Page 72 - 《爆炸与冲击》2026年第2期

第 46 卷 第 2 期 爆 炸 与 冲 击 Vol. 46, No. 2
2026 年 2 月 EXPLOSION AND SHOCK WAVES Feb., 2026

DOI：10.11883/bzycj-2024-0488

固支圆板在多次远场空爆载荷下

位移响应的理论模型 *

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郑晓波 ，赵宏涛 ，李 腾 ，姚伟光 ，宋海生 ，桂毓林 ，王 治 2
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（1. 中国工程物理研究院流体物理研究所，四川 绵阳 621999；
2. 哈尔滨工程大学船舶工程学院，黑龙江 哈尔滨 150001）
摘要： 针对固支圆板在多次远场空爆载荷下的位移响应问题，基于膜理论能量方程，提出一种理论建模方法：通
过将多次空爆载荷简化为线性衰减脉冲序列，首次建立了考虑应变率强化效应与累积硬化效应的固支圆板位移响应
理论模型。首次加载阶段采用线性位移场近似，后续加载阶段引入二次函数位移场假设，推导出多次爆炸下中点位移
的递推公式。LS-Dyna 二次、三次空爆数值模拟验证表明，理论解与模拟结果的误差分别为 20%～30% 和 20% 以下。
理论模型表明，圆板中点位移可表征为末次爆炸单独位移与前期累积位移的加权平方根函数，且后期爆炸的位移增量
随前期累积位移增大而减小。
关键词： 多次爆炸；固支圆板；累积损伤；位移场；远场空爆；膜理论
中图分类号： O347.3; U674.7 国标学科代码： 13015 文献标志码： A

A theoretical model of displacement response of clamped circular plate
under multiple far-field blast loads

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ZHENG Xiaobo , ZHAO Hongtao , LI Teng , YAO Weiguang , SONG Haisheng , GUI Yulin , WANG Zhi 2
（1. Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621999, Sichuan, China;
2. College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, Heilongjiang, China）
Abstract: Regarding the displacement response of clamped circular plates under multiple far-field blast loads, we proposes a
novel theoretical modeling approach based on membrane theory energy equations, by simplifying multiple blast loads into
linearly decaying pulse sequences, a theoretical displacement response model for clamped circular plates is established for the
first time, considering both strain rate strengthening effects and cumulative hardening effects. The linear displacement field
approximation is adopted for the initial loading phase, while a quadratic function displacement field assumption is introduced
for subsequent loading phases, deriving recursive formulas for midpoint displacements under multiple blasts. Numerical
validations were conducted using LS-DYNA for both double and triple blast scenarios. For double blast cases, theoretical
predictions exhibited errors of 20%–30% compared to simulation results, while errors reduced to below 20% for triple blast
conditions. The ASTM A415 steel circular plate model was used for the simulations, and the strain rate strengthening effect
was described by the Cowper-Symonds model. Finite element models with quadrilateral shell elements demonstrated strong
agreement with experimental data (errors＜10%), confirming model reliability. The assumption of quadratic function
displacement field for subsequent loading phases was verified by numerical displacement curves of the middle profiles of the
plates. Further parametric analysis proved that the theoretical model is effective for different tangent modulus, which represents
the strength of the strain strengthening effect. The model reveals that midpoint displacement can be characterized as a weighted

* 收稿日期： 2024-12-17；修回日期： 2025-03-22
第一作者： 郑晓波（1986－ ），男，博士，高级工程师，zxb3710@163.com
通信作者： 桂毓林（1973－ ），男，博士，正高级工程师，guiyulin@21cn.com

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