Formulação do método dos elementos finitos para a análise elástica linear de placas delgadas

Abstract

This work has the purpose of presenting a formulation based on the Finite Element method (FEM) and focused on the linear analysis of plates called slender. To obtain the algebraic system of equations structures were discretized by rectangular finite element endowed with 4 nodes and 3 degrees of freedom per node. The displacement field in the direction perpendicular to the median plane of the elements was approximated by a third-degree polynomial. The matrix of elementary stiffness and the procedure for obtaining the stiffness matrix of the structure as a whole are shown throughout the study. In order to validate the developed formulation, it was elaborated a computer program of free and modular character (consisting of a combination of interdependent calculation routines) able to simulate the structural behavior of thin plates subjected to varying conditions of loading and linking. Finally, after running a few examples, we carried out a quantitative and qualitative analysis of the results obtained through comparison with results provided by the Bar, Czerny and Timoshenko tables, as well as works from other authors.