A comparison of approximate methods for the solution of plate bending problems.
A comparison of approximate methods for the solution of plate bending problems.
复制标题
板弯曲问题求解近似方法的比较。
作者：
W. E. Clausen;A. T. Hopper;L. E. Hulbert;A. Leissa
众所周知，在边界形状不规则和任意横向载荷和约束的情况下，经典的精确解析解方法不能应用于板弯曲问题。本文总结和比较了用点匹配法、边界点最小二乘法、TrefftzMorley法、内部配置法、内部最小二乘法、子域法、Galerkin法、Ritz法和Kantorovich法等九种近似分析方法的结果。为了具体比较的目的，每种方法都被应用于两个问题，它们的精确解虽然复杂，但已知：1)均匀加载的简支椭圆板；2)具有自由边缘的方形板，支承在四个不对称的内点上，并受自身重量的作用。文中给出了比较结果。根据11个重要的技术标准，每种技术都被评为好、可或差，并解释了其基本原理。
It is well known that classical, exact methods of analytical solution cannot be applied to the plate bending problem in cases of irregular boundary shape and arbitrary transverse loading and constraint. The paper summarizes and compares results obtained from using nine approximate analytical methods: point matching, boundary point least squares, TrefftzMorley, interior collocation, interior least squares, subdomain, Galerkin, Ritz, and Kantorovich. For purposes of concrete comparison, each of the methods is applied to two problems for which exact, although intricate, solutions are known: 1) a uniformly loaded, simply supported elliptical plate; 2) a square plate having free edges, supported at four asymmetrically located interior points, and loaded by its own weight. Comparative results are presented. Each technique is rated good, fair, or poor according to 11 important technical criteria and the underlying rationale is explained.