Critical Strain Energy Levels Criterion for Structures with Lumped Parameters

The paper discusses the theory of critical strain energy levels for structures with lumped parameters. The theoretical assumptions and profs for common case are presented. The idea of external actions and strain energy field separation leads to the minimum strain energy principle. It has the self-stress of the structure physical sense. In the general case, a structure's extremal values of parameters are determined from an eigenvalue problem. The critical levels criterion means the self-stress state change. The strain energy consists of two parts: strain energy, which equilibrates the action work, and residual strain energy, which does not allow a deformable body to collapse. This allows for the total and residual strain energy to be calculated. The traditional problem formulation does not give us that option. The proposed theory is illustrated on a rod system, which explains the change in the selfstress state of the structure in a simple manner. The static matrix and stiffness matrix are obtained for the three-bar structure. The eigenvalue problem allows us to obtain the principal values of the nodal reactions and displacements of the structure. New formulations of structural design and structural analysis tasks are given. The results are compared with classical methods of solution. The formulations of weak link problems and progressive limit state problems are given. A structure's residual load capacity is evaluated by the residual strain energy. © 2024 Elsevier B.V., All rights reserved.