Partial Complementary Energy Densities, Their Variational Principles and Applications in Elasticity

Partial complementary energy densities are introduced through partial Legendre transforms from the strain energy density of linear elasticity. They have mixed components of the strain and stress tensors. Mixed variational principles based on these energy densities are presented. It is shown that these variational principles are useful in the derivation of two- and one-dimensional theories of elastic plates and rods.