Boundary Element Method applied to decision-making problems involving geometric variabilities in topology optimization

Topology Optimization is a useful approach in the early stages of engineering design because it provides structural layout satisfying the performance requirements with the less material amount. Optimal topology solutions may not be unique for the same initial conditions. Local minima may be achieved depending on the design parameters. In such cases, deterministic criteria are often used for choosing the most convenient solution. In the present study, a probabilistic framework for obtaining additional information from the design is proposed, in order to improve the decision-making process. This methodology takes into consideration the less sensitive topology with respect to the geometric variabilities. The framework is based on a novel coupling of Boundary Element Method, Surface Response Method and Probability theory. Two engineering applications are utilized for demonstrating the proposed methodology. The results illustrate that the topology chosen based on the straightforward deterministic criterion may not be sufficient to determine a robust solution from the engineering point of view.