Desenvolvimento de programa computacional para otimização estrutural de treliças bidimensionais utilizando o Matlab

Abstract

Structural optimization is a valuable tool in the area of mechanical designs, as it enables obtaining the optimal configuration of a structure. This tool is already widely used in large companies and has been expanding even more over time. Although already being present in the major simulation software, the high cost of these software makes their use unfeasible in many cases. So, the objective of this work is to present a computational program for the implementation of a structural optimization algorithm in plane trusses. The structural analysis step is performed using the finite element method, with the aid of another program developed and published by the authors. The programming language used was matlab, because among other advantages, it has several specific optimization libraries, facilitating the computational implementation. The research presents a totally numerical approach, without the need to carry out practical experiments or simulations. Four optimization methods were studied: Lagrange multipliers, linear programming (LP), sequential linear programming (SLP) and interior point algorithm. For the application of optimization in trusses, the total mass of the structure was defined as an objective function, the areas of the bars as design variables, and the normal stresses and nodal displacements as constraints. After determining the optimization parameters, a code was developed to implement the studied algorithms. To validate the results, tests were carried out with two standards problems, a 3-bar structure and another with 10 bars, with a known analytical or numerical solution. Finally, the results obtained confirmed the accuracy and efficiency of the program, which can be used in structural projects and help in the development of new research in the field of optimization.