Convergence Control And Engineering Application For Reliability Based Optimization Algorithm Of Structures

Reliability-based design optimization (RBDO) of structures combines the structural reliability analysis with the optimization design technique, and considers the balance between the optimal performance and structural safety. As a result, RBDO has distinct theoretical significance and wide application prospect, and it is the development frontier and research focus of computational mechanics. This paper conducts a series of works about the convergence control and engineering application of reliability optimization algorithm of structures. The main works are listed as follows.Firstly, the iterative equations in structurall reliability analysis and optimization design are highly nonlinear, and cannot converge to the expected stable solutions, but obtain instead the oscillating periodic solutions and even the chaotic solutions. The reasons of numerical instability are deeply analyzed based on the matrix eigenvalues of the advanced mean-value (AMV) iterative scheme for reliability evaluation. Further, the stability transformation method of chaos control is suggested to overcome the numerical instabilities of AMV iterative algorithm and sequence optimization and reliability analysis of RBDO. Several typical numerical example shows that the stability transformation method can effectively conque the non-convergence difficulties of iterative algorithms in reliability analysis and optimal design, and achieve the stable convergence solutions.Secondly, the representative five algorithms for reliability-based design optimization are introduced in detail, such as two-level approaches (i.e. RIA/reliability index approach and PMA/performance measure approach), the decoupled approaches (i.e. SORA and SAP/sequential approximate programming with PMA), and the mono-level approaches (SLA/single loop approach). Some benchmark examples are examined to compare the convergence, efficiency, accuracy and robustness of the five algorithms. In addition, the characteristics of uncertainty propagation in structural responses are discussed.Finally, reliability-based design optimization is extended to the practical application of engineering structures. In order to overcome the limitation of traditional software without the function of RBDO, the reliability analysis module with FORTRAN language is developed, and then is linked to the software ANSYS for finite element analysis, thus eventually reliability-based design optimization is realiazed in the general software platfrom. Numerical examples of frame, truss and plate structures validate the feasibility and effectiveness of RBDO. Moreover, the reliability based seismic optimal design of building structures is performed by combining the response spectrum methodof structural seismic analysis with reliability-based design optimization.