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Parametrized multifield variational principle in elasticity. I: Mixed functionals. (English) Zbl 0659.73015

A one-parameter family of mixed variational principles for linear elasticity is constructed. This family includes the generalized Hellinger-Reissner and total potential energy principles as special cases. The presence of the free parameter offers an opportunity for the systematic derivation of energy-balanced finite elements that combine displacement and stress assumptions. It is shown that Fraeijs de Verbeke’s stress-assumption limitation principle takes a particularly elegant expansion in terms of the parametrized discrete form. Other possible parametrizations are briefly discussed.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
49S05 Variational principles of physics
74S05 Finite element methods applied to problems in solid mechanics
65K10 Numerical optimization and variational techniques

Citations:

Zbl 0659.73016
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References:

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