在无单元法里直接准确施加位移边界条件和材料不连续条件

在无单元伽辽金法(EFG)里，由于其滑动最小二乘近似位移函数不满足Kronecker条件，使得它不能准确地施加本质边界条件和材料不连续条件，从而极大地限制了EFG法的发展和进一步应用。本文在位移边界和不同材料交界面的离散结点上采用实际的结点位移值，提出了一种准确施加位移边界和材料不连续条件的方法，该方法实施简单、稳定、求解精度高，而且其推导得出的整体刚度矩阵具有正定、对称和带状分布的特点，可以和有限单元法一样，直接利用各种成熟、高效的线性方程组解法求解系统平衡方程。数值算例结果表明了文中理论和方法的正确性和可靠性。

Direct imposition of essential boundary and material discontinuity conditions in the meshless method

Direct imposition of essential boundary and material discontinuity conditions is always difficult in meshless method because the shape functions from the Moving Least Squares approximation do not have the delta property. By using the actual displacements at the nodes of essential boundary and the material interface in each material domain, the stiffness matrix and load vector at integral point have been rewritten and transformed, and a method for naturally enforcing these two conditions is proposed in this paper. As a result, the proposed method yields a positive, symmetrical and banded global stiffness matrix like it in finite element methods and has the advantages of stabilization and be easy to implement as compared to the penalty method, the Lagrange method, and other methods. The technique is described in EFG method in this paper, but can easily be applicable to other meshless methods and projections. Numerical results indicate that the theory and programs are accurate and effective.