Elementos finitos triangulares compatíveis na análise estrutural de lajes finas

Pedro Miguel de Matos

Key information

Authors:

Pedro Miguel de Matos (Pedro Miguel de Matos Sanches)

Supervisors:

Carlos Manuel Tiago Tavares Fernandes (Carlos Manuel Tiago Tavares Fernandes)

Published in

11/24/2011

Abstract

The basis of linear elasticity theory were grounded about two centuries ago. Its generality allowed the establishment of several technical theories, fundamental in several branches of engineering. From this set the moderately thick plate theory, consistently obtained from the three-dimensional continuum equations by imposing static and kinematic restrictions. Thin plate theory is then obtained as a particular case of the first. The Finite Element Method has proved to be an important tool in this type of plate. It?s constant development aims for solutions, as much as possible, near the exact ones. In this context, convergence analysis is an importante step in the formulation and implementation?s assessment of finite elements. In this dissertation the formulation was revised and four classic compatible triangular finite elements were implemented, viz., the T21, the T18, the HCT12 and the HCT9. In particular, the equivalent nodal force vectors due to distributed effective loads and to linear temperature variations in the thickness of the element were derived. The numerical examples were chosen so that the results were comparable with the exact solutions given in the bibliography. The implementation was made in MATLAB (2010) environment. In the conclusions the convergence of several entities, their errors relatively to the exact solutions and the times spent by computational processing with each element were analyzed. Generalized stress diagrams and deformed shapes were also observed and compared with the exact solution.