动态载荷下薄板加强筋结构拓扑优化设计

温志超1, 2, 孙直3, 胡程涛1, 2, 石姗姗1, 2

振动与冲击 ›› 2025, Vol. 44 ›› Issue (15) : 125-133.

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振动与冲击 ›› 2025, Vol. 44 ›› Issue (15) : 125-133.
振动理论与交叉研究

动态载荷下薄板加强筋结构拓扑优化设计

  • 温志超1,2,孙直3,胡程涛1,2,石姗姗*1,2
作者信息 +

Topology optimization design of thin plate stiffener structure under dynamic load

  • WEN Zhichao1,2, SUN Zhi3, HU Chengtao1,2, SHI Shanshan*1,2
Author information +
文章历史 +

摘要

加强筋板壳结构在工程中有着广泛的应用,加强筋合理的布局可以有效提升加强筋板壳结构的刚度和承载能力。为了实现薄板结构最优的加强筋布局优化设计,提出了一种适用于多相材料的薄板加强筋结构的动态拓扑优化新方法。首先,基于等效刚度理论,将加强筋与基板分别设置为强、弱材料,以不同的抗弯刚度表征加强筋与基板;其次,采用Hilber-Hughes-Taylor-α(HHT-α)方法求解动力学有限元模型,并结合先离散后微分的伴随变量方法进行动态灵敏度分析;再次,通过角点简支方板的加强筋分布拓扑优化算例与传统方法对比,验证了薄板加强筋结构动态拓扑优化方法的有效性。最后,针对不同边界条件和载荷工况下的薄板结构,进行了单相和双相材料下加强筋动态拓扑优化设计。结果表明:提出的动态载荷下薄板加强筋结构拓扑优化方法在复杂动态工况下表现出良好的适应性和稳定性,引入双相材料后,通过合理的材料分布和细化的结构设计,成功克服了单相材料在连续性分布上的不足。优化后的加强筋结构连续,传力路径完整,显著优于传统方法。

Abstract

The stiffened plate structures are widely used in engineering applications, and the rational layout of the stiffeners can effectively enhance the stiffness and load-bearing capacity of these structures. In order to achieve optimal stiffener layout design for thin plate structures, a new dynamic topology optimization method tailored for multi-phase material stiffened structures is proposed. Firstly, the stiffeners and thin plate are respectively considered as strong and weak materials and characterized by different bending stiffness, with use of equivalent stiffness method; Next, the Hilber-Hughes-Taylor-α (HHT-α) method is employed to solve the dynamic finite element model, and dynamic sensitivity analysis is conducted using the adjoint variable method with the discretize-then-differentiate approach; Furthermore, the effectiveness of the dynamic topology optimization method for stiffened plate structures is validated through a comparison of stiffener distribution topology optimization examples of a corner simply supported square plate with traditional methods. Finally, the stiffener topology optimization design is carried out for several typical thin plate structures using both single-phase and bi-phase materials under various loading and boundary conditions. The results show that the proposed dynamic topology optimization method for stiffened plate structures demonstrates flexible and effective optimization capabilities under dynamic conditions. By introducing bi-phase materials, the issues related to continuity distribution in single-phase materials are successfully overcome through reasonable material distribution and refined structural design. The optimized stiffener structure is continuous with complete force transmission paths, and significantly outperforms traditional methods.

关键词

多相材料 / 拓扑优化 / 薄板加强筋设计 / HHT-α法 / 伴随变量方法

Key words

multi-material / topology optimization / design of thin plate stiffeners / HHT-α method / adjoint variable 
method

引用本文

导出引用
温志超1, 2, 孙直3, 胡程涛1, 2, 石姗姗1, 2. 动态载荷下薄板加强筋结构拓扑优化设计[J]. 振动与冲击, 2025, 44(15): 125-133
WEN Zhichao1, 2, SUN Zhi3, HU Chengtao1, 2, SHI Shanshan1, 2. Topology optimization design of thin plate stiffener structure under dynamic load[J]. Journal of Vibration and Shock, 2025, 44(15): 125-133

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