Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.2, pp. 77-94, 2008, DOI:10.3970/cmes.2008.028.077

Abstract The method of fundamental solutions (MFS) is a truly meshless numerical method widely used in the elliptic type boundary value problems, of which the approximate solution is expressed as a linear combination of fundamental solutions and the unknown coefficients are determined from the boundary conditions by solving a linear equations system. However, the accuracy of MFS is severely limited by its ill-conditioning of the resulting linear equations system. This paper is motivated by the works of Chen, Wu, Lee and Chen (2007) and Liu (2007a). The first paper proved an equivalent relation of the Trefftz… More >

J. Sladek¹, V. Sladek¹, P. Solek², P.H. Wen³

CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.1, pp. 57-76, 2008, DOI:10.3970/cmes.2008.028.057

Abstract A meshless local Petrov-Galerkin (MLPG) method is applied to solve thermal bending problems described by the Reissner-Mindlin theory. Both stationary and thermal shock loads are analyzed here. Functionally graded material properties with continuous variation in the plate thickness direction are considered here. The Laplace-transformation is used to treat the time dependence of the variables for transient problems. A weak formulation for the set of governing equations in the Reissner-Mindlin theory is transformed into local integral equations on local subdomains in the mean surface of the plate by using a unit test function. Nodal points are More >

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 More >

G. M. Kulikov¹, S. V. Plotnikova¹

CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.1, pp. 15-38, 2008, DOI:10.3970/cmes.2008.028.015

Abstract This paper presents a robust non-linear geometrically exact four-node solid-shell element based on the first-order seven-parameter equivalent single-layer theory, which permits us to utilize the 3D constitutive equations. The term "geometrically exact" reflects the fact that geometry of the reference surface is described by analytically given functions and displacement vectors are resolved in the reference surface frame. As fundamental shell unknowns six displacements of the outer surfaces and a transverse displacement of the midsurface are chosen. Such choice of displacements gives the possibility to derive strain-displacement relationships, which are invariant under arbitrarily large rigid-body shell More >

Adan Vega¹, Sherif Rashed², Yoshihiko Tango³, Morinobu Ishiyama³, Hidekazu Murakawa²

CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.1, pp. 1-14, 2008, DOI:10.3970/cmes.2008.028.001

Abstract Experimental observations have shown that the inherent deformation produced by multi-heating lines is not a simple addition of the inherent deformation produced by single heating lines. Therefore, to accurately predict inherent deformation, the method of superposing inherent deformation of single heating lines is not appropriate. To overcome this difficulty, the authors investigate the influence of multi-heating lines on line heating inherent deformation. First, the influence of previous heating lines on inherent deformation of overlapping, parallel and crossing heating lines is clarified. The influence of the proximity to plate side edge on inherent deformation is also More >

F. Cosmi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.3, pp. 187-196, 2008, DOI:10.3970/cmes.2008.027.187

Abstract The Cell Method is a recent numerical method that can be applied in several fields of physics and engineering. In this paper, the elastodynamics formulation is extended to include system internal damping, highlighting some interesting characteristics of the method. The developed formulation leads to an explicit solving system. The mass matrix is diagonal (without lumping) and in the most general case a time-dependent damping coefficient can be defined for each node. \newline Accuracy and convergence rate have been tested with reference to the classical problem of a particle free vibration with viscous damping.
An application More >

Chih-Ping Wu¹, Kuan-Hao Chiu, Yun-Ming Wang

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.3, pp. 163-186, 2008, DOI:10.3970/cmes.2008.027.163

Abstract A differential reproducing kernel particle (DRKP) method is proposed and developed for the analysis of simply supported, multilayered elastic and piezoelectric plates by following up the consistent concepts of reproducing kernel particle (RKP) method. Unlike the RKP method in which the shape functions for derivatives of the reproducing kernel (RK) approximants are obtained by directly taking the differentiation with respect to the shape functions of the RK approximants, we construct a set of differential reproducing conditions to determine the shape functions for the derivatives of RK approximants. On the basis of the extended Hellinger-Reissner principle, More >

Chia-Cheng Tsai¹

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.3, pp. 151-162, 2008, DOI:10.3970/cmes.2008.027.151

Abstract In this paper we develop analytical particular solutions for the polyharmonic and the products of Helmholtz-type partial differential operators with Chebyshev polynomials at right-hand side. Our solutions can be written explicitly in terms of either monomial or Chebyshev bases. By using these formulas, we can obtain the approximate particular solution when the right-hand side has been represented by a truncated series of Chebyshev polynomials. These formulas are further implemented to solve inhomogeneous partial differential equations (PDEs) in which the homogeneous solutions are complementarily solved by the method of fundamental solutions (MFS). Numerical experiments, which include More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.3, pp. 137-150, 2008, DOI:10.3970/cmes.2008.027.137

Abstract For the inverse vibration problem, a Lie-group shooting method is proposed to simultaneously estimate the time-dependent damping and stiffness functions by using two sets of displacement as inputs. First, we transform these two ODEs into two parabolic type PDEs. Second, we formulate the inverse vibration problem as a multi-dimensional two-point boundary value problem with unknown coefficients, allowing us to develop the Lie-group shooting method. For the semi-discretizations of PDEs we thus obtain two coupled sets of linear algebraic equations, from which the estimation of damping and stiffness coefficients can be written out explicitly. The present More >

Mira Mitra¹, S. Gopalakrishnan²

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 125-136, 2008, DOI:10.3970/cmes.2008.027.125

Abstract In this paper, the wave characteristics, namely, the spectrum and dispersion relations of multi-wall carbon nanotubes (MWNTs) are studied. The MWNTs are modeled as multiple thin shells coupled through van der Waals force. Each wall of the MWNT has three displacements, i.e, axial, circumferential and radial with variation along the axial and circumferential directions. The wave characteristics are obtained by transforming the governing differential wave equations to frequency domain via Fourier transform. This transformation is first done in time using fast Fourier transform (FFT) and then in one spatial dimension using Fourier series. These transformed equations More >