Multiscale concurrent topology optimization for thermoelastic structures under design-dependent varying temperature field
Tóm tắt
In this paper, a new multiscale concurrent topology optimization method for thermoelastic structures considering the iterative variation of temperature field is proposed for the first time, which breaks the limitation that previous multiscale concurrent topology optimization studies being compliable merely to uniform temperature field. In this method, the iterative variations of macroscopic structural heat transfer, structural temperature, structural force transfer, structural displacement, design-dependent thermal stress load, microscopic effective thermal conductivity, effective elasticity and effective thermal expansion coefficient are all taken into consideration. In order to establish a compact hierarchical thermoelastic coupling equation on the above iterative factors, firstly, a thermoelastic coupling matrix with a distinct physical meaning is proposed to address the issues on accuracy of thermal stress loads and solution of adjoint sensitivity multipliers caused by design-dependent varying temperature field, and this matrix can be used as a new manner to solve homogenized effective thermal stress coefficient. Secondly, the compact coupling equation is derived using multiscale adjoint sensitivity analysis and its effectiveness is illustrated by comparative cases. Finally, the generality and stability of proposed method are illustrated through diverse scenarios involving compliance optimization, multimaterial concurrent design, maximum displacement control, multicellular structure design, asymmetric boundary conditions and three-dimensional structures. It is obvious that this pioneering approach has a broad potential in advanced integrated structures and materials design of thermoelastic structures.
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