RELIABILITY-BASED TOPOLOGY OPTIMIZATION OF FAIL-SAFE STRUCTURES USING RESPONSE SURFACE METHOD

Traditional structures are more susceptible to local stiffness loss due to the lack of redundancy and problem of ignoring the influence of uncertain factors. This paper proposes an effective reliability-based topology optimization methodology for design problem of fail-safe structures under load uncertainty basing on response surface method, to improve the structural safety and ensure that the structure can still meet the service performance and reliability requirements even when local damage occurs. To this end, a double-loop reliability-based topology optimization model of minimizing the volume fraction while satisfying the probabilistic compliance constraint is established, in which the inner loop is used for reliability analysis and the outer loop is used for topology optimization. To solve the problem of high calculation cost of the derivative of response function with respect to random variables in reliability analysis, an explicit expression of response function with respect to random variables was established based on response surface method. The analytic sensitivity formulations of the response function with respect to design variables and random variables are deduced in detail, and the method of moving asymptotes (MMA) is used to solve the optimization problem. The response surface-based reliability design method is compared with the method based on analytic derivative, and Monte Carlo simulation is also carried out to verify the effectiveness and superiority of the proposed method, discussing the influence of standard deviation of random load on the optimization results. The optimization results show that the proposed method can effectively design the fail-safe structures that meets the specified reliability level, and the relative error of the reliability index of the optimized structures does not exceed 1.3%. In addition, the response surface-based reliability design method can save about 74% of the reliability analysis time compared with the reliability design method based on analytical derivative.