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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。
The same basic assumption as the Newmark method and the Wilsonθ method is adopted, that is, the acceleration is changed linearly at each time step, and then a conditionally stable implicit time integral format is obtained through equal weight processing. As a sign of the characteristic of the integral method, its periodic extension rate and amplitude attenuation rate are given in a closed analytical form. The analysis shows that the period extension rate of this method is far less than the Newmark method and the Wilsonθ method, and the amplitude attenuation is much lower than that of the Wilsonθ method. Finally, taking the mass-elastic-rod collision analysis as an example, the results obtained from the above three kinds of implicit time integration methods are compared.