Structural Optimization with Thermal and Mechanical Constraints

Abstract

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.

Structural topology design with multiple thermal criteria

“…These sensitivity strategies were used to solve thermal stress, heat conduction and heat convection problems. Recently, Xu and Grandhi (1999) extended sensitivity analysis approach to a size optimal problem, in which the structural volume was minimized while subject to temperature, displacement and stress constraints. In their solution, the coupling relation between thermal and structural sensitivities was taken in account.…”