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基于Hamilton体系下的精细时程积分方法,通过对载荷项进行离散,应用中值法使载荷项在时间步长内为常值,从而将非齐次动力方程转化为齐次动力方程,避免了矩阵的求逆运算;基于积分区间逐次半分的思想实现了任意时间步长的自适应求积。数值算例结果表明:在同等时间步长的非齐次系统中,精细时程积分的最大误差为中心差分法的2.8%,为Newmark法的2.2%,最大求解误差仅为0.029%。这充分说明了本文的离散精细时程积分的自适应求积算法具有很好的收敛性。
Based on the precise time-integration method in Hamilton system, the load term is discretized, and the load term is constant in time step by using the median method. Thus, the nonhomogeneous dynamic equation is transformed into the homogeneous dynamical equation, which avoids Matrix inversion operation; based on the idea of half-integral integral interval to achieve any time-step adaptive quadrature. The numerical example shows that the maximum error of the precise time integral is 2.8% of the central difference method, 2.2% of the Newmark method and the maximum solution error is only 0.029% in the nonhomogeneous system with the same time step. This fully shows that the discrete quadrature discrete time-based integration algorithm has good convergence.