高阶数值流形方法的速度公式

高阶数值流形方法可以显著提高结构计算精度,但目前在涉及大位移的动力分析中往往得到精度很差、甚至不正确的速度结果。基于平面三角形数学网格和一阶多项式覆盖函数,通过一个刚体杆件旋转算例探讨其中的原因,得出必须考虑构形坐标变化对速度的影响,并提出高阶流形法的3种速度处理方法及相应的高阶速度公式。该方法对一些在结点处增加广义自由度的类似方法(如广义有限元)的几何非线性问题分析也具有一定的参考价值。

Velocity Equations for High-order Numerical Manifold Method

Computational accuracy of structure deformation can be improved greatly by the high-order Numerical Manifold Method (NMM). However, poor accuracy or even incorrect velocity results were obtained in the dynamic analysis involved in large displacement. Based on 2-D triangular mathematical meshes and 1-order polynomial cover functions, the reason of the above cases is discussed through an example of rotation of a rigid bar in this paper. Three treatments and the corresponding equations for high-order velocities are presented for the first time, reflecting the change of configuration coordinates under large displacement. The high-order numerical manifold method is useful to other methods such as Generalized Finite Element Method (GFEM) which introduces generalized freedoms at nodes when solving geometric nonlinear problems.