Critical Energy Properties Study for Unsymmetrical Deformable Structures

Abstract

There are difficulties in the formulation and solution of problems for follower loading, temperature actions, and whether the Lagrange principle is used. By dividing the external loads and internal deformation fields that exist according to their own laws, we focused on the advantages in mechanics of deformable solids. This paper develops an approach to the study of the internal strain energy of deformed systems, based on the criterion of the critical levels of the internal strain energy. According to the criterion, the achievement of the limiting values of the internal strain energy by the system with varying internal parameters of the structure is possible for certain types of “self-stress” (“self-balance”) for deformable bodies. The latter corresponds to the levels of the critical energy of the body determined by the eigenvalues of the internal strain energy. New problems, namely the “weak link” and “progressive limiting state of the system”, are formulated and demonstrated in the examples of the study of asymmetric rod systems. The methodology used here is based on matrix methods of the structural mechanics and a mathematical apparatus for eigenvalue problems.