A mathematical study on a unified variational principle with two constrained parameters

In this paper, a parameterized variational principle based on a mixed functional obtained by a linear combination of the total potential energy functional, the modified Hellinger-Reissner functional, and the Hu-Washizu functional with two constrained parameters is proposed, and the mathematical characteristics of the variational equation of the principle are investigated for the analysis of boundary value problems in linear elasticity. It is first proved that the Euler-Lagrange equations of the variational equation is identical to the governing equations for the given problem. Then existence of the unique solution of the variational equation is systematically proved by showing that the energy bilinear form is weakly-coercive. As an application, the stress/strain smoothing can be obtained as a form of mixed FEM based on the variational equation.