D.L. Young^1,3, C.S. Chen², T.K. Wong³

CMC-Computers, Materials & Continua, Vol.2, No.4, pp. 267-276, 2005, DOI:10.3970/cmc.2005.002.267

Abstract A meshless time domain numerical method based on the radial basis functions using multiquadrics (MQ) is employed to simulate electromagnetic field problems by directly solving the time-varying Maxwell's equations without transforming to simplified versions of the wave or Helmholtz equations. In contrast to the conventional numerical schemes used in the computational electromagnetism such as FDTD, FETD or BEM, the MQ method is a truly meshless method such that no mesh generation is required. It is also easy to deal with the appropriate partial derivatives, divergences, curls, gradients, or integrals like semi-analytic solutions. For illustration purposes, More >

A. La Rocca¹, H. Power¹, V. La Rocca², M. Morale²

CMC-Computers, Materials & Continua, Vol.2, No.4, pp. 239-250, 2005, DOI:10.3970/cmc.2005.002.239

Abstract This work presents a meshless numerical scheme for the solution of time dependent non linear heat transfer problems in terms of a radial basis function Hermite collocation approach. The proposed scheme is applied to foodstuff's samples during freezing process; evaluation of the time evolution of the temperature profile along the sample, as well as at the core, is carried out. The moving phase-change zone is identified in the domain and plotted at several timesteps. The robustness of the proposed scheme is tested by a comparison of the obtained numerical results with those found using a More >

Danny M. Rabah¹, Louis R. Bégin², Abdelrahman Zahran¹, Jacques Corcos¹

Canadian Journal of Urology, Vol.11, No.4, pp. 2344-2349, 2004

Abstract Objective: To evaluate and compare histological tissue reactions of the urinary bladder to human cadaveric fascia lata (CFX) slings and synthetic mesh.
Methods: Thirty rabbits were randomized to three groups: group A (multifilament - Surgipro Mesh®) 12 animals, group B (CFX) 12 animals, and group C (surgical controls) 6 animals. A piece of Mesh or CFX was fixed in direct contact with the anterior bladder neck wall. The control group simply underwent sham bladder manipulation. The animals were sacrificed at 6- and 12-week intervals, and their bladders were collected for histological analysis.
Results: Group A showed fibrosis within… More >

S. G. Bardenhagen^1,2, E. M. Kober³

CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.6, pp. 477-496, 2004, DOI:10.3970/cmes.2004.005.477

Abstract The Material Point Method (MPM) discrete solution procedure for computational solid mechanics is generalized using a variational form and a Petrov–Galerkin discretization scheme, resulting in a family of methods named the Generalized Interpolation Material Point(GIMP) methods. The generalizationpermits identification with aspects of other point or node based discrete solution techniques which do not use a body–fixed grid, i.e. the “meshless methods”. Similarities are noted and some practical advantages relative to some of these methods are identified. Examples are used to demonstrate and explain numerical artifact noise which can be expected inMPM calculations. Thisnoiseresultsin non-physical local More >

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

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.6, pp. 491-514, 2004, DOI:10.3970/cmes.2004.006.491

Abstract The Meshless Finite Volume Method (MFVM) is developed for solving elasto-static problems, through a new Meshless Local Petrov-Galerkin (MLPG) ``Mixed'' approach. In this MLPG mixed approach, both the strains as well as displacements are interpolated, at randomly distributed points in the domain, through local meshless interpolation schemes such as the moving least squares(MLS) or radial basis functions(RBF). The nodal values of strains are expressed in terms of the independently interpolated nodal values of displacements, by simply enforcing the strain-displacement relationships directly by collocation at the nodal points. The MLPG local weak form is then written… More >

J. Sladek¹, V. Sladek¹, S.N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.5, pp. 477-490, 2004, DOI:10.3970/cmes.2004.006.477

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for solution of static and elastodynamic problems in a homogeneous anisotropic medium. The Heaviside step function is used as the test functions in the local weak form. It is leading to derive local boundary integral equations (LBIEs). For transient elastodynamic problems the Laplace transfor technique is applied and the LBIEs are given in the Laplace transform domain. The analyzed domain is covered by small subdomains with a simple geometry such as circles in 2-d problems. The final form of local integral equations has a More >

E. Ferretti ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.5, pp. 453-476, 2004, DOI:10.3970/cmes.2004.006.453

Abstract The Cell Method (CM) code with automatic remeshing for crack propagation analysis [Ferretti (2003)] is here used for modeling the pullout test. Particular emphasis is given to the analysis in the Mohr-Coulomb plane, since previous numerical models were not decisive in describing failure mechanism in pullout tests. The interpretations of experimental and analytical studies vary widely, and none of the existing explanations offer a complete description of the progressive failure of the concrete medium [Yener (1994)]. Nor do most existing interpretations appear to be totally compatible with the experimental evidence. Analysis of the failure mechanism… More >

Z. D. Han¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.2, pp. 169-188, 2004, DOI:10.3970/cmes.2004.006.169

Abstract Three different truly Meshless Local Petrov-Galerkin (MLPG) methods are developed for solving 3D elasto-static problems. Using the general MLPG concept, these methods are derived through the local weak forms of the equilibrium equations, by using different test functions, namely, the Heaviside function, the Dirac delta function, and the fundamental solutions. The one with the use of the fundamental solutions is based on the local unsymmetric weak form (LUSWF), which is equivalent to the local boundary integral equations (LBIE) of the elasto-statics. Simple formulations are derived for the LBIEs in which only weakly-singular integrals are included More >

gping Shen¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.3, pp. 235-256, 2004, DOI:10.3970/cmes.2004.005.235

Abstract A multiscale simulation technique based on the MLPG methods, and finite deformation mechanics, is developed, implemented, and tested. Several alternate time-dependent interfacial conditions, between the atomistic and continuum regions, are systematically studied, for the seamless multiscale simulation, by decomposing the displacement of atoms in the equivalent-continuum region into long and short wave-length components. All of these methods for enforcing the interface conditions can ensure the passage of information accurately between the atomistic and continuum regions, while they lead to different performances at short wavelengths. The presently proposed Solution Method 2 reduces the phonon reflections at More >

A. Rama Mohan Rao¹, T.V.S.R. Appa Rao², B. Dattaguru³

CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.3, pp. 213-234, 2004, DOI:10.3970/cmes.2004.005.213

Abstract This paper presents an algorithm for automatic partitioning of unstructured meshes for parallel finite element computations employing float-encoded genetic algorithms (FEGA). The problem of mesh partitioning is represented in such a way that the number of variables considered in the genome (chromosome) construction is constant irrespective of the size of the problem. In order to accelerate the computational process, several acceleration techniques like constraining the search space, local improvement after initial global partitioning have been attempted. Finally, micro float-encoded genetic algorithms have been developed to accelerate the computational process. More >