传递矩阵法的Z_n误差分析

Analysis of error caused by Z_n in transferring matrix method

以轴对称问题的传递矩阵法为基础。在传递矩阵法的数值计算中,发现最下层弹性体的计算深度Zn引起了很大的误差,甚至使结果变得非常不可靠。将总传递矩阵B理解为两大部分:B=GA,其中G是最下层的传递矩阵,A是其它所有传递矩阵的乘积。其后,再利用矩阵乘法的知识将B展开,这样得到的计算公式不含Zn。

On the bais of the transferring matrix method,which is an explicit solution for axisymmetric problem in layered elastic semi-infinite body,the calculational method given in this paper can reduce the error,which is caused mainly by the depth of the downmost elastic layer.Of course,during the process,how to multiply the matrixes subtly is of great importance.The assembled transferring matrix B is divided into two parts:B=GA,of which the G represents the transferring matrix of the downmost elastic layer,and the A is the product of the other transferring matrixes formed from elastic layer n-1to layer1.