广义节点无网格法在土力学固结分析中的应用

借鉴流形方法思想,引入广义节点的概念,对传统的无网格法进行了改进,建立了可具有任意高阶多项式插值函数的广义节点无网格方法.与传统无网格方法相比,广义节点无网格方法更具有一般性,当选取0阶广义节点位移插值函数时便可得到传统的无网格法.结合土工固结问题,通过推导建立了Blot固结方程的数值计算列式,对静态固结问题进行数值计算,通过对比分析验证了所建议方法的可行性.

Application of generalized-node-based meshfree method to consolidation analysis based on Biot's equations in soil mechanics

A new type of meshfree method is developed by incorporating the generalized node which is originated from manifold method with the conventional meshfree method. The proposed method is termed as the generalized-node-based meshfree method. The fundamental theory together with numerical formulations is presented. When the zero-order displacement interpolation function of the generalized node is chosen, the proposed method will be reduced to the conventional meshfree method. Based on Biot’s consolidation equations, the numerical formulation for analysis of consolidation in soil mechanics are especially established by using the proposed method. The accuracy and rationality of the present analysis are verified by comparing the computational results with the solution obtained by FEM for an example.