Topology optimization with Geometrical Nonlinearity Considering Uncertain loading Condition

The present study proposes a topology optimization method considering finite deformation for loading uncertainty. The loading angle is assumed to be uncertain as a condition. The objective is to minimize expectation and standard deviation of end-compliance obtained by means of a Total Lagrangian finite element formulation. In this case, an analytical estimation of the expectation and the standard deviation is not allowed. In order to solve this problem, we approximate the end-compliance by a Taylor series expansion and derive the mathematical formulation. In this approach, the second derivative of the objective function is necessary to keep the accuracy in sensitivity. This phenomenon is investigated in terms of numerical validations. Finally, some numerical examples demonstrate the usefulness of the proposed method.