极坐标平面问题的四阶差分及应用  

FOURTH ORDER DIFFERENCE OFPLANE PROBLEM IN POLARCOORDINATE SYSTEM AND ITSAPPLICATION

作　　者：孟进军[1] 高慧[2] 董正筑[1] 

机构地区：[1]中国矿业大学理学院,徐州221008 [2]上海交通大学,上海200030

出　　处：《力学与实践》2004年第6期63-65,13,共4页Mechanics in Engineering

摘　　要：推导出了极坐标系下双调和方程的差分公式,用逐次超松弛迭代法求出圆板平面应力问题的差分解,并和解析解作比较,验证了差分公式的正确性,为解决圆域及其类似区域的平面问题提供了新方法.The difference formula of the bi-harmonic equation is derived in the polar coordinate system. The finite difference solution to the elastic plane problem of a disk is carried out by successive overrelaxation. By comparing with the theoretical solution of the problem, the validity of the difference formula is verified. The result provides a new and convenient way to solve the plane problem of disk and other similar shapes.

关 键 词：四阶 平面问题 差分解 类似 平面应力问题 双调和方程 阶差 公式 极坐标 推导 

分 类 号：O343[理学—固体力学] G633[理学—力学]