Bubble-Enriched Smoothed Finite Element Methods for Nearly-Incompressible Solids

This work presents a locking-free smoothed finite element method(S-FEM)for the simulation of soft matter modelled by the equations of quasi-incompressible hyperelasticity.The proposed method overcomes well-known issues of standard finite element methods(FEM)in the incompressible limit:the over-estimation of stiffness and sensitivity to severely distorted meshes.The concepts of cell-based,edge-based and node-based S-FEMs are extended in this paper to three-dimensions.Additionally,a cubic bubble function is utilized to improve accuracy and stability.For the bubble function,an additional displacement degree of freedom is added at the centroid of the element.Several numerical studies are performed demonstrating the stability and validity of the proposed approach.The obtained results are compared with standard FEM and with analytical solutions to show the effectiveness of the method.

A Cell-Based Smoothed Finite Element Method for Modal Analysis of Non-Woven Fabrics

The combination of a 4-node quadrilateral mixed interpolation of tensorial components element(MITC4)and the cell-based smoothed finite element method(CSFEM)was formulated and implemented in this work for the analysis of free vibration and unidirectional buckling of shell structures.This formulation was applied to numerous numerical examples of non-woven fabrics.As CSFEM schemes do not require coordinate transformation,spurious modes and numerical instabilities are prevented using bilinear quadrilateral element subdivided into two,three and four smoothing cells.An improvement of the original CSFEM formulation was made regarding the calculation of outward unit normal vectors,which allowed to remove the integral operator in the strain smoothing operation.This procedure conducted both to the simplification of the developed formulation and the reduction of computational cost.A wide range of values for the thickness-to-length ratio and edge boundary conditions were analysed.The developed numerical model proved to overcome the shear locking phenomenon with success,revealing both reduced implementation effort and computational cost in comparison to the conventional FEM approach.The cell-based strain smoothing technique used in this work yields accurate results and generally attains higher convergence rate in energy at low computational cost.

Selective Smoothed Finite Element Method

The paper examines three selective schemes for the smoothed finite element method （SFEM） which was formulated by incorporating a cell-wise strain smoothing operation into the standard compatible finite element method （FEM）. These selective SFEM schemes were formulated based on three selective integration FEM schemes with similar properties found between the number of smoothing cells in the SFEM and the number of Gaussian integration points in the FEM. Both scheme 1 and scheme 2 are free of nearly incompressible locking, but scheme 2 is more general and gives better results than scheme 1. In addition, scheme 2 can be applied to anisotropic and nonlinear situations, while scheme 1 can only be applied to isotropic and linear situations. Scheme 3 is free of shear locking. This scheme can be applied to plate and shell problems. Results of the numerical study show that the selective SFEM schemes give more accurate results than the FEM schemes.

On the Factors Affecting the Accuracy and Robustness of Smoothed-Radial Point Interpolation Method

In order to overcome the possible singularity associated with the Point Interpolation Method(PIM),the Radial Point Interpolation Method(RPIM)was proposed by G.R.Liu.Radial basis functions(RBF)was used in RPIM as basis functions for interpolation.All these radial basis functions include shape parameters.The choice of these shape parameters has been and stays a problematic theme in RBF approximation and interpolation theory.The object of this study is to contribute to the analysis of how these shape parameters affect the accuracy of the radial PIM.The RPIM is studied based on the global Galerkin weak form performed using two integration technics:classical Gaussian integration and the strain smoothing integration scheme.The numerical performance of this method is tested on their behavior on curve fitting,and on three elastic mechanical problems with regular or irregular nodes distributions.A range of recommended shape parameters is obtained from the analysis of different error indexes and also the condition number of the matrix system.All resulting RPIM methods perform very well in term of numerical computation.The Smoothed Radial Point Interpolation Method(SRPIM)shows a higher accuracy,especially in a situation of distorted node scheme.