A Study On Reliability Based Structural Optimization

An ideal structure shall be designed in such a way that its performance requirements are satisfied during the design working life and in an economic way. The cost-effective criterion requires a perfect balance between cost and safety of a design as safety and economy are contradictory to each other. The balance can be achieved by minimizing the total cost of a structure while preserving a target reliability level for some limit state functions during a specified time horizon. Compared to the traditional deterministic optimization based on safety factors, reliability based optimization should be considered a more rational design philosophy because of its reasonable account of uncertainties in material properties, loading, boundary condition and geometry, and/or even mathematical representation of the structural model.The present study focuses on investigating efficient algorithmic approaches to structural reliability analysis and reliability based structural optimization, specifically developing an application-oriented software for large and realistic structures by combining both technologies with general finite element codes. Some further details is discussed on the total expected failure cost in cost-effective optimization model.The thesis has the following contents:Since a robust reliability analysis algorithm is an essential part of reliability based optimization, an improvement of reliability analysis algorithm is explored. The convergence difficulties of the first order reliability method in some cases is considered and an improved iterative scheme is proposed. Therefore, the applicability of the method is enlarged. To further reduce the computational cost (the number of the finite element analyses) for the large-scale structures, a modified two point function approximation method is utilized. Finally, the algorithms are integrated with general finite element analysis software in order to perform a reliability assessment of various practical structures.Reliability based optimization is essentially a two-level process that embeds the reliability analysis into the design optimization: Namely, the outer one is anoptimization for the design variables and the inner one for reliability analysis. This complex coupling leads to high computation cost and weak convergence stability, with many researchers seeking to improve its efficiency and robustness. Once the inner optimization for reliability is replaced by its first order necessary conditions, Korush-Kuhn-Tucker conditions, a mono-level approach is formed. After approximating the KKT conditions, a Sequential Approximate Programming strategy is developed and the successive solution of the sub-problems approaches the optimal solution of the initial problem. An approximate reliability index and its sensitivity with respect to the design variables instead of the true ones have been used for each sub-problem in order to reduce the computational cost. It has been proved that, for each approximate programming subproblem, if the current design is close to the optimum point and the approximate check point lies in the vicinity of the corresponding true point, the difference between the new approximation of the reliability and the normal linear Taylor expansion at the near-optimal design is of second order of the distance between the current design and optimum design. It is shown that the behavior of the approximate formulation proposed is similar to the conventional sequential approximate programming method. Furthermore, sensitivities of the approximate reliability index with respect to the design variables are derived for the application of the model. Finally, a custom version of ANSYS is created for the optimization of practical structures.System reliability of a structure is generally regarded as its capacity withstanding failure in terms of probability. It is estimated via analyzing a system composed of several interrelated elements with each representing a failure mode or a stable configuration. The sequential approximate programming approach is extensively develo...