Análise não linear geometrica de estruturas reticuladas através de um algoritmo de diferenciação automática

• Autor(a) principal: Santos, Danilo Menezes
• Data de Publicação: 2019
• Tipo de documento: Trabalho de conclusão de curso
• Idioma: por
• Título da fonte: Repositório Institucional da UFS
• Texto Completo: http://ri.ufs.br/jspui/handle/riufs/15849
• topic: Engenharia Civil; Ensino de engenharia civil; Derivação automática; Análise estrutural não linear; Mecânica computacional; Não linearidade geométrica; Treliça plana; Pórtico plano; Automatic differentiation; Nonlinear structural analysis; Computational mechanics; Geometric nonlinearity; Plane truss; Plane frames; CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE::ANALISE FUNCIONAL NAO-LINEAR

This work presents the development of an algorithm for automatic differentiation in python. Implemented through the reverse and forward mode, it is able to differentiate functions introduced through strings and functions. In order to verify its validity, the code was used to obtain the local stiffness matrix of trusses and frame planes in linear and nonlinear geometrically analyzes, through energy methods. The development of the structural theory was carried in a Total Lagrangian approach, and the results were compared with examples found in the technical literature. The results obtained were satisfactory to the examples analyzed as much for the stiffness matrix as for nodal displacements and internal forces.