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  • Open Access


    A Meshless Numerical Method for Kirchhoff Plates under Arbitrary Loadings

    Chia-Cheng Tsai 1

    CMC-Computers, Materials & Continua, Vol.22, No.3, pp. 197-218, 2011, DOI:10.3970/cmc.2011.022.197

    Abstract This paper describes the combination of the method of fundamental solutions (MFS) and the dual reciprocity method (DRM) as a meshless numerical method to solve problems of Kirchhoff plates under arbitrary loadings. In the solution procedure, a arbitrary distributed loading is first approximated by either the multiquadrics (MQ) or the augmented polyharmonic splines (APS), which are constructed by splines and monomials. The particular solutions of multiquadrics, splines and monomials are all derived analytically and explicitly. Then, the complementary solutions are solved formally by the MFS. Furthermore, the boundary conditions of lateral displacement, slope, normal moment,… More >

  • Open Access


    A Meshless Approach Towards Solution of Macrosegregation Phenomena

    Gregor Kosec1, Miha Založnik2, Božidar Šarler1, Hervé Combeau2

    CMC-Computers, Materials & Continua, Vol.22, No.2, pp. 169-196, 2011, DOI:10.3970/cmc.2011.022.169

    Abstract The simulation of macrosegregation as a consequence of solidification of a binary Al-4.5%Cu alloy in a 2-dimensional rectangular enclosure is tackled in the present paper. Coupled volume-averaged governing equations for mass, energy, momentum and species transfer are considered. The phase properties are resolved from the Lever solidification rule, the mushy zone is modeled by the Darcy law and the liquid phase is assumed to behave like an incompressible Newtonian fluid. Double diffusive effects in the melt are modeled by the thermal and solutal Boussinesq hypothesis. The physical model is solved by the novel Local Radial… More >

  • Open Access


    Electromagnetic Shielding Effectiveness of Grid-Mesh Films Made of Polyaniline: a Numerical Approach

    S. H. Kwon1, B. R. Kim2, H. K. Lee2,3

    CMC-Computers, Materials & Continua, Vol.21, No.1, pp. 65-86, 2011, DOI:10.3970/cmc.2011.021.065

    Abstract The electromagnetic shielding effectiveness of grid-mesh films made of polyaniline was numerically investigated, and the optimal size of the polyaniline grid was determined through numerical analyses. The permittivity of polyaniline was first determined from an inverse analysis based on experimental data. A series of numerical analyses were carried out with 225 polyaniline grid-mesh films of different thickness, spacing, and width, and the shielding effectiveness of every grid was examined. In addition to the numerical analysis, the transparency of the grid-mesh films and the amount of polyaniline material required to manufacture the unit grid area (1mx1m) More >

  • Open Access


    Space-Time Adaptive Fup Multi-Resolution Approach for Boundary-Initial Value Problems

    Hrvoje Gotovac1, Vedrana Kozulić2, Blaž Gotovac1

    CMC-Computers, Materials & Continua, Vol.15, No.3, pp. 173-198, 2010, DOI:10.3970/cmc.2010.015.173

    Abstract The space-time Adaptive Fup Collocation Method (AFCM) for solving boundary-initial value problems is presented. To solve the one-dimensional initial boundary value problem, we convert the problem into a two-dimensional boundary value problem. This quasi-boundary value problem is then solved simultaneously in the space-time domain with a collocation technique and by using atomic Fup basis functions. The proposed method is a generally meshless methodology because it requires only the addition of collocation points and basis functions over the domain, instead of the classical domain discretization and numerical integration. The grid is adapted progressively by setting the More >

  • Open Access


    Meshless Local Petrov-Galerkin (MLPG) Method for Laminate Plates under Dynamic Loading

    J. Sladek1, V. Sladek1, P. Stanak1, Ch. Zhang2

    CMC-Computers, Materials & Continua, Vol.15, No.1, pp. 1-26, 2010, DOI:10.3970/cmc.2010.015.001

    Abstract A meshless local Petrov-Galerkin (MLPG) method is applied to solve laminate plate problems described by the Reissner-Mindlin theory. Both stationary and transient dynamic loads are analyzed here. The bending moment and the shear force expressions are obtained by integration through the laminated plate for the considered constitutive equations in each lamina. The Reissner-Mindlin theory reduces the original three-dimensional (3-D) thick plate problem to a two-dimensional (2-D) problem. Nodal points are randomly distributed over the mean surface of the considered plate. Each node is the center of a circle surrounding this node. The weak-form on small More >

  • Open Access


    Boundary Particle Method with High-Order Trefftz Functions

    Wen Chen1,2, Zhuo-Jia Fu1,3, Qing-Hua Qin3

    CMC-Computers, Materials & Continua, Vol.13, No.3, pp. 201-218, 2009, DOI:10.3970/cmc.2009.013.201

    Abstract This paper presents high-order Trefftz functions for some commonly used differential operators. These Trefftz functions are then used to construct boundary particle method for solving inhomogeneous problems with the boundary discretization only, i.e., no inner nodes and mesh are required in forming the final linear equation system. It should be mentioned that the presented Trefftz functions are nonsingular and avoids the singularity occurred in the fundamental solution and, in particular, have no problem-dependent parameter. Numerical experiments demonstrate the efficiency and accuracy of the present scheme in the solution of inhomogeneous problems. More >

  • Open Access


    The Method of Fundamental Solutions for One-Dimensional Wave Equations

    Gu, M. H.1, Young, D. L.1,2, Fan, C. M.1

    CMC-Computers, Materials & Continua, Vol.11, No.3, pp. 185-208, 2009, DOI:10.3970/cmc.2009.011.185

    Abstract A meshless numerical algorithm is developed for the solutions of one-dimensional wave equations in this paper. The proposed numerical scheme is constructed by the Eulerian-Lagrangian method of fundamental solutions (ELMFS) together with the D'Alembert formulation. The D'Alembert formulation is used to avoid the difficulty to constitute the linear algebraic system by using the ELMFS in dealing with the initial conditions and time-evolution. Moreover the ELMFS based on the Eulerian-Lagrangian method (ELM) and the method of fundamental solutions (MFS) is a truly meshless and quadrature-free numerical method. In this proposed wave model, the one-dimensional wave equation… More >

  • Open Access


    A Three-Dimensional Meshless Scheme with Background Grid for Electrostatic-Structural Analysis

    Ming-Hsiao Lee, Wen-Hwa Chen

    CMC-Computers, Materials & Continua, Vol.11, No.1, pp. 59-78, 2009, DOI:10.3970/cmc.2009.011.059

    Abstract On the analysis of electrostatic-structural coupled problems as encountered in many electrostatic driven MEMS devices, the electrostatic analysis domain is often extremely distorted due to the deflection of the structure. This kind of problem is difficult to be dealt with by almost all kinds of available numerical methods. A new three-dimensional meshless scheme with background grid is thus proposed herein. By this scheme, a three-dimensional fixed background grid with regularly-distributed nodes is utilized. Another set of discretized boundary grid is employed to describe the boundary surfaces of both the structure and the electrostatic field. The… More >

  • Open Access


    Solution of Maxwell's Equations Using the MQ Method

    D.L. Young1,3, 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 >

  • Open Access


    A Meshless Approach Based upon Radial Basis Function Hermite Collocation Method for Predicting the Cooling and the Freezing Times of Foods

    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 >

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