Estudo e desenvolvimento de código computacional para análise de chapas utilizando elementos finitos CST e CSQ

Abstract

This work aims to present the mathematical formulation and develop a computational code based on the Finite Element Method for the elastic analysis of plates using Constant Strain Triangle (CST) and Quadrilateral Constant Strain (CSQ) elements. These elements were used to discretize the structure and to obtain the algebraic equations for the solution of the proposed problem. Both elements have two degrees of freedom per node, being they the displacements in the plane, in the direction of the coordinated axes. The CST element has triangular geometry and is defined by 3 nodes located at the vertices, the field of displacements within the approximate element by means of a first-degree polynomial. The location of the nodes are analogous to the CSQ element, that is, nodes in each of its 4 vertices. It has rectangular geometry and displacement field approximated by a second-degree polynomial. The formulation of the stiffness matrix of the finite elements was obtained from the Principle of Virtual Works and the process of analytical integration. In order to validate the presented formulation, a computational code was developed in Python programming language directed to the academic community, able to simulate the structural behavior of plates with geometry, loads and diverse bonding conditions. Finally, this paper presents three examples of different cases of plates, the results obtained being compared with those provided by other authors and specific software in the area.