This paper reports on the testing of the adaptability of the new approximation tools for thermal structural optimization. A finite element based procedure is proposed for obtaining a minimum mass design of structures subjected to stress, displacement, and temperature constraints. The optimization is based on a new two-point approximation method for the function. The coupling between thermal and structural sensitivities is taken into account to ensure the convergence. The direct or adjoint method is used for the sensitivity analysis. The two-point approximation is the incomplete second-order Taylor series expansion in terms of the intervening variables. The exponent of each design variable and the unknown constant in the second-order terms can be obtained in a closed form. This two-point approximation is used for temperature, displacement, and internal force approximations. Stress constraints are calculated by using approximated internal forces. Finally, the optimization procedure is demonstrated by two examples: the first example is the design of a titanium plate with aluminum bars and the second example is a structural wing box. These examples are subjected to external heating and mechanical loads, with temperature, strength, and minimum gauge constraints.
SUMMARYFunction approximation is one of the most important "elds of research in design optimization. Accurate function approximation reduces the repetitive cost of "nite element analysis. Many local approximations, such as one-and two-point local approximations, are already available. These are, however, only valid in a small domain and require stringent move-limits on design variables. The objective of this research is to achieve an e$cient and accurate multipoint approximation to constraints by integrating the most accurate segment of all local approximations previously constructed. The proposed multipoint approximation is constructed by combining weighting functions with local function approximations. With function and gradient information at a series of points, local approximations are established at those points. Once established, all local approximations are blended into a multipoint approximation by use of a weighting function. Function and gradient values of this multipoint approximation correspond directly with exact counterparts at the points where the local approximations were generated. Finally, the multipoint approximation is applied to a plate and wing box thermal-structural optimization. Published in
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