极坐标平面问题的四阶差分及应用
FOURTH ORDER DIFFERENCE OF PLANE PROBLEM IN POLAR COORDINATE SYSTEM AND ITS APPLICATION
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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.Abstract: The difference formula of the bi-harmonic equation isderived in the polar coordinate system. The finite difference solution tothe elastic plane problem of a disk is carried out by successiveoverrelaxation. By comparing with the theoretical solution of theproblem, the validity of the difference formula is verified. The resultprovides a new and convenient way to solve the plane problem of disk andother similar shapes.