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一般的数值流形方法均采用三角形、四边形单元进行计算。对于工程中的有些实际问题,多边形单元能更好的适应复杂计算域形状。为此,研究了采用多边形流形单元进行数值计算的方法。采用任意几何区域的Delaunay三角网格构造出新的凸多边形网格,并以此单元作为计算的流形单元。采用改进的Wachspress插值函数作为多边形流形单元的权函数。为说明该方法的有效性,将该流形方法应用于薄板弯曲计算,推导出用于薄板弯曲分析的流形格式和单元矩阵。计算结果表明:较一般有限元法,计算精度和收敛速度有很大提高。
The general numerical manifold method uses triangle and quadrilateral elements to calculate. For some practical problems in engineering, polygonal elements can better adapt to complex shape of computational domain. Therefore, the method of numerical calculation using polygonal manifold units is studied. A new convex polygon mesh is constructed by using Delaunay triangulation of arbitrary geometric region, and the unit is used as a manifold unit. Adopting the improved Wachspress interpolation function as the weight function of polygon manifold units. To illustrate the effectiveness of this method, the manifold method is applied to sheet bending calculations, and the manifold format and element matrix for sheet bending analysis are derived. The calculation results show that compared with the general finite element method, the computational accuracy and convergence speed are greatly improved.