一种新的三阶隐式直接积分法

New Third-order Implicit Direct Integration Method

将位移的三阶导定义为超加速度,并基于常平均超加速度假设推导了一种新的三阶隐式直接积分法。分析了该方法的稳定性、计算精度和计算效率。证明在不增加所需存储空间和计算量情况下,该方法是稳定的且有三阶精度。最后,用三个算例验证了该方法的准确性和适用性,能够解决实际工程问题中遇到的多种结构动力学问题。

The third-order derivative of displacement is defined as super-acceleration,and a new third-order implicit direct integration method is derived based on the assumption of constant mean super-acceleration.The stability,calculation accuracy and calculation efficiency of the method are analyzed.It is proved that the method is stable and has third-order accuracy without increasing the required storage space and calculation amount.Finally,three examples are used to verify the accuracy and applicability of the proposed method,which can solve many structural dynamics problems encountered in practical engineering problems.