Jeng-Tzong Chen^1,2, Jia-Nan Ke¹, Huan-Zhen Liao¹

CMC-Computers, Materials & Continua, Vol.9, No.2, pp. 93-110, 2009, DOI:10.3970/cmc.2009.009.093

Abstract A null-field approach is employed to derive the Green's function for boundary value problems stated for the Laplace equation with circular boundaries. The kernel function and boundary density are expanded by using the degenerate kernel and Fourier series, respectively. Series-form Green's function for interior and exterior problems of circular boundary are derived and plotted in a good agreement with the closed-form solution. The Poisson integral formula is extended to an annular case from a circle. Not only an eccentric ring but also a half-plane problem with an aperture are demonstrated to see the validity of the present approach. Besides, a… More >

Chein-Shan Liu^1,2

CMC-Computers, Materials & Continua, Vol.5, No.1, pp. 31-42, 2007, DOI:10.3970/cmc.2007.005.031

Abstract By using a meshless regularized integral equation method (MRIEM), the solution of elastic torsion problem of a uniform bar with arbitrary cross-section is presented by the first kind Fredholm integral equation on an artificial circle, which just encloses the bar's cross-section. The termwise separable property of kernel function allows us to obtain the semi-analytical solutions of conjugate warping function and shear stresses. A criterion is used to select the regularized parameter according to the minimum principle of Laplace equation. Numerical examples show the effectiveness of the new method in providing very accurate numerical solutions as compared with the exact ones. More >

J. Sladek¹, V. Sladek¹, Ch. Zhang², F. Garcia-Sanche³, M. Wünsche²

CMC-Computers, Materials & Continua, Vol.4, No.2, pp. 109-118, 2006, DOI:10.3970/cmc.2006.004.109

Abstract Piezoelectric materials have wide range engineering applications in smart structures and devices. They have usually anisotropic properties. Except this complication electric and mechanical fields are coupled each other and the governing equations are much more complex than that in the classical elasticity. Thus, efficient computational methods to solve the boundary or the initial-boundary value problems for piezoelectric solids are required. In this paper, the Meshless local Petrov-Galerkin (MLPG) method with a Heaviside step function as the test functions is applied to solve two-dimensional (2-D) piezoelectric problems. The mechanical fields are described by the equations of motion with an inertial term.… More >

Yi-Hsien Lin¹, Chien-Ching Ma^1,2

CMC-Computers, Materials & Continua, Vol.24, No.1, pp. 15-42, 2011, DOI:10.3970/cmc.2011.024.015

Abstract In this article, explicit transient solutions for one-dimensional wave propagation behavior in multi-layered structures are presented. One of the objectives of this study is to develop an effective analytical method for constructing solutions in multilayered media. Numerical calculations are performed by three methods: the generalized ray method, numerical Laplace inversion method (Durbin's formula), and finite element method (FEM). The analytical result of the generalized ray solution for multilayered structures is composed of a matrix-form Bromwich expansion in the transform domain. Every term represents a group of waves, which are transmitted or reflected through the interface. The matrix representation of the… More >

Weichung Yeih¹, Chein-Shan Liu², Chung-Lun Kuo³, Satya N. Atluri⁴

CMC-Computers, Materials & Continua, Vol.17, No.3, pp. 275-302, 2010, DOI:10.3970/cmc.2010.017.275

Abstract In this paper, a multiple-source-point boundary-collocation Trefftz method, with characteristic lengths being introduced in the basis functions, is proposed to solve the direct, as well as inverse Cauchy problems of the Laplace equation for a multiply connected domain. When a multiply connected domain with genus p (p>1) is considered, the conventional Trefftz method (T-Trefftz method) will fail since it allows only one source point, but the representation of solution using only one source point is impossible. We propose to relax this constraint by allowing many source points in the formulation. To set up a complete set of basis functions, we… More >