刚塑性悬臂梁在三角形脉冲荷载作用下的动力分析  

The dynamic analysis of the rigid-plastic cantilever beam under the triangle impulse load

作　　者：陈玉骥[1] 郭浩宇 罗旗帜[1,2] CHEN Yuji;GUO Haoyu;LUO Qizhi(Department of Civil Engineering,Foshan Science and Technology University,528000,Foshan,China;School of Civil Engineering,Hunan University,410082,Changsha,China)

机构地区：[1]佛山科学技术学院土木工程系,佛山528000 [2]湖南大学土木工程学院,长沙410082

出　　处：《应用力学学报》2021年第6期2284-2290,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金资助项目(50978058);广东省自然科学基金资助项目(9151063101000050)。

摘　　要：三角形脉冲荷载一般用于模拟爆炸荷载,其动态响应分析是结构动力计算的重要内容之一。基于刚塑性本构模型等基本假设和冲击动力学理论,对悬臂梁在三角形脉冲荷载作用下的动态响应进行了研究。根据三角形脉冲荷载幅值的大小,将悬臂梁的动力响应分成了5种情况,每种情况中再按照杆件的塑性铰位置和荷载是否仍作用于结构上等情况划分为若干阶段。利用动量定理和动量矩方程推导了5种不同荷载水平下,杆件各阶段的位移、加速度、塑性铰位置和塑性功等力学量的公式,分析了这些参数在杆件运动时的变化情况。结果表明,对于三角形脉冲荷载幅值不同的取值范围,杆件的塑性铰位置、运动速度、加速度和塑性功等力学参数的变化将有所不同。The triangular impulse load is generally used to simulate the explosion load, of which its dynamic response analysis is one of the important parts in the structural dynamic calculation. Based on some assumption of rigid-plastic constitutive model and the theory of impact dynamics, the paper investigates the dynamic response of cantilever beam under the triangle impulse load. Further, the dynamic response of the beam is divided into five types of motion situations according to the values of the triangle impulse load amplitude. Accordingly, each situation is separated into several stages depending on the plastic hinge position and whether the load still acts on the structure. The formulas of mechanical quantities such as displacement, acceleration, plastic hinge position and plastic work in each stage under five different load levels are derived by employing momentum theorem and moment of momentum equation. Additionally, the changes of these parameters during the movement are analyzed in the five different load levels. Results show that mechanical parameters including the plastic hinge position,velocity, acceleration and plastic work will fluctuate under different values of triangle impulse load amplitude F;.Take plastic work as an example. When 3 F;18 F;,the motion of the beam is divided into two stages. The plastic work in the first stage(loading stage) is more than99% on the total plastic work, while the plastic work in the second stage(no load stage) is less than 1%.

关 键 词：刚塑性悬臂梁 三角形脉冲荷载 动力学 塑性铰 

分 类 号：O342[理学—固体力学]