关键词: 流形方法, 覆盖位移函数, 泰勒展式, 广义自由度, 矩形格子, 混合阶次

Abstract: For manifold method, high-order displacement function is established by using complete polynomial function, which deprives the generalized freedom degrees of physical meaning. To avoid this problem, the cover displacement function can be regarded as Taylor expansion. Based on the Taylor expansion, the relations among displacement function, nodal displacement and strain are obtained, and generalized degrees of freedom have definite physical meaning after degree elevation. Furthermore, rectangular grid is used as mathematical grid to reduce physical piece and simplify preprocessing and post-processing. In the computational domain, cover displacement function with mixed-order is employed to improve computation efficiency and to combine analytical solution and numerical solution. Moreover, improved penalty function and generalized node function are used together to deal with boundary conditions, which is in strict accordance with the physical meaning of boundary condition. Finally, this method is proved to be highly efficient by numerical examples, and the accuracy of numerical solution is also improved.

Key words: manifold method, cover displacement function, Taylor expansion, generalized degrees of freedom, rectangular grid, mixed order