考虑应力约束的板壳结构抗震拓扑优化设计

doi:10.3901/JME.260604

摘要/Abstract

摘要： 地震作用是结构设计时需要考虑的一种重要荷载作用。为研究考虑应力约束的板壳结构抗震拓扑优化问题，构建了地震作用下结构壳单元最大振型反应平方和开方(Square root of the sum of squares，SRSS)的应力凝聚函数表征格式。为准确描述应力的导数，考虑结构等效模态力以及振型的导数项，推导了SRSS的应力凝聚函数的导数。同时，构建了多项分式有理式刚度矩阵惩罚模型，结合伪模态处理措施，较好的解决了板壳结构拓扑优化的局部伪模态问题。采用基于密度过滤技术、Heaviside映射方法的三场方案和SIMP (Solid isotropic material with penalization)插值方法，构建地震荷载作用下以结构模态柔度总和为目标函数、体积约束和多个SRSS应力凝聚函数约束的板壳结构抗震拓扑优化模型。将优化模型转化为能保证应力和体积约束有效的近似优化模型，并采用移动渐近线方法对近似优化模型进行求解。算例结果表明：结构拓扑构型不同会导致等效模态力分布差异；地震荷载下的结构应力场与结构质量分布、振型和等效模态力相关，在优化模型中考虑等效结点模态力和振型的导数更合理；采用提出的方法可以获得满足体积约束和结构SRSS应力约束的清晰的序列0/1分布板壳结构，解决了板壳结构优化中的局部伪模态问题，验证了所提出方法的正确性和有效性。

关键词: 拓扑优化, 应力约束, 地震作用, 板壳结构

Abstract: Seismic excitation is an important load to be considered in structural design. To study the seismic topology optimization problem of plate-shell structures considering stress constraints, a stress condensation function representation format for the sum of squared and square root (SRSS) of the maximum mode response of structural shell elements under seismic excitation is constructed. In order to accurately describe the derivative of stress, the derivative of the stress condensation function of SRSS is derived, considering the equivalent modal force of the structure and the derivative term of the vibration mode. A multi-fraction rational stiffness matrix penalty model is constructed, and the pseudo-modal identification criterion of low order modal energy is combined to solve the local pseudo-modal problem of plate-shell structure topology optimization. A three-field scheme, which incorporates the density filtering technique and the Heaviside mapping method, along with the solid isotropic material with penalization (SIMP) interpolation method, is employed to construct a seismic topological optimization model for plate-shell structures under seismic excitation. The model takes the sum of modal compliance as the objective function, with volume constraints and multiple SRSS stress aggregation constraints. The optimization model is transformed into an approximate optimization model which can guarantee the effective stress and volume constraints. The approximate optimization model is solved by moving asymptote method. The results show that the difference of structural topological configuration will lead to the difference of equivalent modal force distribution, and the structural stress field under seismic excitation is related to the mass distribution, modal and equivalent modal force, so it is more reasonable to consider the derivatives of the equivalent node modal force and modal in the optimization model. The proposed method can obtain a clear sequence 0/1 distributed plate-shell structure satisfying the volume constraint and SRSS stress constraint, solve the local pseudo-modal problem in plate-shell structure optimization, and verify the correctness and effectiveness of the proposed method.

Key words: topological optimization, stress constraints, seismic excitation, plate-shell structure

中图分类号:

O313
TU311

赵志军, 荣见华, 赵磊, 蔡金虎, 易继军, 周泉. 考虑应力约束的板壳结构抗震拓扑优化设计[J]. 机械工程学报, 2026, 62(11): 399-415.

ZHAO Zhijun, RONG Jianhua, ZHAO Lei, CAI Jinhu, YI Jijun, ZHOU Quan. Seismic Topology Optimization Design of Plate-shell Structures Considering Stress Constraints[J]. Journal of Mechanical Engineering, 2026, 62(11): 399-415.

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http://www.cjmenet.com.cn/CN/Y2026/V62/I11/399

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