Reliability-based structural optimization with fatigue crack initiation constraint

To implement the proposed probabilistic optimization method, two numerical examples are considered: the Cantilever Beam and the Scratch Drive Actuator (SDA), which is widely used in micro electromechanical systems (MEMS). Simulation results show that using the proposed optimization methodology significantly improves the accuracy of calculation. These results show that the difference between FOSM and FORM is growing by increasing the prescribed reliability for design. Furthermore, it is confirmed that the strain based fatigue approach is a more accurate design optimization criterion, in which both high cycle and low cycle fatigue life requirements, along with the local elastic-plastic analysis, are considered. The simulation results are also verified by Monte Carlo method or by existing data from the literature. This thesis presents a probabilistic optimization methodology for reliable design of structures with fatigue crack initiation constraint. A commonly used design optimization methodology for engineering systems comprises deterministic modeling. However, the existence of uncertainties in physical quantities, such as manufacturing tolerances, material properties, applied loads and fatigue life cycles, requires the probabilistic optimization technique. Moreover, very little research has been conducted to incorporate the fatigue life constraint into design optimization. To overcome this limitation in optimization techniques, a new reliability-based design optimization is proposed considering fatigue strength or fatigue life as a requirement in performance function. In this method, a multivariable objective function is constructed along with nonlinear probabilistic constraints. The probabilistic constraints consist of probability failure as well as fatigue failure criteria. The corresponding fatigue criterion is defined as the crack initiation phase in both stress- and strain-based models, respectively. The elements required for the probabilistic fatigue life calculations are also addressed. The first-order second-moment method (FOSM), first-order reliability method (FORM), and Monte Carlo method are adopted to assess the probability failure based on the concept of reliability indices. This concept is used to approximate the proposed fatigue life performance function about the most probable point. The sequential quadratic optimization technique is employed and a code is developed to solve the nonlinear optimization problem. The illustrative examples explain that the developed probabilistic optimization is not only more accurate and efficient, but it is also more realistic than the deterministic approach. Since reliability and fatigue failure are two important integrated parts in MEMS design, this proposed method can be applied in design optimization of these devices. This kind of methodology in design optimization is very practical and beneficial to industries, particularly in MEMS.

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