A cell-based smoothed finite element method for finite elasticity

In this study, we present a displacement based polygonal finite element method for compressible and nearly-incompressible elastic solids undergoing large deformations in two dimensions. This is achieved by projecting the dilatation strain onto the linear approximation space, within the framework of volume averaged nodal projection method. To reduce the numerical integration burden over polytopes, a linear strain smoothing technique is employed to compute the terms in the bilinear/linear form. The salient features of the proposed framework are: (a) does not require derivatives of shape functions and complex numerical integration scheme to compute the bilinear and linear form and (b) volumetric locking is alleviated by adopting the volume averaged nodal projection technique. The efficacy, convergence properties and accuracy of the proposed framework is demonstrated through four standard benchmark problems.