Analytical Solution for Plastic Responses of Metal Beams under Repeated Impacts Based on Membrane Factor Method  

基于膜力因子法的金属梁低速重复冲击塑性响应研究

作　　者：GUO Kai-ling ZHANG Yi-jiang MU Meng-ying ZHU Ling 郭开岭;张义江;穆梦颖;朱凌(高性能船舶技术教育部重点实验室(武汉理工大学),武汉430063;武汉理工大学船海与能源动力工程学院,武汉430063)

机构地区：[1]Key Laboratory of High Performance Ship Technology(Wuhan University of Technology),Ministry of Education,Wuhan 430063,China [2]School of Naval Architecture,Ocean and Energy Power Engineering,Wuhan University of Technology,Wuhan 430063,China

出　　处：《船舶力学》2024年第12期1891-1907,共17页Journal of Ship Mechanics

基　　金：国家自然科学基金资助项目(12202328;12172265).

摘　　要：Marine structures are frequently subjected to repeated impact loadings,resulting in failure of the structures,even causing serious accidents.The analytical expressions of dimensionless permanent deflection and impact force of a metal beam based on maximal normal yield surface are derived by membrane factor method(MFM),then the results are compared with repeated impact tests.It can be found that the solutions based on MFM are between the upper and lower bounds,and very close to the results of the repeated impact tests,indicating the theoretical model proposed can predict the plastic responses of the metal beam accurately.What’s more,the influences of impact location and boundary condition on the dynamic responses of the beam subjected to repeated impacts are determined.Results show that,as the distance of impact location from the middle span of the beam increases,the permanent deflection decreases,while the impact force increases.Meanwhile,the influences of impact location enhance as the impact number increases.When the permanent deflection is smaller than the thickness,the effect of boundary condition on the plastic responses is significant.However,when the deflection is larger than the thickness,the beam will be like a string and only axial force works,resulting in little influence of boundary condition on the plastic responses of the beam.船海结构经常遭受重复冲击载荷,导致结构失效破坏,甚至造成严重事故。本文基于最大应力屈服面,利用膜力因子法建立金属梁低速冲击塑性响应理论分析模型,获得无量纲最终挠度和无量纲冲击力的解析表达式,并将理论结果与实验结果进行对比。研究发现膜力因子法的求解结果与实验结果十分接近,且位于内外屈服面求解的结果之间,验证了理论方法具有较好的准确性。在此基础上,利用本文提出的理论方法研究冲击位置和边界条件对金属梁塑性动力响应的影响规律。结果表明,随着冲击位置距跨中增加,最终挠度不断减小,但冲击力峰值不断增大,且冲击位置的影响随着冲击次数的增大而增强。当最终挠度小于梁厚时,边界条件对金属梁塑性响应的影响较大;而当最终挠度大于梁厚时,金属梁将会类似于一根塑性弦,只有轴力做功,就会导致边界条件对塑性响应的影响非常小。

关 键 词：repeated impact theoretical analysis membrane factor method impact location boundary condition 

分 类 号：U661.4[交通运输工程—船舶及航道工程]