A Linear Approach for Sizing Optimization of Isostatic Trussed Structures Subjected to External and Self-Weight Loads

The implementation of a new linear method to optimum weight design of trussed structures subjected to external and self-weight loads is proposed. Design variables are the cross-section areas of the members. Inequality constraints are written based on the force-method for isostatic structures considering maximum and minimum axial stress criteria. The novelty of the proposed approach is the benefit created from the combination of a linear inequality-constrained formulation with interior-point methods to tunnel the solution rapidly and monotonically towards the minimum value through feasible space, also eliminating the need to directly explore the finite-element model. To evaluate the performance of the algorithm, trusses are subject to optimization processes based on different techniques: (i) the proposed method, called by “indirect-method”; (ii) a design problem with constraint evaluated directly from the finite-element model; (iii) optimization based on Genetic Algorithms. The three methods are compared using trusses with 10, 37 and 1240 bar-elements. The results showed that the indirect-method was able to provide great performance for complex topologies, returning weight designs up to 70 times lighter in 1% of the time required by a Genetic Algorithm.