CMC-Vol. 24, No. 2, 2011

Open Access

ARTICLE

The Spring-Damping Regularization Method and the Lie-Group Shooting Method for Inverse Cauchy Problems
Chein-Shan Liu^1,2, Chung-Lun Kuo³, Dongjie Liu⁴
CMC-Computers, Materials & Continua, Vol.24, No.2, pp. 105-124, 2011, DOI:10.3970/cmc.2011.024.105
Abstract The inverse Cauchy problems for elliptic equations, such as the Laplace equation, the Poisson equation, the Helmholtz equation and the modified Helmholtz equation, defined in annular domains are investigated. The outer boundary of the annulus is imposed by overspecified boundary data, and we seek unknown data on the inner boundary through the numerical solution by a spring-damping regularization method and its Lie-group shooting method (LGSM). Several numerical examples are examined to show that the LGSM can overcome the ill-posed behavior of inverse Cauchy problem against the disturbance from random noise, and the computational cost is More >

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ARTICLE

Solution of Inverse Boundary Optimization Problem by Trefftz Method and Exponentially Convergent Scalar Homotopy Algorithm
Hsin-Fang Chan¹, Chia-Ming Fan^1,2, Weichung Yeih¹
CMC-Computers, Materials & Continua, Vol.24, No.2, pp. 125-142, 2011, DOI:10.3970/cmc.2011.024.125
Abstract The inverse boundary optimization problem, governed by the Helmholtz equation, is analyzed by the Trefftz method (TM) and the exponentially convergent scalar homotopy algorithm (ECSHA). In the inverse boundary optimization problem, the position for part of boundary with given boundary condition is unknown, and the position for the rest of boundary with additionally specified boundary conditions is given. Therefore, it is very difficult to handle the boundary optimization problem by any numerical scheme. In order to stably solve the boundary optimization problem, the TM, one kind of boundary-type meshless methods, is adopted in this study,… More >

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A 3D Constitutive Model for Magnetostrictive Materials
Ke Jin¹, Yong Kou¹, Xiaojing Zheng^1,2
CMC-Computers, Materials & Continua, Vol.24, No.2, pp. 143-162, 2011, DOI:10.3970/cmc.2011.024.143
Abstract This paper is concerned with a 3-D general constitutive law of nonlinear magneto-thermo-elastic coupling for magnetostrictive materials. The model considered here is thermodynamically motivated and based on the Gibbs free energy function. A set of closed and analytical expressions of the constitutive relationships for the magnetostrictive materials are obtained, in which all parameters can be determined by those measurable experiments in mechanics and physics. Then the model can be simplified to two cases, i.e. magnetostrictive rods and films. It is found that the predictions from this model are in good accordance with the experimental data More >

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Vibration and Buckling of Truss Core Sandwich Plates on An Elastic Foundation Subjected to Biaxial In-plane Loads
J.W. Chen¹, W. Liu¹, X.Y. Su^1,2
CMC-Computers, Materials & Continua, Vol.24, No.2, pp. 163-182, 2011, DOI:10.3970/cmc.2011.024.163
Abstract Truss-core sandwich plates are thin-walled structures comprising a truss core and two thin flat sheets. Since no direct analytical solution for the dynamic response of such structures exists, the complex three dimensional (3D) systems are idealized as equivalent 2D homogeneous continuous plates. The macroscopic effective bending and transverse shear stiffness are derived. Two representative core topologies are considered: pyramidal truss core and tetrahedral truss core. The first order shear deformation theory is used to study the flexural vibration of a simply supported sandwich plate. The buckling of the truss core plate on an elastic foundation More >

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