热荷载作用下薄板的优化设计

板壳结构是一大类广泛使用的结构元件.在热荷载作用下，当热膨胀受到约束时，板壳结构产生内力及挠度，严重时影响结构的正常服役.由于热荷载的特殊性，简单地均匀加大板壳结构的厚度并不能有效地减少热变形和热应力，热结构设计因此特别困难.该文研究在给定材料体积的条件下，通过优化板壳结构的厚度分布来减少弹性薄板结构在热载荷下的变形.以结构的变形能为优化目标，在给定材料体积的条件下，建立了设计板壳结构厚度分布的优化问题列式，并采用变分法，推导出优化准则，给出了修改厚度的迭代公式.应用商用有限元软件的热结构分析功能，对程序进行二次开发，从而实现该优化算法.算例结果表明，采用该方法优化弹性薄板的厚度分布，可以大幅度地减小结构热变形，是一种有效的热结构设计方法.

Optimal Design of Thin Solid Elastic Plates Under Thermal Load

Plates and shells constitute a large family of widely used structural elements. Under the action of thermal load, if the thermal expansion is restricted, membrane forces and bending moments will occur within the plate and shell structures and lead to large deformation which seriously affected normal service. Due to the particularity of thermal load, uniform increase of the plate or shell thickness can hardly reduce the thermal deformation and thermal stress effectively, and special experience and knowledge are required in thermal structural design. Thickness distribution optimization of the thin elastic plate structure with given material volume under thermal load was studied and aimed at reduction of thermal deformation. For the thickness distribution of the plate with given material volume, mathematical formulation of the optimization problem focused on minimum structural deformation energy was established. According to the formulation and with the variational method, the optimality criteria and the iterative scheme for modification of the thickness distribution were derived. And this optimization algorithm was implemented through secondary development in the commercial finite element programs. Results of the numerical examples show that, the presented method greatly reduces the thermal deformation of thin elastic plate structures through modification of the thickness distribution, and makes an effective optimization method for thermal structures.