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力学与实践 ›› 2009, Vol. 31 ›› Issue (3): 48-51.doi: 10.6052/1000-0879-2008-405

• 应用研究 • 上一篇    下一篇

中厚板的耦合多项式基径向点插值无网格法

胡玮军 龙述尧   

  1. 邵阳学院 机械工程系,湖南 邵阳422000
  • 收稿日期:2008-08-29 修回日期:2009-01-12 出版日期:2009-06-08 发布日期:2009-06-08

THE RADIAL POINT INTERPOLATION WITH POLYNOMIAL BASIS FUNCTIONS IN MESHLESS METHOD FOR A MODERATELY THICK PLATE

  • Received:2008-08-29 Revised:2009-01-12 Online:2009-06-08 Published:2009-06-08

摘要: 采用Mindlin平板理论,通过最小位能原理建立了各向同性中厚板的伽辽金整体弱式方 程,形函数采用耦合多项式基的径向点插值法构造,可以直接施加本质边界条件. 算例表明, 用耦合多项式基的径向点插值无网格法分析中厚板问题,具有效率高、精度高和易于实现等 优点,可以避免薄板弯曲时的剪切自锁现象.

关键词: 耦合多项式基的径向点插值法;中厚板;无网格法;伽辽金整体弱形式

Abstract: The bending of a moderately thick plate is analyzed by the meshless method with the radial point interpolation and polynomial basis functions in this paper. The global Galerkin weak-form equation for isotropic moderately thick plate is established based on Mindlin plate theory and the minimum total potential energy principle. The shape functions constructed using the radial point interpolation method with polynomial basis functions enjoy Kronecker Delta function property, so the essential boundary conditions can be easily imposed. Numerical examples show that the presented method features high efficiency, good accuracy and easy implementation. The shear locking can thus be avoided in the bending analysis for thin plates.

Key words: radial point interpolation with polynomial basis functions, moderatelythick plate , meshless method, the Galerkin global weak-form