A reliability-based topology optimization (RBTO) approach is presented using a new mean-value second-order saddlepoint approximation (MVSOSA) method to calculate the probability of failure. The topology optimizer uses a discrete adjoint formulation. MVSOSA is based on a second-order Taylor expansion of the limit state function at the mean values of the random variables. The first- and second-order sensitivity derivatives of the limit state cumulant generating function (CGF), with respect to the random variables in MVSOSA, are computed using direct-differentiation of the structural equations. Third-order sensitivity derivatives, including the sensitivities of the saddlepoint, are calculated using the adjoint approach. The accuracy of the proposed MVSOSA reliability method is demonstrated using a nonlinear mathematical example. Comparison with Monte Carlo simulation (MCS) shows that MVSOSA is more accurate than mean-value first-order saddlepoint approximation (MVFOSA) and more accurate than mean-value second-order second-moment (MVSOSM) method. Finally, the proposed RBTO-MVSOSA method for minimizing a compliance-based probability of failure is demonstrated using two two-dimensional beam structures under random loading. The density-based topology optimization based on the solid isotropic material with penalization (SIMP) method is utilized.
Reliability-Based Topology Optimization Using Mean-Value Second-Order Saddlepoint Approximation
Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 5, 2017; final manuscript received November 16, 2017; published online January 10, 2018. Assoc. Editor: Nam H. Kim.
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Papadimitriou, D. I., and Mourelatos, Z. P. (January 10, 2018). "Reliability-Based Topology Optimization Using Mean-Value Second-Order Saddlepoint Approximation." ASME. J. Mech. Des. March 2018; 140(3): 031403. https://doi.org/10.1115/1.4038645
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