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There is randomness in both the applied loads and the strength of systems. Therefore, to account for the uncertainty, the safety of the system must be quantified using its reliability. Monte Carlo Simulation (MCS) is widely used for probabilistic analysis because of its robustness. However, the high computational cost limits the accuracy of MCS. Smarslok et al. [2010] developed an improved sampling technique for reliability assessment called Separable Monte Carlo (SMC) that can significantly increase the accuracy of estimation without increasing the cost of sampling. However, this method was applied to time-invariant problems involving two random variables. This paper extends SMC to problems with multiple random variables and develops a novel method for estimation of the standard deviation of the probability of failure of a structure. The method is demonstrated and validated on reliability assessment of an offshore wind turbine under turbulent wind loads.

An experimental study was conducted to evaluate the effect of water absorption on tensile and fatigue behaviors of an impact-modified short glass fiber polyamide-6 and a short glass fiber polybutylene terephthalate. Specimens were prepared in the longitudinal and transverse directions with respect to the injection mold flow direction and immersed in water. Kinetics of water absorption was studied and found to follow the Fick's law. Tensile tests were performed at room temperature with specimens in the longitudinal and transverse directions and with various degrees of water absorption. Mathematical relations were developed to represent tensile properties as a function of water content. Load-controlled tension-tension fatigue tests were conducted in both longitudinal and transverse directions and correlations between tensile and fatigue strengths were obtained. Specimen fracture surfaces were also microscopically studied and mechanisms of tensile and fatigue failures were identified.

An experimental study was conducted to evaluate the variable amplitude fatigue behavior of a neat polymer (polypropylene impact co-polymer) and a polymer composite made of polybutylene terephthalate (PBT) with 30 wt% short glass fibers. Fatigue tests were conducted on un-notched and notched specimens at room temperatures. Plate-type specimens were prepared in the transverse direction with respect to the injection mold flow direction and a circular hole was drilled in the center of notched specimens. Two-step loadings (high-low and low-high) tests at two damage ratio of 0.2 and 0.5 at stress ratios of R = 0.1 and -1 were conducted to investigate load sequence effects and prediction accuracy of the linear damage rule. Different behaviors were observed for unreinforced and short glass fiber reinforced polymers under the two-step loading tests.

This article presents an approach for comparing alternative repairable systems and calculating the value of information obtained by testing a specified number of such systems. More specifically, an approach is presented to determine the value of information that comes from field testing a specified number of systems in order to appropriately estimate the reliability metric associated with each of the respective repairable systems. Here the reliability of a repairable system will be measured by its failure rate. In support of the decision-making effort, the failure rate is translated into an expected utility based on a utility curve that represents the risk tolerance of the decision-maker. The algorithm calculates the change of the expected value of the decision with the sample size. The change in the value of the decision represents the value of information obtained from testing.

A Reliability-Based Design Optimization (RBDO) method for multiple failure regions is presented. The method uses a Probabilistic Re-Analysis (PRRA) approach in conjunction with an approximate global metamodel with local refinements. The latter serves as an indicator to determine the failure and safe regions. PRRA calculates very efficiently the system reliability of a design by performing a single Monte Carlo (MC) simulation. Although PRRA is based on MC simulation, it calculates “smooth” sensitivity derivatives, allowing therefore, the use of a gradient-based optimizer. An “accurate-on-demand” metamodel is used in the PRRA that allows us to handle problems with multiple disjoint failure regions and potentially multiple most-probable points (MPP). The multiple failure regions are identified by using a clustering technique. A maximin “space-filling” sampling technique is used to construct the metamodel. A vibration absorber example highlights the potential of the proposed method.

Importance Sampling is a popular method for reliability assessment. Although it is significantly more efficient than standard Monte Carlo simulation if a suitable sampling distribution is used, in many design problems it is too expensive. The authors have previously proposed a method to manage the computational cost in standard Monte Carlo simulation that views design as a choice among alternatives with uncertain reliabilities. Information from simulation has value only if it helps the designer make a better choice among the alternatives. This paper extends their method to Importance Sampling. First, the designer estimates the prior probability density functions of the reliabilities of the alternative designs and calculates the expected utility of the choice of the best design. Subsequently, the designer estimates the likelihood function of the probability of failure by performing an initial simulation with Importance Sampling.

With improvements in casting technology, cast iron can be an alternative to steel in some applications due to its similar strength. One objective of this study was to analyze cast iron data obtained from the literature and evaluate predictive correlations between its tensile, microstructural, and fatigue properties. Reasonably good correlation of tensile strength and yield strength were found with hardness. However, fatigue strength could not be correlated with hardness or tensile properties. Another objective of this study was to evaluate tensile and compressive means stress effects on fatigue behavior of 120-90-02 ductile cast iron experimentally, as well as analytically by using predictive models. Mean stress levels were chosen such that R ratios in load-controlled tests were −7, −3, −1, 0, 1/3, 0.5, and 0.75. Modified Goodman, Smith-Watson-Topper, FKM and the Fatemi-Socie mean stress parameters were used to account for the mean stress effect on fatigue life.

The strain-life approach is now commonly used for fatigue life analysis and predictions in the ground vehicle industry. This approach requires the use of material properties obtained from strain-controlled uniaxial fatigue tests. These properties include fatigue strength coefficient (σf′), fatigue strength exponent (b), fatigue ductility coefficient (εf′), fatigue ductility exponent (c), cyclic strength coefficient (K′), and cyclic strain hardening exponent (n′). To obtain the aforementioned properties for the material, raw data from stable cyclic stress-strain loops are fitted in log-log scale. These data include total, elastic and plastic strain amplitudes, stress amplitude, and fatigue life. Values of the low cycle fatigue properties (σf′, b, εf′, c) determined from the raw data depend on the method of measurement and fitting. This paper examines the merits and influence of using different measurement and fitting methods on the obtained properties.

Reliability analysis of engineering structures such as bridges, airplanes, and cars require calculation of small failure probabilities. These probabilities can be calculated using standard Monte Carlo simulation, but this method is impractical for most real-life systems because of its high computational cost. Many studies have focused on reducing the computational cost of a reliability assessment. These include bootstrapping, Separable Monte Carlo, Importance Sampling, and the Combined Approximations. The computational cost can also be reduced using an efficient method for deterministic analysis such as the mode superposition, mode acceleration, and the combined acceleration method. This paper presents and demonstrates a method that uses a combination of Sobol quasi-random sequences and bootstrapping to reduce the number of function calls. The study demonstrates that the use of quasi-random numbers in conjunction bootstrapping reduces dramatically computational cost.

The Combined Approximation (CA) method is an efficient reanalysis method that aims at reducing the cost of optimization problems. The CA uses results of a single exact analysis, and it is suitable for different types of structures and design variables. The second author utilized CA to calculate the frequency response function of a system at a frequency of interest by using the results at a frequency in the vicinity of that frequency. He showed that the CA yields accurate results for small frequency perturbations. This work demonstrates a methodology that utilizes CA to reduce the cost of Monte Carlo simulation (MCs) of linear systems under random dynamic loads. The main idea is to divide the power spectral density function (PSD) of the input load into several frequency bins before calculating the load realizations.

Inflatable space structures can have lower launching cost and larger habitat volume than their conventional rigid counterparts. These structures are made of composite laminates, and they are flexible when folded and partially inflated. They contain light-activated resins, and can be cured with the sun light after being inflated in space. A spacecraft can burst due to cracks caused by meteor showers or debris. Therefore, it is critical to identify the important fracture failure modes, and assess their probability. This information will help a designer minimize the risk of failure and keep the mass and cost low. This paper presents a probabilistic approach for finding the required thickness of an inflatable habitat shell for a prescribed reliability level, and demonstrates the superiority of probabilistic design to its deterministic counterpart.