Elaboração de algoritmo com formulação não linear geométrica para cálculo de treliças tridimensionais - Oliveira, Ricardo Lopes de (2015)
The development of new techniques and technologies improved the structural analysis and engineering design. The CAE technology (Computer Aided Engineering) takes the structural analysis to another level, possibiliting to simulate complex structures and achieve reliable results for design. One of the bases of this technology is the Finite Element Method (FEM). From this derives the Positional Finite Element Method, which is used in this work. The Positional FEM has a formulation based on the nodes positions, instead displacements as in conventional FEM formulations, resulting in a geometrically nonlinear descriptions of structural behaviour. This work consisted in the algorithm development for nonlinear elastic analysis of 3-D trusses using the Python programming language. Therefore, it was necessary to study concepts of structural stability analysis of structures, the positional FEM formulation characteristics, the concepts of geometrical nonlinearity, and also the chosen programming language. The developed algorithm was tested on different situations to demonstrate the effectiveness of the used formulation. Examples of 2-D and 3-D trusses were analyzed considering linear and nonlinear structural behavior. The achieved results in all cases analyzed were very close to those found in the literature, and practically identical to those found in the simulations using the MASTAN2 software. Based on the comparison results, it was verified the efficacy of the formulation studied and computationally coded for nonlinear elastic analysis of three-dimensional trusses.