Otimização topológica de treliças hiperestáticas considerando incertezas

Abstract

Although truss topology optimization has been studied since the first researches on structural optimization, problems with buckling constraint still a challenge to scientific community because of discontinuity of the derivative of critical loads and difficulty in defining buckling lengths during optimization. In this context, there is a limited number of studies that considers uncertainties and progressive colapse in the truss optimization problem. This leads to optimal isostatic responses, going against one of the minimum requirements to prevent the progressive collapse by international norms. Redundancy allows loads redistribution after an unexpected element failure, which is essential for the safety of structures. Thus, this research aimed to compare two optimization formulations based on uncertainties: Reliability Based Design Optimization (RBDO) e Risk Optimization (RO), applied to truss topology problem with buckling constraints considering the ability of load redistribution of redundant structures. A deterministic optimization code (Firefly) was developed, which was connected with reliability algorithms considering local and global instabilities. Mechanical models were represented by a non-linear geometric finite element method. Results shown that even considering load redistribution of hyperstatic structures, the RBDO formulations always find isostatic structures as best solution. However, the RO formulation included hyperstatic topologies within results. This is possible by differentiating the cost of direct collapse of isostatic structures, and the cost of sequential collapse of hyperstatic structures.