In the present study, the three-dimensional elastic discrete element method (DEM) and the elastic finite element method (FEM) analysis were, respectively, applied to the randomly distributed identical spheres as a granular target and to the cylindrical projectiles in order to clarify dynamic response during penetration. In the target, it was found that highly densified region was formed just ah...

This paper is about discrete sensitivity analysis. A triangular bending element with constant moment and six degrees of freedom is used. The required derivatives for sensitivity analysis are calculated explicitly. These formulations, finite element method and sequential linear programming are utilized to find shape optimization of plate bending structures. The numerical examples, which show the...

This paper presents a new efficient method for animating sand and other granular materials in 3D scenes. Our method couples 2D and 3D simulation techniques in a physically based way. A surface flow model of granular material-the BCRE model-is used to separate sand piles into two layers: a surface flowing layer and a static layer. The surface layer is simulated using discrete element method (DEM...

Discrete element method (DEM) is a numerical technique pioneered by Cundall for problems in rock mechanics where the continuity between the separate elements does not exist. Discrete numerical simulations with particles are currently used in several different scientific disciplines. The DEM is capable of handling a wide range of material behaviour, inter-body interaction force laws and arbitrar...

Despite the popularity of high-order explicit Runge–Kutta (ERK) methods for integrating semi-discrete systems of equations, ERK methods suffer from severe stability-based time step restrictions for very stiff problems. We implement a discontinuous Galerkin finite element method (DGFEM) along with recently introduced high-order implicit–explicit Runge–Kutta (IMEX-RK) schemes to overcome geometry...

We propose and analyse a lumped surface finite element method for the numerical approximation of reaction–diffusion systems on stationary compact surfaces in R3. The proposed method preserves the invariant regions of the continuous problem under discretization and, in the special case of scalar equations, it preserves themaximumprinciple. On the application of a fully discrete scheme using the ...

Finite element and finite difference methods have been widely used, among other methods, to numerically solve the Fokker-Planck equation for investigating the time history of the probability density function of linear and nonlinear 2d and 3d problems, and also the application to 4d problems has been addressed. However, due to the enormous increase of the computational costs, different strategie...

This paper is about discrete sensitivity analysis. A triangular bending element with constant moment and six degrees of freedom is used. The required derivatives for sensitivity analysis are calculated explicitly. These formulations, finite element method and sequential linear programming are utilized to find shape optimization of plate bending structures. The numerical examples, which show the...