用弹性平板代替球壳计算板块弯曲形变的误差分析

ANALYSIS OF ERROR CAUSED BY USING PLATE MODEL INSTEAD OF SPHERICAL SHELL IN STUDYING THE BENDING DEFORMATION OF LITHOSPHERE

在岩石圈板块弯曲问题的研究中常常忽略地壳曲率，用平板代替球壳计算．本文从弹性扁球壳和薄板形变的基本方程入手，通过对典型问题的解析解，推导出作简化处理所引起误差的表达式，着重分析了区域的几何尺度和地基模量对误差的影响．研究表明，用弹性平板模型取代球壳模型计算板块弯曲形变会引起较大的误差．但如果采用具有适当地基模量的弹性基础板，不但更符合地学实际，且能有效地改善误差状况，获得与用肩球壳计算弯曲问题接近的效果．

The simplification in using a plate model instead of a spherical shell is usually adopted to study the bending defomtion of the lithosphere. This paper proceeds from the differential equations for bending of plates and shallow spherical shell. Then an error expression is derived for the simplification in neglecting the earth curvature. The effect of the model's dimension on the error is discussed. It is proved that if we replace the shallow spherical shell by a plate model to solve the bending deformation of lithospheric plate, a large error will be caused. But when using a plate on a elastic foundation instead, we can obtain an approximate solution closer tO that of spherical shell. The error is reduced effectively and it is also closer to the actual geological condition.