Aplicação do método das diferenças finitas para a obtenção da deflexão de placas delgadas ortotrópicas bi-apoiadas

• Autor(a) principal: Andreotti, Ricardo Augusto
• Data de Publicação: 2018
• Tipo de documento: Trabalho de conclusão de curso
• Idioma: por
• Título da fonte: Repositório Institucional da UTFPR (da Universidade Tecnológica Federal do Paraná (RIUT))
• Texto Completo: http://repositorio.utfpr.edu.br/jspui/handle/1/6394
• topic: Equações diferenciais parciais; Diferenças finitas; Placas (Engenharia); Differential equations, Partial; Finite differences; Plates (Engineering); CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE::EQUACOES DIFERENCIAIS PARCIAIS

In this work we present the numerical solution, by Finite Differences Method, of the fourth-order Partial Differential Equation that controls the bi-supported orthopropic thin plates’ deflection when subjected to an uniformly distributed load. This method transforms the partial differential equation into a system of linear equations. In order to obtain the solution of that system, the Gauss-Seidel iterative solution method was implemented. Finally, to facilitate the interpretation and reading of the results, a program compiled in MatLab R ’s language was developed, using its tool App Designer. The obtained results were compared with a commercial software, based on Finite Element Method. For comparison purposes, a geometric relations between length (L) and width (b) was used to compared both results, being L/b = 1 and L/b = 2, with error order of 0.59% and 0.84%, respectively. The relative error between the two results were relatively low.