Formulação e implementação computacional para análise fisicamente e geometricamente não linear de cascas pelo método dos elementos finitos generalizados

Abstract

The structural analysis of plates and shells is an extremely relevant topic in structural engineering and has received increasing attention in recent decades, composing a vast field of research with many gaps yet to be explored. In this work, the nonlinear physical and geometrical response in problems involving plates and shells is studied. To overcome the shear and membrane locking, an element is adopted that combines the mixed tensorial interpolation method (MITC) with the Generalized Finite Element Method (MEFG), as this method is proven to be less prone to mesh influence, becoming more advantageous for this type of analysis. The shell element is formulated within the context of the Total Lagrangian formulation with deformations/stresses taken into account using the nonlinear Green-Lagrange strain tensor. In the present study, the physical nonlinearity considered refers to the description of elastoplastic behavior under finite strains, evaluated through the adoption of stress-strain relationships suitable for the material response and deduced from the principal hypothesis of the multiplicative decomposition of the deformation gradient. This implementation generically expands the models presented in Oliveira (2016)and ensures that elastoplastic models originally formulated for small strains are also applied to finite strain regime. To capture stress and strain variations through the thickness, the shell element is subdivided into N discrete layers, allowing the measurement of the material's inelastic behavior. In this scenario, the kinematics of flat shell elements in layers adapted to the MEFG is presented. In addition, a formulation for an Implicit/Explicit return algorithm based on the standard Closest Point Projection method for stress integration is presented, adapted for the finite deformation model. To evaluate and validate the proposed element, results from numerical solutions of other shell elements found in the literature and analytical solutions are compared with the element. It is shown that the proposed model, in addition to converging rapidly, presents results consistent with those presented in the literature and in analytical solutions.