In this research we develop a mathematical construct for estimating uncertainties within the bilevel optimization framework of collaborative optimization. The collaborative optimization strategy employs decomposition techniques that decouple analysis tools in order to facilitate disciplinary autonomy and parallel execution. To ensure consistency of the physical artifact being designed, interdisciplinary consistency constraints are introduced at the system level. These constraints implicitly enforce multidisciplinary consistency when satisfied. The decomposition employed in collaborative optimization prevents the use of explicit propagation techniques for estimating uncertainties of system performance. In this investigation, we develop and evaluate an implicit method for estimating system performance uncertainties within the collaborative optimization framework. The methodology accounts for both the uncertainty associated with design inputs and the uncertainty of performance predictions from other disciplinary simulation tools. These implicit uncertainty estimates are used as the basis for a new robust collaborative optimization (RCO) framework. The bilevel robust optimization strategy developed in this research provides for disciplinary autonomy in system design, while simultaneously accounting for performance uncertainties to ensure feasible robustness of the resulting system. The method is effective in locating a feasible robust optimum in application studies involving a multidisciplinary aircraft concept sizing problem. The system-level consistency constraint formulation used in this investigation avoids the computational difficulties normally associated with convergence in collaborative optimization. The consistency constraints are formulated to have the inherent properties necessary for convergence of general nonconvex problems when performing collaborative optimization.
Many practical structural designs require that the structure is easily manufactured. Design concepts synthesized using conventional topology optimization methods are typically not easily manufactured, in that multiple finishing processes are required to construct the component. A manufacturing technique that requires only minimal effort is extrusion. Extrusion is a manufacturing process used to create objects of a fixed cross-sectional profile. The result of using this process is lower costs for the manufacture of the final product. In this paper, a hybrid cellular automaton algorithm is developed to synthesize constant cross section structures that are subjected to nonlinear transient loading. The novelty of the proposed method is the ability to generate constant cross section topologies for plastic-dynamic problems since the issue of complex gradients can be avoided. This methodology is applied to extrusions with a curved sweep along the direction of extrusion as well. Three-dimensional examples are presented to demonstrate the efficiency of the proposed methodology in synthesizing these structures. Both static and dynamic loading cases are studied.
The hybrid cellular automaton (HCA) algorithm was inspired by the structural adaptation of bones to their ever changing mechanical environment. This methodology has been shown to be an effective topology synthesis tool. In previous work, it has been observed that the convergence of the HCA methodology is affected by parameters of the algorithm. As a result, questions have been raised regarding the conditions by which HCA converges to an optimal design. The objective of this investigation is to examine the conditions that guarantee convergence to a Karush-Kuhn-Tucker (KKT) point. In this paper, it is shown that the HCA algorithm is a fixed point iterative scheme and the previously reported KKT optimality conditions are corrected. To demonstrate the convergence properties of the HCA algorithm, a simple cantilevered beam example is utilized. Plots of the spectral radius for projections of the design space are used to show regions of guaranteed convergence.
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