Virtual element method (VEM), which is recently proposed by L. Beirão da Veiga [1], is well-developed since its birth and becomes a powerful tool in the field of computational mechanics. Different from classical finite element method (FEM), VEM has the following features
VEM can be applied to arbitrary polygonal mesh
VEM is able to handle hanging nodes on element edge
A number of researches are implemented to exploit the effectiveness and application of VEM, including elastic analysis [2], finite deformation analysis[3], contact analysis [4], fracture analysis [5] and structural topology optimization [6]. Based on Ref. [4], the study contact analysis with non-matching contact interface by using second-order VEM is investigated as in Fig.1. The results in Fig.2 show that even with irregular element shape and non-matching interface the patch test is also passed without biased stress distribution along the contact interface.
FIG.1: Model of Example 1; (left) Geometry models of two elastic blocks, (right) Second-order VEM discretization
FIG.2: Results of patch test; (left) Deformed shape, (right) Stress contour of $ \sigma_{22} $
There are still a lot more fascinating and interesting properties of VEM to be explored, and right now I would like to dig more on VEM in the areas of structural topology optimization and nonlinear and multiscale analysis.
Benchmark test with L-shaped element using VEM
