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Transformation of the method of weighted residuals to a variational principle and its application in the finite element method with mixed elements. (English) Zbl 0646.73030

In this paper the method of weighted residuals is transformed to a stationary variational principle for systems of linear self-adjoint differential equations. Let \(\pi\) be the functional of the variational principle. The integrals in \(\pi\) contain physical quantities and their derivatives. By applying the integration by parts method to \(\pi\), it is possible to decrease the orders of highessecond (main) module consists of element splitting procedures where algorithms based on graph theory and element splitting templates have been extensively used. The notion of a ‘cross digraph’ introduced to carry multiple ‘weights’ and to avoid duplication in node-generation, is especially useful in three-dimensional element splitting techniques. Finally, numerical inverse isoparametric mapping techniques presented by the authors [Comput. Struct. 22, 1011- 1021 (1986; Zbl 0578.73067)] are also used to interpolate the nodal quantity vectors at the newly generated nodes. These vectors are needed as initial values in subsequent iterations for a dynamic restart. This aspect, together with the node renumbering scheme, is included in the third module of ADFEP. Some illustrative examples are included to elucidate the effectiveness of ADFEP.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
49S05 Variational principles of physics
49M15 Newton-type methods

Citations:

Zbl 0578.73067
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