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