Partitioned parametrized variational procedure for the generation of theorems of structural analysis

Abstract

Structural field modeling of displacements, stresses, and strains is conceptually linked with the generation of functionals. In particular, this work introduces for the first time the Partitioned Parametrized Variational Procedure (PPVP). In-plane stresses and strains are mathematically treated differently than the transverse counterparts. This allows one to generate all the classical variational theorems of elasticity (such as the Principles of Virtual Displacements and Complementary Energy, Hellinger-Reissner, and the Veubeke-Hu-Washizu theorems) and additional new types of variational theorems which can be exploited for the solution of structural problems in various areas, such as reinforced panels and variable angle tow composites. With the proposed variational procedure energetically consistent constraints naturally arise directly from the formulation. PPVP could also be used to formulate new enhancements of the finite element or meshless methods and to quantify functional errors not related to the numerical discretization.