Investigação via método das diferenças finitas em estruturas bidimensionais de barras com análise não linear

Abstract

Advances in materials technology have allowed the development of increasingly lighter and slender structural elements. However, in certain cases, considering that these elements are subject to small displacements is unrealistic. Therefore, it is crucial that structural engineers have specific knowledge that allows them to carry out nonlinear geometric analyses. This work consists in computationally investigating the finite difference method formulation for geometric nonlinear analysis of two-dimensional bar structures. In the formulation, the unknowns of the problem are the vertical positions. Furthermore, the secant method is used for the iterative solution of the nonlinear system of equations. The nonlinear geometric analysis of structures finds application in the civil, mechanical and aerospace industries, enabling the resolution of various structural problems. These problems include dealing with the occurrence of structural instabilities, difficulty in achieving convergence in these systems, modeling nonlinear materials, analyzing large displacements, and finally, interpreting the results