多自由度非线性动力方程的改进增维精细积分法

针对多自由度非线性动力方程，提出了一种改进的增维精细积分法。将非线性项当作载荷来处理，并采用增维的方法使非线性动力方程转化为形式上的齐次方程，使该齐次方程的系数矩阵具有一个定常子矩阵，避免了每一个时间步内要进行若干次矩阵的加、乘迭代来更新指数矩阵，提高了增维精细积分法的计算效率，尤其是对大型结构的长期性态仿真效果十分明显。数值算例表明，该方法对一般的多自由度的非线性动力方程的求解具有精度高、计算速度快的特点。

Improved Increment-Dimensional Precise Integration Method for the Nonlinear Dynamic Equation with Multi-Degree-of-Freedom

An improved increment-dimensional precise integration method for the nonlinear dynamic equation with multi-degree-of-freedom was proposed. First the nonlinear terms were treated as load; then the original nonlinear dynamic equation was converted into homogenous equation by increment-dimensional method; finally an invariant sub-matrix was contained in the coefficient matrix of the homogenous equation. So it is not necessary to update the exponential matrix by times of matrix＇s addition and multiplication for every time-step. Therefore the efficiency of the increment-dimensional precise integration method was improved, and the method is especially efficient for long-term simulation of large-scale structures. The numerical examples show that high precision and fast speed are achieved when the improved numerical method is applied in solving the nonlinear dynamic equation with multi-degree-of-freedom.