Weichung Yeih^1,2, Chein-Shan Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.46, No.2, pp. 107-128, 2009, DOI:10.3970/cmes.2009.046.107

Abstract We consider an inverse problem for estimating an unknown time dependent heat source H(t) in a heat conduction equation u_t(x,t) = u_xx(x,t) + H(t). First this inverse problem is formulated as a three-point boundary value problem (BVP) for ODEs discretized from the transformed homogeneous governing equation. To treat this three-point BVP we develop a two-stage Lie-group shooting method (TSLGSM). The novel approach is examined through numerical examples to convince that it is rather accurate and efficient; the estimation error is small even for identifying discontinuous and oscillatory heat sources under noise. More >

Chia-Cheng Tsai¹

CMES-Computer Modeling in Engineering & Sciences, Vol.45, No.3, pp. 249-272, 2009, DOI:10.3970/cmes.2009.045.249

Abstract Analytical particular solutions of Chebyshev polynomials are obtained for problems of Reissner plates under arbitrary loadings, which are governed by three coupled second-ordered partial differential equation (PDEs). Our solutions can be written explicitly in terms of monomials. By using these formulas, we can obtain the approximate particular solution when the arbitrary loadings have been represented by a truncated series of Chebyshev polynomials. In the derivations of particular solutions, the three coupled second-ordered PDE are first transformed into a single six-ordered PDE through the Hörmander operator decomposition technique. Then the particular solutions of this six-ordered PDE can be found in the… More >

I-L. Chang¹, M.-S. Yeh¹

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.2, pp. 95-106, 2009, DOI:10.3970/cmes.2009.041.095

Abstract One-dimensional copper nanospring with elliptic cross section was studied using molecular statics method based on minimum energy consideration. Various geometric sizes (wire semi-axis length, radius, pitch) and crystal orientations of nanosprings were systematically modeled to investigate the size dependence of elastic properties for both normal and binormal nanosprings. It was observed that as the wire semi-axis increases, and the radius and pitch decrease, the nanospring stiffness would increase irrespective to the crystal orientations. Moreover, it was noticed that the normal nanosprings always behave stiffer than the binormal ones for the same radius, pitch and cross-sectional geometry in our study. More >

Ma Tianbao¹, Wang Cheng, Ning Jianguo

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.2, pp. 155-178, 2008, DOI:10.3970/cmes.2008.033.155

Abstract A multi-material Eulerian hydrodynamic numerical method and hydrocode that can effectively simulate explosion problems in engineering practice were developed in this study. A modified Youngs' interface reconstruction algorithm was proposed for mixed cells, in which the material's volume fractions of the surrounding cells are not only used to reconstruct the material interface but also adopted to determine the transport order of the material. The algorithm developed herein was validated by the modeling of several tests, such as objects with different shapes moving in translational, rotating and shear flow field in two dimensional Descartes coordinates and axis-symmetric cylindrical coordinates. Results show… More >

Thi D. Dang¹, Bhavani V. Sankar²

CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.3, pp. 169-188, 2008, DOI:10.3970/cmes.2008.026.169

Abstract In this paper the meshless local Petrov-Galerkin (MLPG) method is used in the micromechanical analysis of a unidirectional fiber composite. The methods have been extended to include shear loadings, thus permitting a more complete micromechanical analysis of the composite subjected to combined loading states. The MLPG formulation is presented for the analysis of the representative volume element (RVE) of the periodic composite containing material discontinuities. Periodic boundary conditions are imposed between opposite faces of the RVE. The treatment of periodic boundary conditions in the MLPG method is handled by using the multipoint constraint technique. Examples are presented to illustrate the… More >

Sharnappa¹, N. Ganesan², Raju Sethuraman³

CMES-Computer Modeling in Engineering & Sciences, Vol.18, No.2, pp. 121-144, 2007, DOI:10.3970/cmes.2007.018.121

Abstract This article presents the study on buckling and free vibration behavior of sandwich general shells of revolution under thermal environment using Wilkins theory. The temperature assumes to be uniform over the shell structure. The numerical analysis is based on the semi-analytical finite element method applicable to thick shells. The analysis is carried out for different geometry such as truncated conical and hemispherical shells with various facing and core materials under clamped-clamped boundary condition. The parametric study is carried out for different core to facing (t_c / t_f) thickness ratio by considering the temperature dependent and independent material properties of the… More >

Xiaolin Chen, Yijun Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.3, pp. 337-350, 2001, DOI:10.3970/cmes.2001.002.337

Abstract An advanced boundary element method (BEM) is developed in this paper for analyzing thin layered structures, such as thin films and coatings, under the thermal loading. The boundary integral equation (BIE) formulation for steady-state thermoelasticity is reviewed and a special case, that is, the BIE for a uniform distribution of the temperature change, is presented. The new nearly-singular integrals arising from the applications of the BIE/BEM to thin layered structures under thermal loading are treated in the same way as developed earlier for thin structures under the mechanical loading. Three 2-D test problems involving layered thin films and coatings on… More >

Haruhiko Kohno, Takahiko Tanahashi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 155-170, 2001, DOI:10.3970/cmes.2001.002.155

Abstract Three-dimensional (3D) unsteady numerical simulations are carried out by means of the finite element method (FEM) with the generalized simplified marker and cell (GSMAC) method in silicon melt with a non-deformable free surface with Prandtl number Pr = 1.8534 × 10^-2, Marangoni number Ma = 0.0 - 6.2067 × 10², Grashof number Gr = 7.1104 × 10⁶, and the aspect ratio As = 1.0 in the Czochralski (CZ) method. The flow state becomes unstable earlier by increasing the absolute value of the thermal coefficient of surface tension in the range of σ_T =0.0 - 1.5 × 10^-5N/mK. Although the velocity… More >

N. Miyazaki¹, T. Tamura², K. Yamamoto¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.1, pp. 99-106, 2000, DOI:10.3970/cmes.2000.001.099

Abstract Quantitative estimation of the failure of a gadolinium orthosilicate (Gd₂SiO₅, hereafter abbreviated as GSO) single crystal induced by thermal stress was investigated. A GSO cylindrical test specimen was heated in a silicone oil bath, then subjected to large thermal stress by room temperature silicone oil. Cracking occurred during cooling. The transient heat conduction analysis was performed to obtain temperature distribution in the test specimen at the time of cracking, using the surface temperatures measured in the test. Then the thermal stress was calculated using the temperature profile of the test specimen obtained from the heat conduction analysis. It is found… More >

J.R. Lin¹, L.M. Chu², T.L. Chou³, L.J. Liang³, P.Y. Wang³

FDMP-Fluid Dynamics & Materials Processing, Vol.10, No.2, pp. 163-177, 2014, DOI:10.3970/fdmp.2014.010.163

Abstract We investigate the influence of non-Newtonian micropolar fluids on the dynamic characteristics of wide tapered-land slider bearings. The study is carried out on the basis of the micro-continuum theory originally developed by Eringen (1966). Analytical expressions for the linear dynamic coefficients are provided and compared with earlier results in the literature. In particular, direct comparison with the Newtonian fluid-lubricated tapered-land bearings by Lin et al. (2006) indicates that the use of non-Newtonian micropolar fluids can lead to a significant increase in the values of stiffness and damping coefficients. Such improvements are found to be even more pronounced for larger values… More >