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Probabilistic studies can be prohibitively expensive because they require repeated finite element analyses of large models. Re-analysis methods have been proposed with the premise to estimate accurately the dynamic response of a structure after a baseline design has been modified, without recalculating the new response. Although these methods increase computational efficiency, they are still not efficient enough for probabilistic analysis of large-scale dynamic systems with low failure probabilities (less or equal to 10-3). This paper presents a methodology that uses deterministic and probabilistic re-analysis methods to generate sample points of the response. Subsequently, tail modeling is used to estimate the right tail of the response PDF and the probability of failure a highly reliable system. The methodology is demonstrated on probabilistic vibration analysis of a realistic vehicle FE model.

The overstress probe fatigue testing method, although codified to characterize fatigue strength, is poorly understood. While it yields data confirming whether minimum fatigue strength may be met, it does not directly reveal the mean fatigue strength. Procedures for conducting the test are somewhat arbitrary and rely on fitting a 3-parameter Weibull model. In this paper, a Monte Carlo procedure is developed to simulate the overstress probe test. The effect of various parameters used in the test is also discussed. A comparison is made between Weibull and Gaussian models. Suggestions for conducting the overstress probe test are provided.

Fatigue strength mean and standard deviation may be estimated by the Probit and 2-Point test methods. In this paper, methodologies for conducting the tests are developed and results from Monte Carlo simulation are presented. The results are compared with those from concurrent testing with the staircase method. While the Probit and 2-Point methods are intuitively attractive, their results are significantly different from those from the staircase method. The latter remains the best of the three.

The staircase fatigue test method is a well-established, but poorly understood probe for determining fatigue strength mean and standard deviation. The sensitivity of results to underlying distributions was studied using Monte Carlo simulation by repeatedly sampling known distributions of hypothetical fatigue strength data with the staircase test method. In this paper, the effects of the underlying distribution on staircase test results are presented with emphasis on original normal, lognormal, Weibull and bimodal data. The results indicate that the mean fatigue strength determined by the staircase testing protocol is largely unaffected by the underlying distribution, but the standard deviation is not. Suggestions for conducting staircase tests are provided.

Springback is one of the main detrimental factors affecting the dimensional quality of stamped parts in automotive industry. Accurate determination of springback is vital to the design of tools used in the automotive sheet stamping operations. Generally the least distance from a point on a stamped part to the die surface is used as a measurement of the amount of springback. This paper presents a reversed finite element method for assessing the springback of stamped parts. First, the point cloud (coordinate measurement data) scanned from actual stamped parts is triangulated to generate a finite element mesh with triangles. Contrary to the traditional finite element mesh from an existing CAD model, this is a reversed process in which the actual CAD data for the surface is unknown. Then finite element method is utilized to determine the deformation the stamped part needed to conform to the die surface using the minimum amount of work.