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

TL;DR

This paper introduces partial complementary energy densities derived via partial Legendre transforms in linear elasticity, establishing mixed variational principles that facilitate deriving lower-dimensional elastic theories.

Contribution

It presents a novel class of energy densities and associated variational principles that aid in simplifying complex elasticity problems into lower-dimensional models.

Findings

New partial complementary energy densities introduced

Mixed variational principles derived for elasticity

Applications in elastic plate and rod theories

Abstract

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.