Improved Stability Transformation Method to Control Convergence of Structural Performance Measure Approach

Performance measure approach (PMA) is a method for evaluating the probabilistic constraints in reliability-based design optimization of structures. The advanced mean-value (AMV) method is suitable for PMA, simply and efficiently. The iterative AMV scheme could be yielded to unstable solutions such as periodic-oscillation and chaos for highly nonlinear performance functions. In the present paper, an improved stability transformation method (ISTM) is proposed for appropriate convergence of nonlinear performance functions. This iterative approach has been established based on a suitable stepsize between one and zero that is simply calculated on the basis of the new results of AMV scheme and the previous results of the improved stability transformation iterative formula. The descent condition was applied in the iterative sequences of the ISTM to achieve stable convergence. The results of several nonlinear performance functions in reliability-based design optimization demonstrate that the ISTM is laded to control instability solutions of PMA and also, it is more robust than AMV and more efficient that stability transformation method in structural problems with nonlinear performance functions.