空爆载荷作用下固支弹塑性圆板的动力学模型

吴迪; 米国; 郭香华; 张庆明

doi:10.11858/gywlxb.20220525

空爆载荷作用下固支弹塑性圆板的动力学模型

doi: 10.11858/gywlxb.20220525

北京理工大学机电学院, 北京　100081

详细信息

作者简介:
吴　迪（1997－），女，硕士研究生，主要从事结构冲击动力学研究. E-mail：15010059608@163.com

通讯作者:
郭香华（1974－），男，博士，副教授，主要从事爆炸与冲击仿真、材料与结构动力学研究.E-mail：guoxh@bit.edu.cn

中图分类号: O383
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出版历程
- 收稿日期: 2022-03-07
- 修回日期: 2022-03-21
- 刊出日期: 2022-10-11

Dynamic Model of Clamped Elastoplastic Circular Plate under Air Blast Loading

School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China

摘要

摘要: 基于等效单自由度模型理论，考虑变形过程中弯矩和膜力的联合承载，建立了空中近爆作用下固支弹塑性圆板的动力学模型，实现了圆板加载和卸载的全过程描述。基于文献中的试验工况建立有限元模型，利用有限元数值模拟对空爆作用下固支圆板的动态响应进行分析，并将动力学模型计算结果与试验结果及有限元数值模拟结果进行对比，验证了动力学模型计算结果的准确性。结果表明，理论计算结果与试验结果及数值模拟结果吻合较好，建立的动力学模型可以应用于固支圆板在空中近爆载荷作用下的大变形预测，为结构抗爆提供技术支持。
- 单自由度模型 /
- 弹塑性响应 /
- 空爆载荷 /
- 膜力 /
- LS-DYNA
Abstract: Based on equivalent single degree-of-freedom (SDOF) theory, a dynamic model of clamped elastoplastic circular plate under near air blast loading is established by considering the bending moment and the membrane force during the deformation process, and the whole process containing loading and unloading for circular plate is described. The finite element model is established using test parameters in the literature, and the dynamic response of clamped circular plate under air blast loading is analyzed by finite element simulation. After comparing the calculation results of the dynamic model and the finite element simulation results, the accuracy of the calculation results of the dynamic model is verified. The results show that the theoretical calculation results are in good agreement with the test results and the finite element simulation results. The proposed dynamic model can be applied to predict the large deformation of clamped circular plate under near air blast loading, and provides technical support for blast resistant structure.
- single degree-of-freedom model /
- elastoplastic response /
- air blast loading /
- membraneforce /
- LS-DYNA

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图 1 载荷等效示意图

Figure 1. Equivalent load diagram

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图 2 式 $\left(4\right)$ 和式 $\left(5\right)$ 的计算结果对比

Figure 2. Comparison of calculation results between Eq. (4) and Eq. (5)

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图 3 板元受力分析

Figure 3. Force analysis of plate microelement

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图 4 弯矩和膜力联合承载的屈服条件

Figure 4. Yield condition of combined bending moment and membrane force

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图 5 固支圆板发生弹塑性大变形后的应力场分布

Figure 5. Stress field of clamped circular plate after large elastic-plastic deformation

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图 6 加载阶段的等效质量-弹簧-阻尼模型

Figure 6. Equivalent mass-spring-damper model in loading phase

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图 7 卸载阶段的等效质量-弹簧-阻尼模型

Figure 7. Equivalent mass-spring-damper model in unloading phase

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图 8 试验布置

Figure 8. Test setup

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图 9 有限元模型

Figure 9. Finite element model

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图 10 各工况下有限元数值模拟得到的中心点位移-时间曲线

Figure 10. Displacement-time curves of center point by finite element simulation under various calculation cases

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图 11 峰值压力点及其拟合函数

Figure 11. Peak pressure points and fitting functions

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图 12 各工况下动力学模型计算结果与试验及有限元数值模拟结果的对比

Figure 12. Comparison of dynamic model results with test and finite element simulation results under various cases

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图 13 各工况下动力学模型与试验得到的靶板轮廓线的对比

Figure 13. Comparison of circular plate deformations between dynamic model and test under various cases

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表 1 3种高强度钢的试验参数^[12]

Table 1. Test parameters of three kinds of high strength steel^[12]

Case	Material	Thickness/mm	Yield strength/MPa	Mass of TNT/kg	Detonation distance/mm
1	Weldox700E steel	8	800	6	250
2	B1 steel	8	1070	6	250
3	B2 steel	8	1600	6	250
4	Weldox700E steel	12	800	10	250
5	B1 steel	12	1070	10	250
6	B2 steel	12	1600	10	250

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表 2 各工况下试验与有限元模拟得到的中心点位移对比

Table 2. Comparison of center point displacements between test and finite element simulation under various calculation cases

Case	Maximum displacement of center point			Final displacement of center point
Case	Test/mm	Sim./mm	Error/%	Test/mm	Sim./mm	Error/%
1	145	148.84	2.65	129	137.42	6.53
2	128	134.67	5.21	102	111.88	9.69
3	103	99.52	−3.38	85	79.07	−6.98
4	166	152.44	−8.17	153	141.95	−7.22
5	148	133.87	−9.55	118	120.12	1.80
6	115	106.74	−7.18	83	79.28	−4.48

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表 3 各工况下动力学模型计算结果与试验结果的对比

Table 3. Comparison between dynamic model results and test results under various cases

Case	Maximum displacement			Final displacement
Case	Test/mm	SDOF model/mm	Error/%	Test	SDOF model/mm	Error/%
1	145	141.48	−2.43	129	129.22	0.17
2	128	126.03	−1.54	102	110.06	7.90
3	103	101.49	−1.47	85	86.21	1.42
4	166	160.24	−3.47	153	148.57	−2.90
5	148	141.27	−4.55	118	127.66	8.19
6	115	114.19	−0.70	83	95.03	14.49

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