Exploratory analysis of the finite cell method in structural applications

• Autor(a) principal: Carvalheiro, Márcio Pinheiro
• Data de Publicação: 2017
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10773/23871
• topic: Finite Cell Method (FCM); Finite Element Method (FEM); Elastoplastic analysis

The Finite Element Method (FEM) is a structural analysis method that appeared in the last century, being still to this day the reference in the modelling and numerical simulation elds. However, as any approximation method, there are a few limitations in the FEM. The di culty in generating a nite element mesh represents one of these limitations. It's precisely in response to this limitation that emerges the Finite Cell Method (FCM). The possibility of creating analysis elements inserted in perfectly structured meshes allows the bypass of the need of the mesh to conform to the boundaries of the domain, situation which happens in the FEM and that can alter the accuracy of the obtained results. In this context, the goal of this work was an implementation, in Matlab, of a structural analysis code based on the FCM for twodimensional structural problems, in both linear and non-linear (elastoplastic analysis) regimes. To contextualize the developed tool, the mathematical formulations and analysis algorithms, for both methods, are initially presented. Afterwards, based on some reference benchmarks, the reliability of the FCM implementation is evaluated, in terms of stress and displacement determination. It was concluded that the developed computational product can achieve the intended results with some reliability. In the results context, the in uence of some parameters inherent to FCM was also evaluated. As result from this work, a structural analysis tool based on the FCM, for linear and material non linear analysis and for small strains, was successfully created. The developed program can be used for investigation and pedagogical purposes, with the intention that it may serve as a foundation for future developments. The function created in the context of this work are available at https://fcmua.wordpress.com, where more information on the developed code can be found.