自然单元法在Winkler地基薄板计算中的应用

Application of natural element method to solution of elastic thin plate bending on Winkler soil foundation

自然单元法是一种基于Voronoi图及Delaunay三角形剖分图,以自然邻接点插值为试函数的一种无网格数值方法。本文以目前该方法中自然邻接点的Laplace插值形函数为基础,求出了其一阶及二阶导函数,建立了Winkler地基上薄板弯曲挠度的自然单元法求解控制方程,并编制了相应的计算程序,通过算例分析表明了本文方法的可行性和有效性。

Natural element method （NEM） is a new numerical computational method based on Voronoi diagram and Delaunay triangulation. It is a Galerkin-based meshless method built on the natural neighbor interpolation shape function. The first and second derivatives of natural neighbor Laplace interpolation function in NEM are deduced and the governing equations of natural element method to the deflection solution of elastic thin plate bending on Winkler soil foundation are achieved. Numerical results indicate that the above theory and the corresponding program are feasible and effective.