现有自适应成长技术根据数学规划理论中的库恩塔克条件推导迭代公式,对以应变能为目标,体积为约束的板壳结构加强筋分布优化问题,设计效率高且结果好。但对不同类型的优化问题需要重新推导迭代公式,通用性差,且难以推广到多约束问题。针对现有技术的不足,采用移动渐近线算法(The method of moving asymptotes,MMA)迭代更新设计变量,将自适应成长技术推广应用于桁架结构拓扑优化设计中。讨论了单约束和多约束的典型桁架结构设计问题,并对多载荷工况进行了研究。算例结果表明,所提方法可以得到清晰的杆件分布和具体尺寸信息,设计效率高,适用性好,便于实际工程加工,具有较好的应用前景。
The application of the adaptive growth method is limited because several key techniques during the design process need manual intervention of designers. Key techniques of the method including the ground structure construction and seed selection are studied, so as to make it possible to improve the effectiveness and applicability of the adaptive growth method in stiffener layout design optimization of plates and shells. Three schemes of ground structures, which are comprised by different shell elements and beam elements, are proposed. It is found that the main stiffener layouts resulted from different ground structures are almost the same, but the ground structure comprised by 8-nodes shell elements and both 3-nodes and 2-nodes beam elements can result in clearest stiffener layout, and has good adaptability and low computational cost. An automatic seed selection approach is proposed, which is based on such selection rules that the seeds should be positioned on where the structural strain energy is great for the minimum compliance problem, and satisfy the dispersancy requirement. The adaptive growth method with the suggested key techniques is integrated into an ANSYS-based program, which provides a design tool for the stiffener layout design optimization of plates and shells. Typical design examples, including plate and shell structures to achieve minimum compliance and maximum bulking stability are illustrated. In addition, as a practical mechanical structural design example, the stiffener layout of an inlet structure for a large-scale electrostatic precipitator is also demonstrated. The design results show that the adaptive growth method integrated with the suggested key techniques can effectively and flexibly deal with stiffener layout design problem for plates and shells with complex geometrical shape and loading conditions to achieve various design objectives, thus it provides a new solution method for engineering structural topology design optimization.
