Robust Structural Topology Optimization

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Topology optimization is a powerful tool for goal-oriented generative design of multifunctional engineering structures. In contrast to size and shape optimization approaches that work with a finite-dimensional parametric geometry model, topology optimization algorithms can, in theory, search for the best solution in an infinite-dimensional space of possible topologies. Even though significant advances have been made in the field of topology optimization, most methods currently in use are based on the implicit assumption of determinism, i.e., the loading conditions, boundary conditions and material constitutive properties are assumed to be known precisely. The proposed research program will address the key fundamental, theoretical issues and computational challenges associated with the development of efficient algorithms for robust structural topology optimization. The methodology used in this project will involve efficient numerical schemes for solving the stochastic linear elasticity equations coupled with level-set methods. Advances made in this research program will enable designers to fully exploit the potential of advanced additive manufacturing techniques for a broad range of practical engineering applications where performance robustness is a crucial design requirement.