A novel twice-interpolation finite element method for solid mechanics problems

Formulation and numerical evaluation of a novel twice-interpolation finite element method （TFEM） is presented for solid mechanics problems. In this method, the trial function for Galerkin weak form is constructed through two stages of consecutive interpolation. The primary interpolation follows exactly the same procedure of standard FEM and is further reproduced according to both nodal values and averaged nodal gradients obtained from primary interpolation. The trial functions thus constructed have continuous nodal gradients and contain higher order polynomial without increasing total freedoms. Several benchmark examples and a real dam problem are used to examine the TFEM in terms of accuracy and convergence. Compared with standard FEM, TFEM can achieve significantly better accuracy and higher convergence rate, and the continuous nodal stress can be obtained without any smoothing operation. It is also found that TFEM is insensitive to the quality of the elemental mesh. In addition, the present TFEM can treat the incompressible material without any modification.

Analysis of large deformation geotechnical problems using implicit generalized interpolation material point method

This paper presents a quasi-static implicit generalized interpolation material point method(i GIMP)with B-bar approach for large deformation geotechnical problems.The i GIMP algorithm is an extension of the implicit material point method(iMPM).The global stiffness matrix is formed explicitly and the Newton-Raphson iterative method is used to solve the equilibrium equations.Where possible,the implementation procedure closely follows standard finite element method(FEM)approaches to allow easy conversion of other FEM codes.The generalized interpolation function is assigned to eliminate the inherent cell crossing noise within conventional MPM.For the first time,the B-bar approach is used to overcome volumetric locking in standard GIMP method for near-incompressible non-linear geomechanics.The proposed i GIMP was tested and compared with i MPM and analytical solutions via a 1 D column compression problem.Results highlighted the superiority of the i GIMP approach in reducing stress oscillations,thereby improving computational accuracy.Then,elasto-plastic slope stabilities and rigid footing problems were considered,further illustrating the ability of the proposed method to overcome volumetric locking due to incompressibility.Results showed that the proposed i GIMP with B-bar approach can be used to simulate geotechnical problems with large deformations.