Reliability-based Topology Optimization of Trusses with Stochastic Stiffness

A new method is proposed for reliability-based topology optimization of truss structures with random geometric imperfections and material variability. Such imperfections and variability, which may result from manufacturing processes, are assumed to be small in relation to the truss dimensions and mean material properties and normally distributed. Extensive numerical evidence suggests that the trusses, when optimized in terms of a displacement-based demand metric, are characterized by randomness in the stiffness that follow the Gumbel distribution. Based on this observation, it was possible to derive analytical expressions for the structural reliability, enabling the formulation of a computationally efficient single-loop reliability-based topology optimization algorithm. Response statistics are estimated using a second-order perturbation expansion of the stiffness matrix and design sensitivities are derived so that they can be directly used by gradient-based optimizers. Several examples illustrate the accuracy of the perturbation expressions and the applicability of the method for developing optimal designs that meet target reliabilities

Sensitivity of sample for simulation-based reliability analysis methods

In structural reliability analysis, simulation methods are widely used. The statistical characteristics of failure probability estimate of these methods have been well investigated. In this study, the sensitivities of the failure probability estimate and its statistical characteristics with regard to sample, called 'contribution indexes', are proposed to measure the contribution of sample. The contribution indexes in four widely simulation methods, i.e., Monte Carlo simulation (MCS), importance sampling (IS), line sampling (LS) and subset simulation (SS) are derived and analyzed. The proposed contribution indexes of sample can provide valuable information understanding the methods deeply, and enlighten potential improvement of methods. It is found that the main differences between these investigated methods lie in the contribution indexes of the safety samples, which are the main factors to the efficiency of the methods. Moreover, numerical examples are used to validate these findings. © This work is licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Reliability-based design with system reliability and design improvement

This thesis focuses on developing a methodology for accurately estimating series system probability of failure. Existing methods for series system based design optimization are not that accurate because they assign reliability to each failure mode; as a result complete system reliability goes down. According to method proposed in this work, the user will assign required system reliability at the start and then optimizer will apportion reliability to every failure mode in order to meet required system reliability level. Detlevson second order upper bounds are used to estimate system probability of failure. Several examples have been shown to verify the results obtained --Abstract, page iii