Łukasz Kaczmarczyk¹

CMC-Computers, Materials & Continua, Vol.4, No.2, pp. 55-62, 2006, DOI:10.3970/cmc.2006.004.055

Abstract In recent years the multiscale computational homogenisation has been extensively developed. Such micro-macro modelling does not require any constitutive assumptions at the macro-level. The multi-scale computational homogenisation has also been extended for the second order continuum at the macro level Kouznetsova V.G., Geers M.G.D., and Brekelmans V.A.M (2004). The second-order framework is based on incorporation of the gradient of macroscopic deformation in micro to macro multiscale transition. The introduction of the secondorder continuum at macro-scale takes into account the size effect and gives more accurate results in case of insufficient scale separation. The general framework More >

D.L. Young^1,2, C.C. Tsai³, Y.C. Lin¹, C.S. Chen⁴

CMC-Computers, Materials & Continua, Vol.4, No.1, pp. 1-10, 2006, DOI:10.3970/cmc.2006.004.001

Abstract This paper describes the method of fundamental solutions (MFS) to solve eigenfrequencies of plate vibrations by utilizing the direct determinant search method. The complex-valued kernels are used in the MFS in order to avoid the spurious eigenvalues. The benchmark problems of a circular plate with clamped, simply supported and free boundary conditions are studied analytically as well as numerically using the discrete and continuous versions of the MFS schemes to demonstrate the major results of the present paper. Namely only true eigenvalues are contained and no spurious eigenvalues are included in the range of direct More >

C.W. Chen¹, C.M. Fan¹, D.L. Young^1,2, K. Murugesan¹, C.C Tsai³

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.1, pp. 29-44, 2005, DOI:10.3970/cmes.2005.008.029

Abstract We use a meshless numerical method to analyze the eigenanalysis of thin circular membranes with degenerate boundary conditions, composed by different orientations and structures of stringers. The membrane eigenproblem is studied by solving the two-dimensional Helmholtz equation utilizing the method of fundamental solutions and domain decomposition technique as well. The method of singular value decomposition is adopted to obtain eigenvalues and eigenvectors of the resulting system of global linear equation. The proposed novel numerical scheme was first validated by three circular membranes which are structured with a single edge stringer, two opposite edge stringers and… More >

Yunfa Zhang¹, Zihui Xia^1,2

CMC-Computers, Materials & Continua, Vol.2, No.3, pp. 213-226, 2005, DOI:10.3970/cmc.2005.002.213

Abstract In the present study, the initiation and evolution of the interphase damage and their influences on the global stress-strain relation of composite laminates are predicted by finite element analysis on a micromechanical unit cell model. A thin layer of interphase elements is introduced and its stress-strain relation is derived based on a cohesive law which describes both normal and tangential separations at the interface between the fiber and matrix. In addition, a viscous term is added to the cohesive law to overcome the convergence difficulty induced by the so-called snap-back instability in the numerical analysis. More >

S.-P. Zhu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 227-236, 2001, DOI:10.3970/cmes.2001.002.227

Abstract Problems defined on infinite domains must be treated on a finite computational domain. The treatment of the artificially placed boundaries (usually referred to as open boundaries) of such domain truncations can be quite subtle; an over truncation would normally result in large, undesirable reflection of signals back to the computational domain whereas an under truncation would imply an injudicious use of computational resources. In particular, problems occur when strongly nonlinear free surface waves generated in a numerical wave tank are passing through such an open boundary.
In this paper, some recent numerical test results of… More >

W.W. Liou¹, Y.C. Fang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 119-128, 2000, DOI:10.3970/cmes.2000.001.571

Abstract A simple implicit treatment for the low speed inflow and outflow boundary conditions for the direct simulation Monte Carlo (DSMC) of the flows in microelectromechanical systems (MEMS) is proposed. The local mean flow velocity, temperature, and number density near the subsonic boundaries were used to determine the number of molecules entering the computational domain and their corresponding velocities at every sample average step. The proposed boundary conditions were validated against micro-Poiseuille flows and micro-Couette flows. The results were compared with analytical solutions derived from the Navier-Stokes equations using first-order and second order slip-boundary conditions. The More >

Igor Patlashenko¹, Dan Givoli²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.2, pp. 61-70, 2000, DOI:10.3970/cmes.2000.001.221

Abstract The method of Absorbing Boundary Conditions (ABCs) is considered for the numerical solution of a class of nonlinear exterior wave scattering problems. Recently, a scheme based on the exact nonlocal Dirichlet-to-Neumann (DtN) ABC has been proposed for such problems. Although this method is very accurate, it is also highly expensive computationally. In this paper, the nonlocal ABC is replaced by a low-order local ABC, which is obtained by localizing the DtN condition in a certain "optimal'' way. The performance of the new local scheme is compared to that of the nonlocal scheme via numerical experiments More >