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Strain smoothing operation has been recently adopted to soften the stiffness of the model created using tetrahedron mesh, such as the Face-based Smoothed Finite Element Method (FS-FEM), with the aim to improve solution accuracy and the applicability of low order tetrahedral elements. In this paper, a new method with strain smoothing operation based on the edge of four-node tetrahedron mesh is proposed, and the edge-based smoothing domain of tetrahedron mesh is serving as the assembly unit for computing the 3D stiffness matrix. Numerical results demonstrate that the proposed method possesses a close-to-exact stiffness of the continuous system and gives better results than both the FEM and FS-FEM using tetrahedron mesh or even the FEM using hexahedral mesh in the static and dynamic analysis. In addition, a novel domain-based selective scheme is proposed leading to a combined ES-T-/NS-FEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The proposed method is an innovative and unique numerical method with its distinct features, which possesses strong potentials in the successful applications for static and dynamics problems. [ABSTRACT FROM AUTHOR]

In this paper, a linearly conforming radial point interpolation method (LC-RPIM) is presented for the linear analysis of shells. The first order shear deformation shell theory is adopted, and the radial and polynomial basis functions are employed to construct the shape functions. A strain smoothing stabilization technique for nodal integration is used to restore the conformability and to improve the accuracy. Convergence studies are performed in terms of the number of nodes and the nodal distribution patterns, including the regular distribution and the irregular distribution. Comparisons are made with the existing results available in the literature and good agreements are obtained. The numerical examples have demonstrated that the present approach provides very stable and accurate results and effectively eliminates the membrane locking and shear locking in shell problems. [ABSTRACT FROM AUTHOR]

A novel gradient smoothing method (GSM) is proposed in this paper, in which a gradient smoothing together with a directional derivative technique is adopted to develop the first- and second-order derivative approximations for a node of interest by systematically computing weights for a set of field nodes surrounding. A simple collocation procedure is then applied to the governing strong-from of system equations at each node scattered in the problem domain using the approximated derivatives. In contrast with the conventional finite difference and generalized finite difference methods with topological restrictions, the GSM can be easily applied to arbitrarily irregular meshes for complex geometry. Several numerical examples are presented to demonstrate the computational accuracy and stability of the GSM for solid mechanics problems with regular and irregular nodes. The GSM is examined in detail by comparison with other established numerical approaches such as the finite element method, producing convincing results. [ABSTRACT FROM AUTHOR]

To simulate the contact nonlinearity in 2D solid problems, a contact analysis approach is formulated using incremental form of the subdomain parametric variational principle (SPVP). The formulation is based on a linearly conforming radial point interpolation method (LC-RPIM) using nodal integration technique. Contact interface equations are also presented using a modified Coulomb frictional contact model and discretized by contact point-pairs. In the present approach, the global discretized system equations are transformed into a standard linear complementarity problem (LCP) that can be solved readily using the Lemke method. The present approach can simulate various contact behaviors including bonding/debonding, contacting/departing, and sticking/slipping. An intensive numerical study is performed to validate the proposed method via comparison with the ABAQUS® and to investigate the effects of the various parameters used in computations. These parameters include normal and tangential adhesions, frictional coefficient, nodal density, the dimension of local nodal support domain, nodal irregularity, shape parameters used in the radial basis function and the external load. The numerical results have demonstrated that the present approach is accurate and stable for contact analysis of 2D solids. [ABSTRACT FROM AUTHOR]