Thermoelastic topology optimization for structures under the thermal stress singularity issue
摘要
In thermoelastic topology optimization for thermal structures, most work uses fixed boundary conditions, but this is sometimes too rigid to represent the boundary thermal expansion at high temperature constrained boundaries. The result is that the stress level is much higher than the actual level, and even the deformation mode is different from the actual mode, leading to an unreasonable design. To address this issue, a novel sequential coupling-based representation for boundary thermal expansion (SC-BTE) is proposed in this study to remove the limitation of oversimplified fixed boundary conditions. The core idea is to divide the thermoelastic finite element (FE) equilibrium equation into a mechanical part and a thermal part, but with different constrained boundary conditions. The mechanical part still uses the original fixed boundary conditions, but the thermal part is set to free thermal expansion. The advantage is that the modified boundary is rigid under mechanical loading but flexible under thermal loading, which naturally overcomes the thermal stress singularity issue. To avoid the rigid motion due to thermal expansion, a ‘super spring element’ is created by an additional node and all nodes at the original fixed boundary to provide a weakly constrained stiffness. The results show that the optimal designs using the proposed method can avoid the hinge phenomena, grayscale issues and material-less effect of designs using fixed boundary conditions, which will be a useful complement to the existing thermoelastic topology optimization methods.