The virtual element method for wheel-rail contact problems.

• Ano de defesa: 2021
• Autor(a) principal: Moherdaui, Tiago Fernandes
• 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: Computational mechanics; Contact mechanics; Ferrovias; Finite element method; Mecânica dos sólidos; Método dos elementos finitos; Métodos numéricos; Virtual element method; Wheel-rail interface
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/3/3144/tde-04032022-120650/

The virtual element method was first published in 2012 and has since been explored for a wide range of applications. The method consists of a generalization of the finite element method for general polygonal elements by introducing a novel procedure to define the interpolation function spaces. These spaces are designed to contain a full polynomial subspace (which defines the elements order), along with additional nonpolynomial functions. This space is built upon a determined set of degrees of freedom, deliberately devised so that the problems weak form and stiffness matrix are computable without full knowledge of the nonpolynomial functions. The projection of those onto the polynomial subspace and an approximation for terms arising from said projections residual are enough to ensure the methods consistency and stability. Thus, leading to a more versatile method regarding element geometry. The present work prospects the virtual element method as a tool for wheel-rail contact problems. This is achieved through a series of applications of increasing complexity, aiming to compare the method to the finite elements in different scenarios. The first application compares both methods convergence characteristics using a scalar field problem. The second compares them for plane linear elasticity, a two-component vector field problem. The third introduces the Node-toSegment contact discretization technique, comparing both methods, and the analytic solution, for a Hertzian contact problem. Finally, the fourth application compares both methods for a simple wheel-rail contact problem.