Reliability-Based Topology Optimization Using Mean-Value Second-Order Saddlepoint Approximation

[+] Author and Article Information
Dimitrios Papadimitriou

Mechanical Engineering Department, Oakland University, 2200 N. Squirrel Road, Rochester MI 48309

Zissimos P. Mourelatos

Mechanical Engineering Department, Oakland University, 2200 N. Squirrel Road, Rochester MI 48309

1Corresponding author.

ASME doi:10.1115/1.4038645 History: Received July 05, 2017; Revised November 16, 2017


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 is based on 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 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 computed using the adjoint approach. The accuracy of the proposed MVSOSA reliability method is demonstrated using a nonlinear mathematical example. The results are compared with the available mean value first-order saddlepoint approximation (MVFOSA) method and Monte Carlo simulation. Finally, the proposed RBTO-MVSOSA method for minimizing compliance-based probability of failure, is demonstrated using two 2D beam structures under random loading.

Copyright (c) 2017 by ASME
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