Estudo da minimização da massa de treliças tridimensionais

Abstract

Trusses are structures formed by bar connected at the ends. The minimization of the total mass of a truss is generally employed in engineering projects where light and resistant structures are sought. In this work the problem of minimization of the mass of tridimensional trusses with stress constraints is considered. To define this problem, we introduce the mathematical model of optimization and truss structures.We describe the finite element model for trusses and the nonlinear programming model for the optimization problem. To solve the proposed optimization problem, the Feasible Arc Interior Point Algorithm (FAIPA) is used. Numerical results obtained with FAIPA are presented for different types of three-dimensional structures.The optimal structures calculated with this technique show the usefulness of the problem solved in this work: the optimal structures use less material (they are cheaper) and are feasible since every bar verify the required stress constraint.