On duality principles for one and three-dimensional non-linear models in elasticity

2019/10/03 by Fabio Botelho, Botelho, Fabio
Computer Science · Engineering · #49N15 #Advanced Mathematical Modeling in Engineering #Contact Mechanics and Variational Inequalities #Elasticity and Material Modeling #FOS: Mathematics #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1910.01118

openalex publication_date 2019/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we develop duality principles applicable to primal variational formulations found in the non-linear elasticity theory. As a first application, we establish the concerning results in details for one and three-dimensional models. We emphasize such duality principles are applicable to a larger class of variational optimization problems, such as non-linear models of plates and shells and other models in elasticity. Finally, we formally prove there is no duality gap between the primal and dual formulations, in a local extremal context.

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