爆炸与冲击2024，Vol.44Issue(1)：1-10,10.DOI:10.11883/bzycj-2023-0414
结构刚塑性动力解的弹性补偿
Elastic compensation for dynamic rigid-plastic solutions of structures
摘要
Abstract
In recent years,by combining membrane factor method(MFM)and saturation analysis(SA)as a powerful theoretical tool,scholars in China have made comprehensive studies on the large dynamic plastic deformation of beams,plates and other structures under pulse loading,leading to the best rigid-plastic predictions for the final deflection of the pulse-loaded structures,which are superior to the previously proposed various approximate rigid-plastic solutions.However,due to the complexity of the dynamic elastic-plastic response of structures used in engineering and the limitations of numerical simulations,it is critical to clarify how large is the error generated from the rigid-plastic solutions in predicting the final deflection of pulse-loaded structures compared to the result that takes the elastic effect of material into consideration.Our preliminary study on this issue,which has been published in leading international journals,reveals the effect of material's elasticity on the large dynamic plastic deformation of structures under pulse loading,and quantitatively evaluates the discrepancies between the final deflection predicted by the best theoretical rigid-plastic solutions and that extracted from elastic-plastic numerical simulations.On this basis,the present paper proposes a strategy to compensate for elastic effect;that is,(1)adding a compensation term to the final deflection predicted by the existing best rigid-plastic solution;(2)expressing the compensation term as an elemental function of variables separation to respectively represent the effects of the pulse intensity and the structural stiffness;and(3)adopting minimum number of undetermined coefficients(or power)in the fitting function to achieve concise formulae.Meanwhile,the variation ranges of structural stiffness and dimensionless load parameter are investigated with reference to metallic structures used in their main application fields.Finally,by implementing the fitting and compensation for the cases of fully-clamped beams and square plates,simple and engineer-friendly formulae for predicting the final deflection of beams and plates are eventually obtained.With the compensation terms being added,the rigid-plastic-solution-based predictions on the final deflection of beams and plates possess a relative error within the range of 3％,which are appropriate and suitable for applications in the engineering design stage.A table at the end of the paper summarizes the major notations and formulae,as well as the comparison between the results on beams and square plates.关键词
结构塑性动力响应/脉冲载荷/固支梁和固支方板/弹性效应补偿/最终挠度的最佳预测Key words
dynamic plastic response of structure/pulse-loading/fully-clamped beams and square plates/compensation for elastic effect/best prediction of final deflection分类
数理科学引用本文复制引用
余同希,胡庆洁,朱凌..结构刚塑性动力解的弹性补偿[J].爆炸与冲击,2024,44(1):1-10,10.基金项目
国家自然科学基金(12172265) （12172265）
武汉理工大学特聘教授科研启动基金(471-40120163) （471-40120163）
