Reliability-based topology optimization of geometrically nonlinear structures with loading and material uncertainties

A reliability-based design optimization method is developed to apply to topology design problems. Using the total Lagrangian formulation, the spatial domain is discretized using Mindlin plate elements with the von Karman strain-displacement relation. The topology optimization problem is reformulated as a volume minimization problem having probabilistic displacement constraints using the performance measure approach. For the efficient computation of the sensitivity with respect to the design and random variables, an adjoint variable method for geometrically nonlinear structures is employed. Since the converged tangent stiffness is available from the response analysis, the computing cost for the sensitivity analysis is trivial. The uncertainties such as material property and external loads are considered. Numerical results show that the developed sensitivity analysis method is very efficient and the topology optimization method effectively yields reliable designs. (C) 2004 Elsevier B.V. All rights reserved.