G. C. Bourantas¹, E. D. Skouras^2,3,4, G. C. Nikiforidis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.1, pp. 1-26, 2009, DOI:10.3970/cmes.2009.043.001

Abstract The extent of application of meshfree methods based on point collocation (PC) techniques with adaptive support domain for strong form Partial Differential Equations (PDE) is investigated. The basis functions are constructed using the Moving Least Square (MLS) approximation. The weak-form description of PDEs is used in most MLS methods to circumvent problems related to the increased level of resolution necessary near natural (Neumann) boundary conditions (BCs), dislocations, or regions of steep gradients. Alternatively, one can adopt Radial Basis Function (RBF) approximation on the strong-form of PDEs using meshless PC methods, due to the delta function… More >

Shang Ma¹, Xiong Zhang^1,2, Yanping Lian¹, Xu Zhou³

CMES-Computer Modeling in Engineering & Sciences, Vol.39, No.2, pp. 101-124, 2009, DOI:10.3970/cmes.2009.039.101

Abstract Numerical simulation of high explosive explosion problems is a big challenge to traditional numerical methods because explosion usually involves extremely large deformation and multi-material interaction of different phases. Recently developed meshfree methods show much advantages over mesh-based method for problems associated with very large deformation. Some of them have been successfully applied to impact and explosion problems, such as smoothed particle hydrodynamics (SPH). Similar to SPH, material point method (MPM) is an efficient meshfree particle method solving continuum problems. With combination of the advantages of Eulerian and Lagrangian methods, MPM is a promising numerical tool… More >

Leevan Ling¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.8, No.4, pp. 133-138, 2008, DOI:10.3970/icces.2008.008.133

Abstract The history of meshless collocation methods featured plenty of nicely calculated practical solutions, but a solid mathematical basis was long missing for the most popular asymmetric technique introduced by E. Kansa. Thus the impact of this work will be to supply a lasting mathematical foundation which will also improve our general understanding of such technique. Our previous research gave a convergent algorithm. More >

H. Nguyen-Van¹, N.Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.1, pp. 65-96, 2008, DOI:10.3970/cmes.2008.036.065

Abstract A novel node-based smoothing element for triangular and quadrilateral meshes is presented for static analysis of planar piezoelectric structures. In contrast to the smoothed finite element formulation that was based on sub-cells within an original quadrilateral element, this new method transforms a general original finite element mesh into a mesh of new smoothing cells individually associated with a single node which is termed as node-based elements. The displacement fields of the element are approximated by the linear interpolation functions of the original mesh while the approximations of mechanical strains and electric potential fields are normalized More >

Nicolas Ali Libre^1,2, Arezoo Emdadi², Edward J. Kansa^3,4, Mohammad Shekarchi², Mohammad Rahimian²

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.3, pp. 263-284, 2008, DOI:10.3970/cmes.2008.038.263

Abstract We present a wavelet based adaptive scheme and investigate the efficiency of this scheme for solving nearly singular potential PDEs. Multiresolution wavelet analysis (MRWA) provides a firm mathematical foundation by projecting the solution of PDE onto a nested sequence of approximation spaces. The wavelet coefficients then were used as an estimation of the sensible regions for node adaptation. The proposed adaptation scheme requires negligible calculation time due to the existence of the fast Discrete Wavelet Transform (DWT). Certain aspects of the proposed adaptive scheme are discussed through numerical examples. It has been shown that the More >

B. Chrasekhar¹, Sadasiva. M. Rao²

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.2, pp. 199-214, 2008, DOI:10.3970/cmes.2008.033.199

Abstract In this work, the acoustic scattering problem based on double layer formulation is solved with a novel numerical technique using method of moment's solution. A new set of basis functions, namely, Edge based Adaptive Basis Functions (EABF) are defined in the method of moment's solution procedure. The geometry of the body is divided into triangular patches and basis functions are defined on the edges. Since the double layer formulation involves the evaluation of the hyper-singular integral, the edge based adaptive basis functions are used to make the solution faster. The matrix equations are derived for More >

E. Ferretti¹, E. Casadio, A. Di Leo¹

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.3, pp. 163-190, 2008, DOI:10.3970/cmes.2008.030.163

Abstract In this study, the Cell Method (CM) is applied in order to investigate the failure mechanisms of masonry walls under shear force. The direction of propagation is computed step-wise by the code, and the domain is updated by means of a propagation technique of intra-element nodal relaxation with re-meshing. The crack extension condition is studied in the Mohr/Coulomb plane, using the criterion of Leon. The main advantage of using the CM for numerical analyses of masonry is that the mortar, the bricks and the interfaces between mortar and bricks can be modeled without any need… More >

H. Nguyen-Van¹, N. Mai-Duy², T. Tran-Cong³

CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.3, pp. 209-222, 2008, DOI:10.3970/cmes.2008.023.209

Abstract This paper reports a study of linear elastic analysis of two-dimensional piezoelectric structures using a smoothed four-node piezoelectric element. The element is built by incorporating the strain smoothing method of mesh-free conforming nodal integration into the standard four-node quadrilateral piezoelectric finite element. The approximations of mechanical strains and electric potential fields are normalized using a constant smoothing function. This allows the field gradients to be directly computed from shape functions. No mapping or coordinate transformation is necessary so that the element can be used in arbitrary shapes. Through several examples, the simplicity, efficiency and reliability More >

Abdulnaser M. Alshoaibi^1,2, M. S. A. Hadi², A. K. Ariffin²

Structural Durability & Health Monitoring, Vol.3, No.1, pp. 15-28, 2007, DOI:10.3970/sdhm.2007.003.015

Abstract An adaptive finite element method is employed to analyze two-dimensional linear elastic fracture problems. The mesh is generated by the advancing front method and the norm stress error is taken as a posteriori error estimator for the h-type adaptive refinement. The stress intensity factors are estimated by a displacement extrapolation technique. The near crack tip displacements used are obtained from specific nodes of natural six-noded quarter-point elements which are generated around the crack tip defined by the user. The crack growth and its direction are determined by the calculated stress intensity factors as the maximum circumference More >

Zhenquan Li¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.4, pp. 251-256, 2007, DOI:10.3970/icces.2007.003.251

Abstract An adaptive three-dimensional mesh refinement method based on the law of mass conservation has been introduced and tested using some analytical velocity fields as accurate in identifying singular point, asymptotic plane and drawing closed streamlines. This paper further investigates the adaptive mesh refinement method using a velocity field that is due to a uniform strain and a point vortex. Similar results have been obtained. More >