Abstract

Thermal stress is an important design factor that will influence structural responses and cause local warping deformations. In this paper, such temperature variation effect is considered in the structural optimization and the shape preserving design approach is extended into thermo-elastic problems to prevent local thermal damages. Based on the weak-coupled thermo-elastic system, nonlinear structural responses at large thermo-mechanical loads are accurately analyzed. The complementary elastic work is minimized to obtain a reasonable rigid structure. Corresponding integrated deformation energy is utilized to calculate the warping deformation accumulated in the incremental thermo-mechanical loading process. Shape preserving effect is then achieved by an additional constraint on the local deformation energy. Through the adjoint method, sensitivity analysis is derived in the coupled field with design-dependent heat conduction and geometrical nonlinearity. In the numerical implementation, an energy interpolation scheme is applied to circumvent numerical instability in low stiffness regions and further modified for multi-material design. Optimization results show that local distortions in thermo-elastic structures are effectively eliminated by the proposed shape preserving design approach.

中文翻译：

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考虑几何非线性的热弹结构保形设计

摘要

热应力是一个重要的设计因素，它将影响结构响应并引起局部翘曲变形。本文在结构优化中考虑了这种温度变化的影响，并将形状保持设计方法扩展到热弹性问题中，以防止局部热损伤。基于弱耦合热弹系统，可以准确分析大热机械载荷下的非线性结构响应。互补弹性功被最小化以获得合理的刚性结构。利用相应的综合变形能来计算在增量热机械加载过程中累积的翘曲变形。然后通过对局部变形能量的附加约束来实现形状保持效果。通过伴随方法，灵敏度分析是在耦合场中进行的，其取决于设计的热传导和几何非线性。在数值实现中，采用能量插值方案来规避低刚度区域中的数值不稳定性，并进一步对其进行修改以进行多材料设计。优化结果表明，所提出的形状保持设计方法可以有效消除热弹性结构中的局部变形。