Development of a modular software based on the finite element method for incompressible problems

• Autor(a) principal: Lourenço, Rúben Miguel Borges
• Data de Publicação: 2018
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10773/27884
• topic: Finite element method; Incompressibility; Locking; Enhanced strain; Selective integration; MATLAB; Software development; Numerical simulation

The importance of numerical simulation in the engineering field makes relevant the development of computational tools, based on the Finite Element Method, to solve structural problems. However, the application of the classical Finite Element approach to incompressible (or near-incompressible) situations has been a source of numerical problems, such as volumetric locking. This Dissertation describes several formulations used in the analysis of incompressible problems, with focus on the four-node bi-linear quadrilateral element. Over the last decades special attention has been given to improve the performance of this element under incompressibility due to its computational effectiveness, making it attractive to be used in complex problems. The devised solutions are often targeted at treating the effects of volumetric locking, although some of them were originally targeted at the treatment of shear locking. In this context, the studied formulations were the selective integration approach, the B-bar method, the mixed (u/p) method and the enhanced strain method, which includes compatible and incompatible mode elements. In order to computationally implement these finite element formulations, a revision of the fundamental concepts and basic formulas of the classical method, and for each alternative formulation, is carried out. In the context of incompressibility, the underlying concept is presented and the problem of locking is described. The development of an in-house software, also in the context of this Dissertation, targeted at solving incompressible problems is discussed. Some important sub-routines and programming approaches are referred to with code examples. Finally, the quality of implementation and efficiency of the finite element formulations is evaluated by analyzing a series of benchmark tests, using the developed in-house software and comparing the results against the ones coming from a commercial finite element software.