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.


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


Zbl 0659.73016
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