Virtual element method applied to the linear elastic model.

• Ano de defesa: 2021
• Autor(a) principal: Enabe, Paulo Akira Figuti
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Equação de Poisson; Finite element method; Geotecnia; Linear elastic model; Método dos elementos finitos; Método dos elementos virtuais; Métodos numéricos; Modelo elástico linear; Poisson equation; Virtual element method
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/3/3144/tde-06012023-091154/

Considering the evolution of computers in the recent years and the notorious increase in the complexity of engineering problems, it is natural that new numerical methods come up in order to take part in this reality. The Virtual Element Method (VEM) main proposal is to generalize the classical Finite Element Method (FEM), being more permissive regarding the mesh discretization, embracing every convex and non-convex polygon. Using this large variety of polygons types brings as consequence the necessity of working with nonpolynomial functions. The method computes these functions implicitly, without the need of any quadrature formula. The Virtual Element Method was originally developed for the Poisson Equation and, for being relatively recent, the range of applications related to structural engineering is still very limited when compared to the Finite Element Method or the Generalized Finite Element Method. In this sense, there are a lot of possible paths that can be followed aiming to expand the state of art related to VEM. On this project, it is presented a methodology for the application of Virtual Element Method on the linear elastic rheological model. Consequently, comparisons with the classical FEM were made with respect the performance alongside simple and complex geometries, considering the particularities and characteristics of each method.