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| Multi Geometrical Scale Optimization for Porous Structure and Material with Multi-Objective of Structural Compliance and Thermo Deformation |
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Abstract Light weight is the eternal pursuit of spacecraft structures. Load carrying spacecraft structures experience severe mechanical loads and thermo environments, which lead the thermo deformation and stress to be the key issues of performance of spacecraft and equipment. Porous ceramic is one of the most competitive materials to compose this kind of structures because of its excellent mechanical properties in high temperature circumstance and potentials in multi-functional application. The authors attempt to use topology optimization technique to design the light weight structure composed of porous ceramic with uniform microstructure, which combines high stiffness with low thermal expansion in a predefined domain.
A new multi-objective optimization formulation is developed for the multi geometrical scale topology optimization of structures and materials concurrently. The objective function is composed of two items. One is to minimize the structural compliance when only the mechanical loads are applied on structures, while the other is to minimize the thermal expansion of the outer spacecraft structure surface when only the thermo loads are applied. The two items are both normalized and then jointed through weighted coefficients to form a multi-objective function. The independent macro and micro densities are introduced as the design variables and penalization approaches are adopted in both scales, i.e. SIMP (Solid Isotropic Material Penalization) in micro material scale and PAMP (Porous Anisotropic Material Penalization) in macro structure scale. Optimizations of the two geometrical scales are integrated into one system through homogenization theory. In order to improve computational efficiency, the adjoint method is utilized to obtain the sensitivity. The SQP method is adopted and the volume preserving nonlinear density filtering based on Heaviside step function is used to prevent checkerboard patterns and to obtain a clear design. We apply the proposed multi-objective optimization model to a sandwich elliptically curved shell to investigate the concurrent multi-scale design of structure configuration and microstructure of porous ceramic. The numerical examples demonstrate that the porous material is conducive to enhance the multi-objective performance of curve shell structure when the available amount of material is insufficiently given. And an “optimum” material volume fraction is observed for the multi-objective optimization problem, and the performance of structures can not be improved by increasing material volume when the “optimum” volume fraction is reached. The influence of thickness of surface sheets on the optimal design is investigated at last.
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Received: 02 November 2009
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2011, Vol. 32 
