Structural models based on 3D constitutive laws: Variational structure and numerical solution

Abstract

In all structural models, the section or fiber response is a relation between the strain measures and the stress resultants. This relation can only be expressed in a simple analytical form when the material response is linear elastic. For other, more complex and interesting situations, kinematic and kinetic hypotheses need to be invoked, and a constrained threedimensional constitutive relation has to be employed at every point of the section in order to implement non-linear and dissipative constitutive laws into dimensionally reduced structural models. In this article we explain in which sense reduced constitutive models can be expressed as minimization problems, helping to formulate the global equilibrium as a single optimization problem. Casting the problem this way has implications from the mathematical and numerical points of view, naturally defining error indicators. General purpose solution algorithms for constrained material response, with and without optimization character, are discussed and provided in an open-source library. arXiv:1907.11089v1 [physics.class-ph]

Determination of the Residual Strain Energy of a Structure and the Method of Progressive Limiting State

“…Currently, this parameter is determined mainly by probabilistic methods. An attempt to determine the full (maximum) load-bearing capacity of structures using the Lagrange approach [8][9][10][11][12][13][14] leads to consideration of all possible options for loading load-bearing structures, i.e. the need to solve an infinite sequence of problems.…”