结构弹性碰撞分析三种隐式时间积分法结果的比较

 采用与Newmark法和Wilsonθ法相同的基本假设，即设在每一时间步长内加速度为线性变化，然后经过等加权处理而得到一种条件稳定的隐式时间积分格式。作为积分法特性的标志，其周期延长率和幅值衰减率均以封闭的解析形式给出。分析表明，此法的周期延长率远小于Newmark法和Wilsonθ法，而幅值衰减也远低于Wilsonθ法。最后以质点-弹性杆碰撞分析为例，比较了上述3种隐式时间积分法所得的结果。

COMPARISON OF RESULTS OBTAINED BY THREE KINDS OF IMPLICIT TIME INTEGRATION METHODS FOR ELASTIC STRUCTURAL IMPACT

A kind of conditionally stable implicit time integration scheme is obtained based upon the average weighting method and the assumption that the acceleration in each time step is linear, which is the same as employed in the Newmark or Wilson  θ method. As the indicators of the characteristics of time integration methods, its period elongation and the amplitude decay are given in the closed form. It is shown that the period elongation of this method is much smaller than that of Newmark or Wilson  θ  method and the amplitude decay is much smaller than that of Wilson θ method. Comparison of results obtained by the above three methods in the case of mass elastic rod impact analysis is also given.