Implementação computacional e analise crítica de elementos finitos de placas

Abstract

This masters thesis describes the computacional implementation of several plate finite elements based in the Kirchho theory, for thin plates, and Reissner-Mindlin theory, that is applicable to plates of any thickness. It presents a brief discussion about the formulations for the mathematical and discrete models based in these theories, showing their main differences and particularities, as well as the need of the use of special techniques for the use of the Reissner-Mindlin theory in the studyof thin plates. Among the several finite elements for analysis of plates based on the Kirchhoff theory, it has been implemented the rectangular elements developed by Melosh, Zienkiewicz and Cheung (MZC) and by Bogner, Fox and Schmit (BFS) and the triangular elements developed by Cheung, King and Zienkiewicz (CKZ) and by Cowper, Kosko, Lindberg and Olson (Cowper); the elements based on the Reissner-Mindlin theory chosen for the analysis of thick plates were the quadrilaterais of fournode (Q4), eight node (Q8), nine node (Q9), nine node Heterosis, developed by Hughes and Cohen (Q9H), and the triangular of three node (T3), of six node (T6) and the of ten node (T10); for use of the Reissner-Mindlin theory in the modelling of thin plates, are adopted the Reduced Integration or Selective Integration with the elements quadrilaterais mentioned previously and the technique of Substitute Shear Strain Fields with the elements Q4, Q8, Q9 and T6. The implementation of these models was made in the numerical nucleus of INSANE (INteractive Structural ANalysis Environment) that is a system developed according to the Object Oriented Programming (OOP) paradigm using the JAVA language. This implementation is detailed through the use of UML (Unified Modelling Language) diagrams, where the several classes and interfaces used in the numerical nucleus are presented. To know the implemented elements better, mesh tests and convergence studies, besides several numerical simulations, are presented.