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A systematic construction of B-bar functions for linear and nonlinear mixed-enhanced finite elements for plane elasticity problems. (English) Zbl 0947.74067

Summary: In a previous paper [the authors, Int. J. Numer. Methods Eng. 38, No. 11, 1783-1808 (1995; Zbl 0824.73073)], a modified Hu-Washizu variational formulation has been used to derive an accurate four node plane strain/stress finite element denoted QE2. For the mixed element QE2 two enhanced strain terms are used and the assumed stresses satisfy the equilibrium equations a priori for the linear elastic case. In this paper an alternative approach is discussed. The new formulation leads to the same accuracy for linear elastic problems as the QE2 element; however it turns out to be more efficient in numerical simulations, especially for large deformation problems. Using orthogonal stress and strain functions, we derive \(\overline {\mathbf B}\) functions which avoid numerical inversion of matrices. The \(\overline {\mathbf B}\)-strain matrix is sparse and has the same structure as the strain matrix \({\mathbf B}\) obtained from a compatible displacement field. The implementation of the derived mixed element is basically the same as the one for a compatible displacement element. The only difference is that we have to compute a \(\overline {\mathbf B}\)-strain matrix instead of the standard \({\mathbf B}\)-matrix. Accordingly, existing subroutines for a compatible displacement element can be easily changed to obtain the mixed-enhanced finite element which yields a higher accuracy than the Q4 and QM6 elements.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74B20 Nonlinear elasticity
74B05 Classical linear elasticity

Citations:

Zbl 0824.73073
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References:

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