A meshfree-enriched finite element method for compressible and near-incompressible elasticity

作者：Wu C T^*; Hu W; Chen J S

来源：International Journal for Numerical Methods in Engineering, 2012, 90(7): 882-914.

DOI：10.1002/nme.3349

• meshfree
• finite element
• convex
• volumetric locking
• near-incompressible

In this paper, a two-dimensional displacement-based meshfree-enriched FEM (ME-FEM) is presented for the linear analysis of compressible and near-incompressible planar elasticity. The ME-FEM element is established by injecting a first-order convex meshfree approximation into a low-order finite element with an additional node. The convex meshfree approximation is constructed using the generalized meshfree approximation method and it possesses the Kronecker-delta property on the element boundaries. The gradient matrix of ME-FEM element satisfies the integration constraint for nodal integration and the resultant ME-FEM formulation is shown to pass the constant stress test for the compressible media. The ME-FEM interpolation is an element-wise meshfree interpolation and is proven to be discrete divergence-free in the incompressible limit. To prevent possible pressure oscillation in the near-incompressible problems, an area-weighted strain smoothing scheme incorporated with the divergence-free ME-FEM interpolation is introduced to provide the smoothing on strains and pressure. With this smoothed strain field, the discrete equations are derived based on a modified HuWashizu variational principle. Several numerical examples are presented to demonstrate the effectiveness of the proposed method for the compressible and near-incompressible problems.

• 出版日期2012-5-18