Reliability-based design optimization of cantilever beams under fatigue constraint

This paper presents an optimization methodology in reliability design of a prismatic cantilever beam with a point load applied at the tip. In this methodology, the constraints consist of probability failures as well as fatigue failure criteria. The first-order second-moment and first-order reliability methods are adopted to assess the probability failure based on the concept of reliability indices. The corresponding fatigue criterion is defined as the crack initiation phase in both stress and strain models, respectively. The elements required for the probabilistic fatigue life calculations are then discussed. In this optimization model, the total weight of the beam is considered as the objective function. However, all geometries, applied loads, and material properties are considered as random variables. The sequential quadratic optimization technique is implemented and a code is developed to solve the nonlinear optimization problem. Results show that using the proposed optimization methodology significantly improves the accuracy of calculation in comparison with using the conventional deterministic analysis. We also conclude that the strain-based fatigue criterion is more realistic than the traditional stress-based analysis. Finally, the Monte Carlo simulation is conducted to validate the results in each case.