On a variational theorem for incompressible and nearly-incompressible orthotropic elasticity

Abstract

A mixed variational theorem for linear orthotropic thermoelastic solids is presented. The mechanical state variables are taken to be the displacement vector and a scalar stress variable. The Euler equations of the variational principle are the displacement equations of equilibrium and a condition relating the stress variable to strain and temperature change. An important feature of the principle is that the field equations for both compressible and incompressible solids may be generated. In connection with applications to the development of finite element computer algorithms for the solution of boundary value problems a well-conditioned system of equations is obtained for nearly-incompressible solids.