Seismic Topology Optimization Design of Plate-shell Structures Considering Stress Constraints

doi:10.3901/JME.260604

Abstract

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

CLC Number:

O313
TU311

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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URL: http://www.cjmenet.com.cn/EN/10.3901/JME.260604

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

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