On Generalizations of the Minimal Complementary Energy Variational Principle in Linear Elastostatics

TL;DR

This paper generalizes the minimal complementary energy variational principle in linear elastostatics by formulating a new three-field unconstrained variational principle involving displacement, stress, and strain fields, with potential applications beyond elastostatics.

Contribution

It introduces a novel, unconstrained three-field variational principle derived via Lagrange multipliers, expanding the theoretical framework of energy principles in linear elastostatics.

Findings

Derivation of a new three-field variational principle without constraints.

The new principle differs from existing three-field variational principles.

The approach is mathematical and applicable to other physics domains.

Abstract

It is shown that when the well-known minimal complementary energy variational principle in linear elastostatics is written in a different form with the strain tensor as an independent variable and the constitutive relation as one of the constraints, the removal of the constraints by Lagrange multipliers leads to a three-field variational principle with the displacement vector, stress field and strain field as independent variables. This three-field variational principle is without constrains and its variational functional is different from those of the existing three-field variational principles. The generalization is not unique. The procedure is mathematical and may be used in other branches of physics.