S. S. Chen¹, Y. H. Liu^1,2, Z. Z. Cen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.1, pp. 39-56, 2008, DOI:10.3970/cmes.2008.028.039

Abstract In most engineering applications, solutions derived from the lower-bound theorem of plastic limit analysis are particularly valuable because they provide a safe estimate of the load that will cause plastic collapse. A solution procedure based on the meshless local Petrov-Galerkin (MLPG) method is proposed for lower-bound limit analysis. This is the first work for lower-bound limit analysis by this meshless local weak form method. In the construction of trial functions, the natural neighbour interpolation (NNI) is employed to simplify the treatment of the essential boundary conditions. The discretized limit analysis problem is solved numerically with the reduced-basis technique. The self-equilibrium… More >

Thi D. Dang¹, Bhavani V. Sankar²

CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.3, pp. 169-188, 2008, DOI:10.3970/cmes.2008.026.169

Abstract In this paper the meshless local Petrov-Galerkin (MLPG) method is used in the micromechanical analysis of a unidirectional fiber composite. The methods have been extended to include shear loadings, thus permitting a more complete micromechanical analysis of the composite subjected to combined loading states. The MLPG formulation is presented for the analysis of the representative volume element (RVE) of the periodic composite containing material discontinuities. Periodic boundary conditions are imposed between opposite faces of the RVE. The treatment of periodic boundary conditions in the MLPG method is handled by using the multipoint constraint technique. Examples are presented to illustrate the… More >

Shu Li¹, S. N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.1, pp. 61-74, 2008, DOI:10.3970/cmes.2008.026.061

Abstract The Meshless Local Petrov-Galerkin (MLPG) "mixed collocation'' method is applied to the problem of topology-optimization of elastic structures. In this paper, the topic of compliance minimization of elastic structures is pursued, and nodal design variables which represent nodal volume fractions at discretized nodes are adopted. A so-called nodal sensitivity filter is employed, to prevent the phenomenon of checkerboarding in numerical solutions to the topology-optimization problems. The example results presented in the paper demonstrate the suitability and versatility of the MLPG "mixed collocation'' method, in implementing structural topology-optimization. More >

Q.W. Ma¹

CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.2, pp. 75-90, 2008, DOI:10.3970/cmes.2008.023.075

Abstract In the MLPG_R (Meshless Local Petrove-Galerkin based on Rankine source solution) method, one needs a meshless interpolation scheme for an unknown function to discretise the governing equation. The MLS (moving least square) method has been used for this purpose so far. The MLS method requires inverse of matrix or solution of a linear algebraic system and so is quite time-consuming. In this paper, a new scheme, called simplified finite difference interpolation (SFDI), is devised. This scheme is generally as accurate as the MLS method but does not need matrix inverse and consume less CPU time to evaluate. Although this scheme… More >

J. Sladek¹, V. Sladek¹, Ch. Zhang², P. Solek³

CMES-Computer Modeling in Engineering & Sciences, Vol.22, No.3, pp. 217-234, 2007, DOI:10.3970/cmes.2007.022.217

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of boundary value problems for coupled thermo-electro-mechanical fields. Transient dynamic governing equations are considered here. To eliminate the time-dependence in these equations, the Laplace-transform technique is applied. Material properties of piezoelectric materials are influenced by a thermal field. It is leading to an induced nonhomogeneity and the governing equations are more complicated than in a homogeneous counterpart. Two-dimensional analyzed domain is subdivided into small circular subdomains surrounding nodes randomly spread over the whole domain. A unit step function is used as the test functions in the… More >

Chany Lee¹, Chang-Hwan Im², Hyun-Kyo Jung³, Hong-Kyu Kim⁴, Do Wan Kim⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 35-42, 2007, DOI:10.3970/cmes.2007.020.035

Abstract In the present study, a residual-based a posteriori error estimation for a kind of meshless method, called fast moving least square reproducing kernel (FMLSRK) method is proposed. The proposed error estimation technique does not require any integration cells in evaluating error norm but recovers the exact solutions in a virtual area defined by a dilation parameter of FMLSRK and node density. The proposed technique was tested on typical electrostatic problems with gird or random node sets and the simulation results show that the proposed error estimation technique can be applied to adaptive node refinement process for more efficient meshless analysis… More >

J. Sladek¹, V. Sladek¹, Ch. Zhang², P. Solek³, L. Starek³

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.3, pp. 247-262, 2007, DOI:10.3970/cmes.2007.019.247

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2-D) and three-dimensional (3-D) axisymmetric piezoelectric solids with continuously varying material properties. Axial symmetry of geometry and boundary conditions reduces the original 3-d boundary value problem into a 2-d problem. Stationary problems are considered in this paper. The axial cross section is discretized into small circular subdomains surrounding nodes randomly spread over the analyzed domain. A unit step function is used as the test functions in the local weak-form. Then, the derived local integral equations (LBIEs) involve only contour-integrals on the surfaces of subdomains.… More >

Y.F. Nie¹, S. Chang¹, X.K. Fan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.2, pp. 135-144, 2007, DOI:10.3970/cmes.2007.019.135

Abstract A new parallel mechanism for Node-based Seamless Finite Element Method was proposed in this paper, which possessed the following three prominent points: realizing the workload balance for the parallel processes naturally, achieving synchronization of all the schedules under complex parallel environment, and filling up the gap between pre-processing and main processing. To support the scheme, three specific solutions of the parallel mechanism were proposed in this paper, all of which achieved the highly efficient parallel seamless connection between the FEM mesh generation process and structure analysis process. Two of the three schemes, i.e. dynamic scheme and self-adaptive scheme, enabled both… More >

T. Jarak¹, J. Sorić¹, J. Hoster¹

CMES-Computer Modeling in Engineering & Sciences, Vol.18, No.3, pp. 235-246, 2007, DOI:10.3970/cmes.2007.018.235

Abstract A meshless computational method based on the local Petrov-Galerkin approach for the analysis of shell structures is presented. A concept of a three dimensional solid, allowing the use of completely 3-D constitutive models, is applied. Discretization is carried out by using both a moving least square approximation and polynomial functions. The exact shell geometry can be described. Thickness locking is eliminated by using a hierarchical quadratic approximation over the thickness. The shear locking phenomena in case of thin structures and the sensitivity to rigid body motions are minimized by applying interpolation functions of sufficiently high order. The numerical efficiency of… 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 >