Lihai Zhang^*, Bruce S. Gardiner^*, David W. Smith^*, Peter Pivonka^*, Alan Grodzinsky^†

Molecular & Cellular Biomechanics, Vol.5, No.2, pp. 133-154, 2008, DOI:10.3970/mcb.2008.005.133

Abstract Cartilage maintains its integrity in a hostile mechanical environment. This task is made more difficult because cartilage has no blood supply, and so nutrients and growth factors need to be transported greater distances than normal to reach cells several millimetres from the cartilage surface. The chondrocytes embedded within the extracellular matrix (ECM) are essential for maintaining the mechanical integrity of the ECM, through a balance of degradation and synthesis of collagen and proteoglycans. A chondrocyte senses various chemical and mechanical signals in its local microenvironment, responding by appropriate adaption of the local ECM. Clearly a… More >

Meiling Zhao¹, Yufeng Nie²

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.2, pp. 97-112, 2008, DOI:10.3970/cmes.2008.037.097

Abstract Meshless local Petrov-Galerkin (MLPG) method is successfully applied for electromagnetic field computations. The moving least square technique is used to interpolate the trial and test functions. More attention is paid to imposing the essential boundary conditions of electromagnetic equations. A new coupled meshless local Petrov-Galerkin and finite element (MLPG-FE) method is presented to enforce the essential boundary conditions. Unlike the conventional coupled technique, this approach can ensure the smooth blending of the potential variables as well as their derivatives in the transition region between the meshless and finite element domains. Then the boundary singular weight More >

Chih-Ping Wu^1,2, Kuan-Hao Chiu², Yung-Ming Wang²

CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.3, pp. 181-214, 2008, DOI:10.3970/cmes.2008.035.181

Abstract A mesh-free collocation method based on differential reproducing kernel (DRK) approximations is developed for the three-dimensional (3D) analysis of simply-supported, doubly curved functionally graded (FG) magneto-electro-elastic shells under the mechanical load, electric displacement and magnetic flux. The material properties of FG shells are firstly regarded as heterogeneous through the thickness coordinate and then specified to obey an identical power-law distribution of the volume fractions of the constituents. The novelty of the present DRK-based collocation method is that the shape functions of derivatives of reproducing kernel (RK) approximants are determined using a set of differential reproducing… More >

Briti Sundar Deb¹, Srinivasan Natesan²

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.2, pp. 179-200, 2008, DOI:10.3970/cmes.2008.038.179

Abstract This paper presents an almost second--order uniformly convergent Richardson extrapolation method for convection- dominated coupled system of boundary value problems. First, we solve the system by using the classical finite difference scheme on the layer resolving Shishkin mesh, and then we construct the Richardson approximation solution using the solutions obtained on N and 2N mesh intervals. Second-order parameter--uniform error estimate is derived. The proposed method is applied to a test example for verification of the theoretical results for the case ε ≤ N⁻¹. More >

P. Bettini, E. Brusa, M. Munteanu, R. Specogna, F. Trevisan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.3, pp. 215-242, 2008, DOI:10.3970/cmes.2008.033.215

Abstract Electrostatic microactuator is a paradigm of MEMS. Cantilever and double clamped microbeams are often used in microswitches, microresonators and varactors. An efficient numerical prediction of their mechanical behaviour is affected by the nonlinearity of the electromechanical coupling. Sometimes an additional nonlinearity is due to the large displacement or to the axial-flexural coupling exhibited in bending. To overcome the computational limits of the available numerical methods two new formulations are here proposed and compared. Modifying the classical beam element in the Finite Element Method to allow the implementation of a \emph {Non incremental sequential approach} is… More >

Dong Ju Woo¹, Jin Oh Yang¹, Beom-Soo Kim¹, Seungsoo Lee¹, Jin Yeon Cho²

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.3, pp. 149-162, 2008, DOI:10.3970/cmes.2008.030.149

Abstract A new orphan-cell-free overset method is proposed to carry out the coupled analysis of overlapping finite element substructures. In the proposed overset method, the meshless MLS (Moving Least Squares) approximation is used to obtain the boundary data for the overlapped interface, whereas the Lagrange interpolation scheme has been commonly used in the conventional overset methods. The meshless character of MLS approximation makes it possible to overcome the problem of orphan-cell, which is often encountered in the conventional overset methods. Further, a new connectivity matrix solution procedure is developed to reduce the computational time in the More >

Q. Ma¹, C. Levy², M. Perl³

CMES-Computer Modeling in Engineering & Sciences, Vol.29, No.2, pp. 95-110, 2008, DOI:10.3970/cmes.2008.029.095

Abstract Networks of radial and longitudinally-coplanar, internal, surface cracks are typical in rifled, autofrettaged, gun barrels. In two previous papers, the separate effects of large arrays of either radial or longitudinally-coplanar semi-elliptical, internal, surface cracks in a thick-walled, cylindrical, pressure vessel under both ideal and realistic autofrettage were studied. When pressure is considered solely, radial crack density and longitudinal crack spacing were found to have opposing effects on the prevailing stress intensity factor, K_IP. Furthermore, the addition of the negative stress intensity factor (SIF), K_IA, resulting from the residual stress field due to autofrettage, whether ideal or… 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 >

Vadiraja D. N.¹, A. D. Sahasrabudhe²

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 49-62, 2008, DOI:10.3970/cmes.2008.027.049

Abstract Rotating beams are flexible structures, which are often idealized as cantilever beams. Structural modelling of rotating thin-walled composite beam with embedded MFC actuators and sensors using higher shear deformation theory (HSDT) is presented. A non-Cartesian deformation variable (which represents arc length stretch) is used along with two Cartesian deformation variables. The governing system of equations is derived from Hamilton's principle and solution is obtained by extended Galerkin's method. Optimal control problem is solved using LQG control algorithm. Vibration characteristics and optimal control for a box beam configuration are discussed in numerical examples. Gyroscopic coupling between More >

Z. Chen^1,2, Y. Gan¹, J.K. Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.2, pp. 123-138, 2008, DOI:10.3970/cmes.2008.026.123

Abstract A coupled thermo-mechanical constitutive model with decohesion is proposed to simulate the material failure evolution due to localized heating. A discontinuous bifurcation analysis is performed based on a thermoviscoplasticity relation to identify the transition from continuous to discontinuous failure modes as well as the orientation of the discontinuous failure. The thermo-mechanical model is then implemented within the framework of the Material Point Method (MPM) so that the different gradient and divergence operators in the governing differential equations could be discretized in a single computational domain and that continuous remeshing is not required with the evolution More >