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Monte Carlo simulation (MCS) is a useful tool for computation of probability of failure in reliability analysis. However, the large number of samples, often required for acceptable accuracy, makes it time-consuming. Importance sampling is a method on the basis of MCS which has been proposed to reduce the computational time of MCS. In this paper, a new adaptive importance sampling-based algorithm applying the concepts of first-order reliability method (FORM) and using (1) a new simple technique to select an appropriate initial point as the location of design point, (2) a new criterion to update this design point in each iteration and (3) a new sampling density function, is proposed to reduce the number of deterministic analyses. Besides, although this algorithm works with the position of design point, it does not need any extra knowledge and updates this position based on previous generated results. Through illustrative examples, commonly used in the literature to test the performance of new algorithms, it will be shown that the proposed method needs fewer number of limit state function (LSF) evaluations.

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Structural reliability theory allows structural engineers to take the random nature of structural parameters into account in the analysis and design of structures. The aim of this research is to develop a logical framework for system reliability analysis of truss structures and simultaneous size and geometry optimization of truss structures subjected to structural system reliability constraint. The framework is in the form of a computer program called RBO-S>S. The objective of the optimization is to minimize the total weight of the truss structures against the aforementioned constraint. System reliability analysis of truss structures is performed through branch-and-bound method. Also, optimization is carried out by genetic algorithm. The research results show that system reliability analysis of truss structures can be performed with sufficient accurately using the RBO-S>S program. In addition, it can be used for optimal design of truss structures. Solutions are suggested to reduce the time required for reliability analysis of truss structures and to increase the precision of their reliability analysis.

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One of the most important problems discussed recently in structural engineering is the structural reliability analysis considering uncertainties. To have an efficient optimization process for designing a safe structure, firstly it is required to study the effects of uncertainties on the seismic performance of structure and then incorporate these effects on the optimization process. In this study, a new procedure developed for incorporating two important sources of uncertainties in design optimization process of steel moment resisting frames, is proposed. The first source is related to the connection parameter uncertainties and the second one to seismic demand uncertainty. Additionally Mont Carlo (MC) simulation and a variance reduction technique (VRT) are utilized to deal with uncertainties and to reduce the corresponding computational cost. In the proposed procedure two design objectives are considered, which are structural weight and collapse prevention reliability index for a moment resisting frame in such a way that leads to a set of optimum designs with minimum weight and less possible amounts of sensitivity to connection parameters uncertainties and spectral acceleration uncertainty as seismic demand variation. Additionally, in this procedure the reliability index is computed considering all FEMA-356 performance acceptance criteria, the approach that has never been investigated in other studies. The efficiency of this approach is illustrated by exhibiting a set of optimum designs, in the form of both objective values and investigating nonlinear behavior of optimum designs compared with non-optimum designs. This procedure is introduced in this paper with emphasize on the collapse limit state and applying pushover analysis for studying the nonlinear behavior of structural elements.

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This paper presents a design process using a course grained parallel genetic algorithm to optimize three-dimensional steel moment frames by considering the axial force and biaxial bending moments interaction in plastic hinge formation. The objective function is to minimize the total weight of the structure subjected to the reliability constraint of the structural system. System reliability analysis is performed through the proposed Modified Latin Hypercube Simulation (M-LHS) Method. For optimization, a 3DSMF-RBO program is written in CSHARP programming language. The reliability analysis results show a large decrease in the number of simulation samples and subsequently a decrease in the execution time of optimization computation. The optimization results indicate that by considering interaction of the axial force and biaxial bending moments in plastic hinge formation rather than the only bending moment, to some extent increases the total weight of the designed structure.