Linear and nonlinear hirarchical plate models and a posteriori kinematical error estimator.

• Ano de defesa: 2015
• Autor(a) principal: Simões, Eduardo Tenório
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Erro na hipótese cinemática; Error in the kinematical hypothesis; Geometrical nonlinear hierarchical shell model; Hierarchical plate models; Método dos elementos finitos; Modelo hierárquicos de casca geométricamente não linear; Modelos hierárquicos de placa
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/3/3144/tde-26072016-151855/

This study explores the use of hierarchical models to represent three-dimensional solids in a computationally inexpensive way. First, it is investigated the choice of the finite element spaces and how it affects the convergence in relation to the thickness parameter. It was studied three different models. It was shown that the best lowest order suitable combination of spaces grows in all fields as the model order is enriched. After, it is presented a theory to evaluate the error in the discretization and the kinematical hypothesis. It is shown that the implemented error in discretization technique is capable of capturing the boundary layer in automated way for any model. It is also given a posteriori error procedure for kinematical hypothesis. The method is based on the equilibrium error of higher order models. Good results are shown. In the end, it is presented a geometrical nonlinear hierarchical shell model and its discretization. It is shown that the model succeeds in representing the three-dimensional solution when compared with solid elements in a commercial code.