Reliability-based optimization of structural topologies using artificial neural networks

In this paper, a topology optimization approach is presented, where uncertain load and uncertain material parameters are considered. The concept of compliance minimization, i.e., stiffness maximization, is applied based on a plane stress finite element formulation. In order to take uncertain structural load parameters and uncertain material behavior into account, the topology optimization is embedded into a reliability-based design optimization approach. Uncertain structural parameters and design variables are quantified as random variables, intervals and probability boxes (p-boxes). This allows to consider aleatory and epistemic uncertainties by means of polymorphic uncertainty models within the topology optimization. Solving optimization problems with random variables, intervals and p-boxes leads to a high computational effort, because the objective functions and constraints have to evaluated millions of times. To speed up the optimization process, the finite element simulation of the topology optimization is replaced by artificial neural networks. This includes the topology dependent maximal stresses and displacements of the structure, which are used as constraints, and also the material density distribution inside the design domain. The reliability-based optimization of structural topologies approach is applied to a cantilever structure and a single span girder.