A novel node-based smoothed finite element method with linear strain fields for static, free and forced vibration analyses of solids

Abstract

This paper presents a novel node-based smoothed finite element method (NS-FEM) with a higher order strain field. It uses piecewise linear displacements on 3-node triangular elements, together with strain field which is also linear but over the node-based smoothed domains. This high-order strain NS-FEM is fundamentally different from the standard FEM that uses piecewise linear displacement and constants strain fields. In our high-order strain NS-FEM, the smoothed strains are expressed with complete order of polynomials which have coefficients, linear and high-order terms. This is also different from the smoothed strain used in the existing standard NS-FEM which is a constant obtained by a generalized smoothing technique. The unknown coefficients in assumed strain functions can be uniquely determined by linearly independent weight functions. This is because the smoothed strain and compatible strain within a local region are equal in an integral sense when weighted by continuous functions. We present, with proofs on convergence, two versions of high-order strain NS-FEMs which are termed as: NS-FEM-1 that uses 1st order smoothed strains and NS-FEM-2 that uses 2nd order smoothed strains. The new developed high-order strain NS-FEM is applied for static, free and forced vibration analyses of solids, and our numerical results support our theorems.