Parametrized multifield variational principle in elasticity. I: Mixed functionals

Abstract

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 Veubeke's stress-assumption limitation principle takes a particulary elegant expression in terms of the parametrized discrete form. Other possible parametrizations are briefly discussed.