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A unified continuum formulation for design sensitivity analysis of critical loads is developed for nonlinear structural systems that are subjected to conservative loading. Sizing design variables such as cross-sectional areas of beam or truss design components and thicknesses of plate or membrane design components are included in development of the continuum design sensitivity analysis method. For nonlinear structural analysis, both geometric and material nonlinear effects are considered. The total Lagrangian formulations for incremental equilibrium analysis and one-point linear eigenvalue problems for stability analysis are utilized. Numerical methods are presented to evaluate design sensitivity expressions, using structural analysis results from established finite element codes. For design sensitivity of the estimated critical load, a continuum design sensitivity analysis method is developed using the lowest eigenvalue of the linear eigenvalue problem.

Reliability-based design optimization (RBDO), which includes design optimization in design space and inverse reliability analysis in standard normal space, has been recently developed under the assumption that all input variables are independent because it is difficult to construct a joint probability distribution function (PDF) of input variables with limited data such as the marginal PDF and covariance matrix. However, since in real applications, it is common that some of the input variables are correlated, the RBDO results might contain a significant error if the correlation between input variables for RBDO is not considered. In this paper, Rosenblatt and Nataf transformations, which are the most representative transformation methods and have been widely used in the reliability analysis, have been studied and compared in terms of applicability to RBDO with correlated input variables.

The Army continues to improve its Reliability-based Design Optimization (RBDO) process, expanding from component optimization to system optimization. We are using the massively parallel computing power of the Department of Defense (DoD) High Performance Computing (HPC) systems to simultaneously optimize multiple components which interact with each other in a mechanical system. Specifically, we have a subsystem of a military ground vehicle, consisting of more than four components and are simultaneously optimizing five components of that subsystem using RBDO methods. We do not simply optimize one component at a time, sequentially, and iterate until convergence. We actually simultaneously optimize all components together. This can be done efficiently using the parallel computing environment. We will discuss the results of this optimization, and the advantages and disadvantages of using HPC systems for this work.

Reliability-based robust design optimization deals with two objectives of structural design methodologies subject to various uncertainties: reliability-based design and robust design. A reliability-based design optimization deals with the probability of failure, while a robust design optimization minimizes the product quality loss. In general, the product quality loss is described by using the first two statistical moments: mean and standard deviation. In this paper, a performance moment integration (PMI) method is proposed by using numerical integration scheme for output response to estimate the product quality loss. For the reliability part of the reliability-based robust design optimization, the performance measure approach (PMA) and its numerical method, hybrid-mean value (HMV) method, are used.

Since deterministic optimum designs obtained without considering uncertainty lead to unreliable designs, it is vital to develop design methods that take account of the input uncertainty. When the input data contain sufficient information to characterize statistical distribution, the design optimization that incorporates the probability method is called a reliability-based design optimization (RBDO). It involves evaluation of probabilistic output performance measures. The enriched performance measure approach (PMA+) has been developed for efficient and robust design optimization process. This is integrated with the enhanced hybrid mean value (HMV+) method for effective evaluation of non-monotone and/or highly nonlinear probabilistic constraints. When sufficient information of input data cannot be obtained due to restrictions of budgets, facilities, human, time, etc., the input statistical distribution is not believable.

In the Army mechanical fatigue subject to external and inertia transient loads in the service life of mechanical systems often leads to a structural failure due to accumulated damage. Structural durability analysis that predicts the fatigue life of mechanical components subject to dynamic stresses and strains is a compute intensive multidisciplinary simulation process, since it requires the integration of several computer-aided engineering tools and considerable data communication and computation. Uncertainties in geometric dimensions due to manufacturing tolerances cause the indeterministic nature of the fatigue life of a mechanical component.

This paper presents a summary of recently developed unified method of continum design sensitivity analysis of linear and nonlinear structural systems. Sizing design variables, such as thickness and cross sectional areas, and shape design variables, such as length and geometric shape, of structural components of built-up structures are considered. For design sensitivity analysis of nonlinear structures, both geometric and material nonlinearities are considered using the total and updated Lagrangian formulations. For sizing design variables, a distributed parameter structural design sensitivity analysis approach that retains the continum elasticity formulation throughout the derivation of design sensitivity analysis results is used. For shape design variables, the material derivative concept of continuum mechanics is used to relate variations in structural shape to measures of structural performance.