多层地基条带基础动力刚度矩阵的精细积分算法

提出应用精细积分算法计算多层地基的动力刚度问题. 精细积分是计算层状介质中波传播的高效而精确的数值方法. 利用傅里叶积分变换将层状地基的波动方程转换为频率-波数域内的两点边值问题的常微分方程组, 运用精细积分方法求解格林函数, 最后再将得到的频率-波数域内地基表面的动力刚度矩阵转换到频率-空间域内, 进而得到刚性条带基础频率域的动力柔度或刚度矩阵. 所建议的精细积分算法, 可以避免一般传递矩阵计算中的指数溢出问题, 对各种情况有广泛的适应性, 计算稳定, 在高频段可以保障收敛性, 并能达到较高的计算精度.

A PRECISE INTEGRATION APPROACH FOR THE DYNAMIC-STIFFNESS MATRIX OF STRIP FOOTINGS ON A LAYERED MEDIUM

A precise integration method(PIM) is applied to the evaluation of dynamic-stiffness matrix of strip footings on a layered medium.PIM is an efficient and accurate numerical method to study the wave motion in layered earth strata.Through Fourier transform,the governing equation of wave propagation is formulated in the frequency-wavenumber domain as a set of ordinary differential equations with two-point boundary value conditions,and the Green’s functions are solved by PIM.Finally,the dynamic-stiffness matrix of rigid strip footing on layered medium is converted from frequency-wavenumber domain into frequency-spatial domain. The proposed algorithm has the advantages that it avoids the exponential overflow generally encountered in the case of transmission matrix.In addition,it is versatile and adaptable to various cases of footings.It ensures convergence at high-frequency range,while perfect accuracy can be achieved.