2019/04/03 by Fabio Botelho, Botelho, Fabio
Computer Science · Decision Sciences · Engineering · #49N15 #74P99 #Advanced Mathematical Modeling in Engineering #Contact Mechanics and Variational Inequalities #Elasticity and Material Modeling #FOS: Mathematics #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.1904.02286
openalex publication_date 2019/04/03 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
This article develops a new primal dual formulation for the Kirchhoff-Love\nnon-linear plate model. At first we establish a duality principle which\nincludes sufficient conditions of global optimality through the dual\nformulation. At this point we highlight this first duality principle is\nspecially suitable for the case in which the membrane stress tensor is negative\ndefinite. In a second step, from such a general principle, we develop a primal\ndual variational formulation which also includes the corresponding sufficient\nconditions for global optimality. The results are based on standard tools of\nconvex analysis and on a well known Toland result for D.C. optimization.\nFinally, in the last section, we present a multi-duality principle and\nqualitative relations between the critical points of the primal and dual\nformulations. We formally prove there is no duality gap between such primal and\ndual formulations in a local extremal context.\n