P. C. Wallstedt¹, J. E. Guilkey¹

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.3, pp. 223-232, 2007, DOI:10.3970/cmes.2007.019.223

Abstract The standard velocity projection scheme for the Material Point Method (MPM) and a typical form of the GIMP Method are examined. It is demonstrated that the fidelity of information transfer from a particle representation to the computational grid is strongly dependent on particle density and location. In addition, use of non-uniform grids and even non-uniform particle sizes are shown to introduce error. An enhancement to the projection operation is developed which makes use of already available velocity gradient information. This enhancement facilitates exact projection of linear functions and reduces the dependence of projection accuracy on particle location and density for… More >

Shunde Yin¹, Leo Rothenburg¹, Maurice B. Dusseault¹

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.2, pp. 111-120, 2007, DOI:10.3970/cmes.2007.019.111

Abstract Subsidence problem is of great importance in petroleum engineering and environmental engineering. In this paper, we firstly apply a hybrid Displacement Discontinuity-FEM modeling to this classic problem: the evaluation of subsidence over a compacting oil reservoir. We use displacement discontinuity method to account for the reservoir surrounding area, and finite element methods in the fully coupled simulation of the reservoir itself. This approach greatly reduces the number of degrees of freedom compared to an analyzing fully coupled problem using only a finite element or finite difference discretization. More >

J. Perko¹, B. Šarler²

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.1, pp. 55-68, 2007, DOI:10.3970/cmes.2007.019.055

Abstract This work introduces a procedure for automated determination of weight function free parameters in moving least squares (MLS) based meshless methods for non-uniform grids. The meshless method used in present work is Diffuse Approximate Method (DAM). The DAM is structured in 2D with the one or two parameter Gaussian weigh function, 6 polynomial basis and 9 noded domain of influence. The procedure consists of three main elements. The first is definition of the reference quality function which measures the difference between the MLS approximation on non-uniform and hypothetic uniform node arrangements. The second is the construction of the object function… More >

Q.W. Ma¹

CMES-Computer Modeling in Engineering & Sciences, Vol.18, No.3, pp. 223-234, 2007, DOI:10.3970/cmes.2007.018.223

Abstract Two methods have been recently developed by the author and his group: one called MLPG_R (Meshless Local Petrov-Galerkin method based on Rankine source solution) and the other called QALE-FEM (Quasi Arbitrary Lagrangian-Eulerian Finite Element Method). The former is a meshless method developed from a general MLPG (Meshless Local Petrov-Galerkin) method and is more computationally efficient than the general one when applied to modelling nonlinear water waves. The later is a mesh-based method similar to a conventional finite element method (FEM) when discretizing the governing equations but different from the conventional one in managing the mesh. In this paper, they are… More >

R.L. Huston¹, C.-Q. Liu²

CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.2, pp. 143-152, 2005, DOI:10.3970/cmes.2005.010.143

Abstract This paper presents a summary of recent developments in computational methods for multibody dynamics analyses. The developments are presented within the context of an automated numerical analysis. The intent of the paper is to provide a basis for the easy development of computational algorithms. The principal concepts discussed are: differentiation algorithms, partial velocities and partial angular velocities, generalized speeds, Euler parameters, Kane's equations, orthogonal complement arrays, lower body arrays and accuracy testing functions. More >

P. A. C. Porto¹, A. B. Jorge¹, G. O. Ribeiro²

CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.1, pp. 65-78, 2005, DOI:10.3970/cmes.2005.010.065

Abstract This work deals with a numerical solution technique for the self-regular gradient form of Green's identity, the flux boundary integral equation (flux-BIE). The required C^1,α inter-element continuity conditions for the potential derivatives are imposed in the boundary element method (BEM) code through a non-symmetric variational formulation. In spite of using Lagrangian C⁰ elements, accurate numerical results were obtained when applied to heat transfer problems with singular or quasi-singular conditions, like boundary points and interior points which may be arbitrarily close to the boundary. The numerical examples proposed show that the developed algorithm based on the self-regular flux-BIE are highly efficient,… More >

Z. D. Han¹, A. M. Rajendran², S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.1, pp. 1-12, 2005, DOI:10.3970/cmes.2005.010.001

Abstract A nonlinear formulation of the Meshless Local Petrov-Galerkin (MLPG) finite-volume mixed method is developed for the large deformation analysis of static and dynamic problems. In the present MLPG large deformation formulation, the velocity gradients are interpolated independently, to avoid the time consuming differentiations of the shape functions at all integration points. The nodal values of velocity gradients are expressed in terms of the independently interpolated nodal values of displacements (or velocities), by enforcing the compatibility conditions directly at the nodal points. For validating the present large deformation MLPG formulation, two example problems are considered: 1) large deformations and rotations of… More >

Qing-Sheng Yang^1,2, Wilfried Becker³

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.4, pp. 319-332, 2004, DOI:10.3970/cmes.2004.006.319

Abstract The present paper focuses on the comparative investigation of different homogenization methods for fiber composites, void solids and rigid inclusion media. The effective properties of multi-phase media are calculated by three methods, i.e. direct average method of stress and strain, direct average method of strain energy and two-scale expansion method. A comprehensive comparison, in principle and numerically, of these methods is emphasized. It is obvious that the two direct average methods are identical in principle and therefore they give the same numerical results. It is shown that the two-scale expansion method is the same as the direct average concept of… More >

Q. Li¹, S. Shen¹, Z. D. Han¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.5, pp. 571-586, 2003, DOI:10.3970/cmes.2003.004.571

Abstract In this paper, a truly meshless method, the Meshless Local Petrov-Galerkin (MLPG) Method, is developed for three-dimensional elasto-statics. The two simplest members of MLPG family of methods, the MLPG type 5 and MLPG type 2, are combined, in order to reduce the computational requirements and to obtain high efficiency. The MLPG5 method is applied at the nodes inside the 3-D domain, so that any domain integration is eliminated altogether, if no body forces are involved. The MLPG 2 method is applied at the nodes that are on the boundaries, and on the interfaces of material discontinuities, so that the boundary… More >

L. F. Qian^1,3, R. C. Batra², L. M. Chen³

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 161-176, 2003, DOI:10.3970/cmes.2003.004.161

Abstract We use two meshless local Petrov-Galerkin formulations, namely, the MLPG1 and the MLPG5, to analyze infinitesimal deformations of a homogeneous and isotropic thick elastic plate with a higher-order shear and normal deformable plate theory. It is found that the two MLPG formulations give results very close to those obtained by other researchers and also by the three-dimensional analysis of the problem by the finite element method. More >