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research-article

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
dpapadimitriou@oakland.edu

Zissimos P. Mourelatos

Mechanical Engineering Department, Oakland University, 2200 N. Squirrel Road, Rochester MI 48309
mourelat@oakland.edu

1Corresponding author.

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

Abstract

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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