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精细积分法既可得到在计算机精度意义下的精确解,又能够保持哈密顿体系的辛结构。其是求解一阶线性常微分方程组的精确数值方法,既可以用于时间域的初值问题,又可以应用于空间域的两点边值问题。运用精细积分法求解微层区段矩阵,并对微层区段矩阵合并得到整个层状地基的区段矩阵,最终得到层状地基的动力柔度值。运用数值算例验证了本文方法的计算精度。
The precise integration method can obtain the exact solution in the sense of computer precision and maintain the symplectic structure of the Hamiltonian system. It is an exact numerical method for solving first-order linear ordinary differential equations. It can be used for the initial value problem in time domain and the two-point boundary value problem in space domain. The precise integration method is used to solve the micro-layer segment matrix, and the micro-layer segment matrix is combined to obtain the segment matrix of the entire layered ground. Finally, the dynamic compliance value of the layered ground is obtained. Numerical examples are used to verify the accuracy of the proposed method.