Many engineering applications are characterized by implicit response functions that are expensive to evaluate and sometimes nonlinear in their behavior, making reliability analysis difficult. This paper develops an efficient reliability analysis method that accurately characterizes the limit state throughout the random variable space. The method begins with a Gaussian process model built from a very small number of samples, and then adaptively chooses where to generate subsequent samples to ensure that the model is accurate in the vicinity of the limit state. The resulting Gaussian process model is then sampled using multimodal adaptive importance sampling to calculate the probability of exceeding (or failing to exceed) the response level of interest. By locating multiple points on or near the limit state, more complex and nonlinear limit states can be modeled, leading to more accurate probability integration. By concentrating the samples in the area where accuracy is important (i.e., in the vicinity of the limit state), only a small number of true function evaluations are required to build a quality surrogate model. The resulting method is both accurate for any arbitrarily shaped limit state and computationally efficient even for expensive response functions. This new method is applied to a collection of example problems including one that analyzes the reliability of a microelectromechanical system device that current available methods have difficulty solving either accurately or efficiently.

Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions

PROTRACED COUNTERINSURGENCY: CHINESE COIN STRATEGY IN XINJIANG by MAJ J. Scott LaRonde, USA, 95 pages. In 1949, following the conclusion of its revolutionary war against the Chinese Nationalist forces, the People’s Liberation Army (PLA) peacefully occupied China’s western most province of Xinjiang. For nearly sixty years, the PLA has conducted a counterinsurgency against several, mostly Uyghur-led, separatist movements. Despite periods of significant violence, particularly in the early 1950s and again in the 1990s, the separatist forces have not gained momentum and remained at a level one insurgency. Mao ZeDeng is revered as a master insurgent and the father of Fourth Generation Warfare. Strategists in armies worldwide study his writings on revolutionary and guerilla warfare. This monograph concludes that Mao, as well as the communist leaders who followed him, was also successful at waging protracted counterinsurgency. For nearly sixty years, separatist movements in Xinjiang, Tibet, and Taiwan have all failed. This monograph analyzes the conflict in Xinjiang and concludes that the Chinese continue to defeat the separatist movement in Xinjiang through a strategy that counters Mao’s seven fundamentals of revolutionary warfare.

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Approved for Public Release; Distribution is Unlimited

This paper presents recent developments in efficient structural reliability analysis methods. The paper proposes an efficient, adaptive importance sampling (AIS) method that can be used to compute reliability and reliability sensitivities. The AIS approach uses a sampling density that is proportional to the joint PDF of the random variables. Starting from an initial approximate failure domain, sampling proceeds adaptively and incrementally with the goal of reaching a sampling domain that is slightly greater than the failure domain to minimize over-sampling in the safe region. Several reliability sensitivity coefficients are proposed that can be computed directly and easily from the above AIS-based failure points. These probability sensitivities can be used for identifying key random variables and for adjusting design to achieve reliability-based objectives. The proposed AIS methodology is demonstrated using a turbine blade reliability analysis problem.

Computational methods for efficient structural reliability and reliability sensitivity analysis

Published fatigue crack closure mechanisms are reviewed in the context of the following five ideas that have been developed over the past twenty years to explain the closure effects on near-threshold crack growth behaviour: (1) oxide, (2) asperity, (3) plasticity, (4) phase transformation and (5) viscous fluids. The first three have been considered as more important than the last two. Our analysis indicates that (a) there can be no contribution from plasticity to crack closure, (b) the crack closure contribution can be significant only if it is closed fully, which is reflected as an infinite slope in the load-displacement curve, (c) formation of oxide asperities from a fretting action is a random process and not a deterministic one, and therefore cannot explain the deterministic behaviour of the effect of load ratio on the threshold, and (d) the closure contribution from the asperities resulting from oxides or corrosion products,or surface roughness, it is less than 20% of what has been deduced based on the change in the slope of the load-displacement curves. Thus the analyses show that crack closure can exist, but its magnitude is either small or negligible. The critical evaluation of the literature data on (1) the threshold stress intensity variation with load ratio on many materials, and (2) and examination of the experimentally observed load-displacement curves confirm the above conclusions. Hence to rationalize the observed variations in the fatigue crack threshold with load ratio, we have proposed a new model. It postulates a requirement for two critical stress intensity parameters, namely ΔK th ∗ and K max ∗ , that must be satisfied simultaneously as the crack tip driving forces for fatigue crack growth. This requirement is fundamental to fatigue, since an unambiguous description of cyclic loads requires two independent load parameters. Several experimental results from the literature are presented in support of this postulation. Using these two critical parameters, the entire functional relationship between Kmax, ΔKth and R is explained without invoking an entrinsic factor, namely crack closure. In addition, for a given material and its crack tip environment, a unique relationship between ΔKth and Kmax exists that is independent of test methods used in determining thresholds. Finally, because of this two parameter requirement, all fatigue crack growth data need to be represented in terms of three-dimensional plots involving da/dN, ΔK and Kmax. For a two-dimensional representation, the data need to be transformed correctly, defining the net driving force involving both ΔK and Kmax parameters. The concepts presented are independent of whether crack closure exists or not, or even whether cracks exist or not.

A review of crack closure, fatigue crack threshold and related phenomena

Model verification and validation (VV thus, V&V cannot prove that a model is correct and accurate for all possible scenarios, but, rather, it can provide evidence that the model is sufficiently accurate for its intended use. Model V&V is fundamentally different from software V&V. Code developers developing computer programs perform software V&V to ensure code correctness, reliability, and robustness. In model V&V, the end product is a predictive model based on fundamental physics of the problem being solved. In all applications of practical interest, the calculations involved in obtaining solutions with the model require a computer code, e.g., finite element or finite difference analysis. Therefore, engineers seeking to develop credible predictive models critically need model V&V guidelines and procedures. The expected outcome of the model V&V process is the quantified level of agreement between experimental data and model prediction, as well as the predictive accuracy of the model. This report attempts to describe the general philosophy, definitions, concepts, and processes for conducting a successful V&V program. This objective is motivated by the need for highly accurate numerical models for making predictions to support the SSP, and also by the lack of guidelines, standards and procedures for performing V&V for complex numerical models.« less

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Concepts of Model Verification and Validation

Elastic-plastic finite element simulations of growing fatigue cracks in both plane stress and plane strain are used as an aid to visualization and analysis of the crack closure phenomenon Residual stress and strain fields near the crack tip are depicted by both color fringe plots and x-y graphs Development of the residual plastic stretch in the wake of a growing plane stress fatigue crack is shown to be associated with the transfer of material from the thickness direction to the axial direction Finite element analyses indicate that crack closure does occur under pure plane strain conditions The development of the residual plastic stretch in plane strain is shown to be associated with the transfer of material from the in-plane transverse direction to the axial direction This in-plane contraction also leads to the generation of complex residual stress fields The total length of closed crack at minimum load in plane strain is shown to be a small fraction of the total crack length, especially for positive stress ratios This suggests that experimental measurement of plane strain closure would be extremely difficult, and may explain why some investigators have concluded that closure does not occur in plane strain

Finite element visualization of fatigue crack closure in plane stress and plane strain

Probabilistic engineering analysis using the NESSUS software

The ability to quantify the uncertainty of complex engineering structures subject to inherent randomness in loading, material properties, and geometric parameters is becoming increasingly important in the design and analysis of structures. Probabilistic analysis provides a means to quantify the reliability of complex systems in such areas as aerospace and automotive industries. Since structural analysis predictions are often based on the results of commercial finite element (FEM) programs (e.g., ABAQUS, ANSYS, and MSC/NASTRAN), probabilistic analysis methods must be linked to such programs to achieve useful reliability results. The NESSUS probabilistic analysis software combines state-of-the-art probabilistic analysis algorithms with general-purpose analysis packages to compute the probabilistic response and the reliability of engineering structures. In this paper, the NESSUS capabilities are presented and demonstrated for several application problems. Introduction and Background Numerical simulation is now routinely used to predict the behavior and response of complex systems. Computational simulation is being increasingly used as performance requirements for engineering structures increase and as a means of reducing testing. Since structural performance is directly affected by uncertainties associated with models or in physical parameters and loadings, the development and Senior Research Engineer, Member AIAA Principal Engineer, Senior Member AIAA Principal Engineer, Member AIAA Staff Engineer, Senior Member AIAA Senior Research Engineer ABAQUS is a registered trademark of Hibbitt, Karlsson, and Sorensen, Inc. ANSYS is a registered trademark of ANSYS, Inc. MSC is a registered trademark of the McNeal-Schwendler Corporation NESSUS is a registered trademark is SwRI. application of probabilistic analysis methods suitable for use with complex numerical models is needed. The traditional method of probabilistic analysis is Monte Carlo simulation. This approach generally requires a large number of simulations to calculate low or high probabilities, and is impractical when each simulation involves extensive finite element computations. Approximate fast probability integration (FPI) methods have been shown to be many times more efficient than Monte Carlo simulation and can often provide sufficient accuracy for engineering predictions. In many situations, the advanced mean value (AMV) procedure, based on FPI, can predict the probabilistic response of complex structures with relatively few response calculations. These methods also provide probabilistic sensitivity measures indicating the input parameters that influence the reliability the most. Beginning with the development of the NESSUS probabilistic analysis computer program, Southwest Research Institute (SwRI) has been addressing the need for efficient probabilistic analysis methods for over fifteen years. NESSUS can be used to simulate uncertainties in loads, geometry, material behavior, and other user-defined random variables to predict the probabilistic response, reliability and probabilistic sensitivity measures of systems. NESSUS provides a built-in finite element structural modeling capability as well as interfaces to many commercially available finite element programs. This paper discusses the current capabilities of the NESSUS software and presents several application problems to demonstrate its effectiveness.

Ben H. Thacker

Papers

Concepts of Model Verification and Validation

Finite element visualization of fatigue crack closure in plane stress and plane strain

Probabilistic engineering analysis using the NESSUS software

Probabilistic engineering analysis using the NESSUS software

The effect of three-dimensional shape optimization on the probabilistic response of a cemented femoral hip prosthesis.