基于三角网格多节点覆盖的数值流形方法

以任意三角网格作为数学网格,应用无网格法理论,提出了一种新的权函数构造方法,建立基于任意三角网格的一种多节点流形单元覆盖。针对小挠度变形的薄板弯曲问题,推导出应用于薄板问题的流形格式和单元矩阵。单元节点的覆盖位移采用C0,C1阶的局部多项式形式,积分采用面积坐标的hammer积分。算例表明,与有限元分析相比,该方法的流形单元在计算精度和收敛性上,可得到大幅度提高。

A new triangular element of numerical manifold method

Based on cover system with triangular mathematic mesh.A new weight function is constructed to form a multi-node global cover function.This numerical manifold method is applied to analyze the plate bending deformation.Numerical manifold formulas and element matrices are derived in this paper.C0 and C1 local polynomial is adopted as the node cover function.The result show that numerical manifold method with multi-node triangular element,compared with finite element method,can improve accuracy and convergence greatly.