层状地基上梁的边界元边界元耦合解法

BEM-BEM Coupling Method for a Beam on Multilayered Soils

分别对地基接触面和梁进行离散,假定地基反力的分布情况,并确定梁单元节点和反力未知量;将无限长EulerBernoulli梁的基本解作为梁边界单元法的核函数,然后把Euler-Bernoulli梁边界积分方程应用到各节点,建立起基础梁的边界积分方程组;将层状地基的基本解作为地基边界积分方程的核函数,通过边界积分方程建立起梁各节点竖向位移与地基反力未知量的沉降-反力柔度矩阵;最后,根据地基与梁接触面的位移协调条件,建立起层状地基与EulerBernoulli梁共同作用问题总的边界元-边界元耦合方程组.根据该理论,编制了相应的程序,通过与现有文献对比验证该理论的正确性,并分析了分层地基特性对基础梁的影响.研究结果表明:相比有限元-边界元耦合法,边界元-边界元耦合法的效率更高.

Dividing the foundation interface and the beam into several segments, and assuming the distribution of the foundation reaction, the beam nodes and the reaction variables are confirmed. By taking the fundamental solutions of the infinite Euler-Bernoulli beam as the kernel functions of the boundary element method （BEM） of the beam, the boundary integral equation of Euler-Bernoulli beam is applied to each node so as to establish the boundary integral equations of the foundation beam. The settlement-reaction flexibility matrix between the vertical displacements of beam nodes and the foundation reacting forces is formed through Gauss integral byadopting the fundamental solution of layered soils as the kernel function of the boundary element method （BEM） of the subgrade. Finally, the global BEM-BEM coupling equations of the soil-beam interaction problem are obtained according to the compatible displacement condition at the soil-beam interface. According to the above theory, the corresponding program is compiled, and further the accuracy of the theory is verified by comprising the results of this paper with the existing reference. Moreover, the influence of the characteristics of the soil layers is analyzed, showing that the BEM-BEM coupling method is more efficient than the FEM- BEM coupling method.