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研究了梁以一定初始速度(冲量)撞击固定支座的动力响应问题。分别采用Euler梁单元理论和Timoshenko梁单元理论建立了弹性梁撞击固定支座的动力方程,得出了梁动剪力、动弯矩和跨中挠度的解析表达式并进行了对比分析。采用考虑应变速率的二维Timoshenko梁单元有限元分析程序对梁撞击固定支座问题进行了非线性动力分析,通过与弹性情况下的计算结果进行对比,分析了梁延性比和高跨比对动剪力、动弯矩以及跨中挠度的影响。分析结果表明:由于Euler梁单元理论没有考虑剪切变形和转动惯量的影响,不能得出梁端部最大动剪力的收敛解且跨中最大动弯矩相对于Timoshenko梁单元理论产生了很大误差。相对于线弹性材料,材料非线性对梁撞击支座的动力响应的影响也较显著,并且这种影响随着梁延性比和高跨比的不同而变化。
The dynamic response of a beam to a fixed bearing at a certain initial velocity (impulse) is studied. The dynamic equation of the elastic beam striking the fixed bearing is established respectively by Euler beam element theory and Timoshenko beam element theory. The analytic expressions of dynamic shear moment, mid-span deflection and mid-span deflection of the beam are obtained and compared. The two-dimensional finite element analysis program of Timoshenko beam considering the strain rate is used to conduct the nonlinear dynamic analysis of the beam-impacting fixed bearing problem. By comparing with the calculation results under elastic conditions, the effects of beam ductility ratio and ratio of high span ratio Shear force, dynamic bending moment and mid-span deflection. The analysis results show that the convergence of the maximum dynamic shear force at the beam ends can not be obtained because the Euler beam element theory does not consider the influence of shear deformation and moment of inertia, and the maximum dynamic bending moment in the midspan has a great effect on the Timoshenko beam element theory error. The nonlinear effect of material nonlinearity on the dynamic response of the beam impact bearing relative to the linear elastic material is also significant, and this effect varies with the beam ductility ratio and the high span ratio.