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结构刚塑性动力解的弹性补偿OACSTPCD

Elastic compensation for dynamic rigid-plastic solutions of structures

中文摘要英文摘要

近年来,我国学者以膜力因子法和饱和分析方法相结合为理论工具,对梁、板等结构件在脉冲载荷作用下的塑性大变形行为作了全面深入的研究,为脉冲加载下结构的最终挠度提供了优于历史上各种刚塑性近似解的最佳刚塑性预测公式.然而,由于实际工程应用中金属结构弹塑性动力响应的复杂性和数值模拟的局限性,与考虑材料弹性效应的结果相比,刚塑性解对脉冲加载下结构所预测的最终挠度的误差有多大,是一个亟待解决的关键问题.对这个问题的首阶段研究成果厘清了材料弹性对脉冲加载下结构塑性动态大变形的影响,定量评估了由最佳刚塑性理论解与弹塑性数值模拟得到的最终挠度预测结果之间的差异.在此基础上,提出了补偿弹性效应的策略和方法,即:在已有的最佳刚塑性解预测的挠度基础上添加一个补偿项,将补偿项表达为脉冲载荷强度的效应与结构自身刚度的效应分离的变量函数,并尽量减少待定系数/指数的数量,以求表达式的简洁;根据这些原则在金属结构的主要工程应用领域内选定结构刚度和外载参数的变化范围,对固支梁和固支方板的案例实施拟合与补偿,最后得到了对梁和板增添补偿项后的简单而实用的最终挠度预测公式,其相对误差在3%的范围之内,很适合工程设计应用.文末列表给出了符号与公式的一览,并对梁和方板的结果作了综合和比较.

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.

余同希;胡庆洁;朱凌

香港科技大学机械与航空航天工程系,香港九龙武汉理工大学船海与能源动力工程学院,湖北武汉 430063

力学

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

dynamic plastic response of structurepulse-loadingfully-clamped beams and square platescompensation for elastic effectbest prediction of final deflection

《爆炸与冲击》 2024 (001)

复杂脉冲载荷下轻质夹芯结构塑性动力行为与饱和脉冲等效方法研究

1-10 / 10

国家自然科学基金(12172265);武汉理工大学特聘教授科研启动基金(471-40120163)

10.11883/bzycj-2023-0414

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