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A Envelope-Criterion Method for Thin Plate Optimization Under a Transient Heat Transfer Process

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 作者 单位 E-mail 孙国 大连理工大学 sunguo@dlut.edu.cn

刚度和强度是薄板结构的两个主要性能。在瞬态传热过程中，考虑热-力耦合，随时间和空间变化的非均匀温度场在结构中引起热变形和热应力，温度场随时间变化的规律和空间分布依赖于板的厚度变化，进而影响板的刚度和强度。因此，考虑瞬态传热的薄板优化问题具有更强的非线性，更加难以求解。本文给出一种包络-准则方法处理这类结构优化问题。首先针对外力荷载，进行一个结构柔顺性的优化设计；以这一设计为基础，通过瞬态热-力耦合分析及优化准则，计算多个时刻的优化设计变量并取其包络，对上述优化结果进行迭代修正，以消除瞬态温度场作用下较高的局部应力。进行了优化算例分析，显示该方法对于考虑瞬态传热薄板优化问题的有效性。

Stiffness and strength are main performance of thin plate structures. In the transient heat transfer process, considering thermo-mechanical coupling, the temperature distribution is nonuniform and time variant, resulting in thermal deformation and thermal stress in the structure. The variation of the temperature field depends on the thickness of the plate, and then affects the stiffness and strength of the plate. Hence, the complex influence of the temperature field makes the optimization problem more nonlinear and more difficult to solve. In this paper, an envelope-criterion method is presented to deal with the structural optimization with such a complex temperature field. First, a structural compliance optimization design is carried out for external loads. Based on this design, by calculating multiple time index functions and taking the envelope, the above optimization results are modified iteratively to eliminate the higher local stress under transient temperature field. Some numeric examples are given and the results show that the method is effective for thin plate optimization under a transient heat transfer process.
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