In this paper, Reliability-Based Design Optimization (RBDO) is carried out using two distinct ways, the Reliability Index Approach (RIA) and the Performance Measure Approach (PMA). It has been theoretically explained that RIA shows instability but PMA is stable and efficient in identifying a probabilistic failure mode in the RBDO process. The PMA is compared to RIA with regard to the stable evaluation of a probabilistic constraint in the RBDO using a large deformation problem. In addition, an efficient Design Sensitivity Analysis (DSA) method is developed to support reliability analysis and reliability-based optimization for a hyper-elastic structure with factional contact using a meshfree method. A numerical result is presented to demonstrate the comparative study between RIA and PMA.

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