Hsin-Yi Lai¹, C. K. Chen^1,2, Jung-Chang Hsu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.1, pp. 87-116, 2008, DOI:10.3970/cmes.2008.034.087

Abstract An innovative solver for the free vibration of an elastically restrained non-uniform Euler-Bernoulli beam with tip mass of rotatory inertia and eccentricity resting on an elastic foundation and subjected to an axial load is proposed. The technique we have used is based on applying the Adomian modified decomposition method (AMDM) to our vibration problems. By using this method, any$i$th natural frequencies can be obtained one at a time and some numerical results are given to illustrate the influence of the physical parameters on the natural frequencies of the dynamic system. The computed results agree well with those analytical and numerical… More >

O.O. Oyekoya, D.U. Mba¹, A.M. El-Zafrany

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.1, pp. 55-86, 2008, DOI:10.3970/cmes.2008.034.055

Abstract In this paper, two new Mindlin-type plate bending elements have been derived for the modelling of functionally graded plate subjected to various loading conditions such as tensile loading, in-plane bending and out-of-plane bending. The properties of the first Mindlin-type element (i.e. Average Mindlin-type element) are computed by using an average fibre distribution technique which averages the macro-mechanical properties over each element. The properties of the second Mindlin-type element (i.e. Smooth Mindlin-type element) are computed by using a smooth fibre distribution technique, which directly uses the macro-mechanical properties at Gaussian quadrature points of each element. There were two types of non-linearity… More >

Shueei-Muh Lin^1,3, Sen-Yung Lee², Cheng-Chuan Tsai², Chien-Wi Chen²,Wen-Rong Wang³, Jenn-Fa Lee³

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.1, pp. 33-54, 2008, DOI:10.3970/cmes.2008.034.033

Abstract The conventional theories for circulation of arteries are emphasized on fluid behavior or some simplified models for experimental utility. In this study, a new mathematical theory is proposed to describe the wave propagation through the elastic tube filled with viscous and incompressible fluid. The radial, longitudinal and flexural vibrations of a tube wall are introduced simultaneously. Meanwhile, the linearlized momentum and continuity equations of tube flow field are expressed in the integral form. Based on these considerations, three wave modes are obtained simultaneously. These wave modes are the flexural, Young and Lamb modes, respectively. The characteristics of these modes are… More >

Song-Jeng Huang^1,2, Lin-Wei Chiu²

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.1, pp. 1-32, 2008, DOI:10.3970/cmes.2008.034.001

Abstract The composite sandwich plate is one of the most common composite structures. Local stress concentrations can be caused by localized bending effects where a load is introduced. Although a sandwich structure with an insert is one of the classical load bearing structures, little work has been conducted on the adhesive layers or inserts. This study involves a linear elasticity analysis of five-layer sandwich plates with ``through-the-thickness'' inserts, using sandwich plate theory to analyze deformation behavior. Governing equations are formulated as partial differential equations, which are solved numerically using the multi-segment integration method. Sandwich plates with ``through-the-thickness'' inserts subjected to axisymmetric… More >

Sen Yung Lee¹, Shin Yi Lu², Yen Tse Liu², Hui Chen Huang²

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.3, pp. 293-312, 2008, DOI:10.3970/cmes.2008.033.293

Abstract A new analytic solution method is developed to find the exact static deflection of a Timoshenko beam with nonlinear elastic boundary conditions for the first time. The associated mathematic system is shifted and decomposed into six linear differential equations and at most four algebra equations. After finding the roots of the algebra equations, the exact solution of the nonlinear beam system can be reconstructed. It is shown that the proposed method is valid for the problem with strong nonlinearity. Examples, limiting studies and numerical analysis are given to illustrate the analysis. The exact solutions are compared with the perturbation solutions.… More >

C. Gato and Y. Shie¹

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.3, pp. 269-292, 2008, DOI:10.3970/cmes.2008.033.269

Abstract Numerical simulations of large deformation dynamic fracture in thin shell structures using 3-D meshfree method is presented. Due to the smoothness of the meshfree shape functions, they are well suited to simulate large deformation of thin shell structures while avoiding ill-conditioning as well as stiffening in numerical computations. Dynamic fracture is modeled by simple criterion, i.e. removing connectivity between adjacent nodes once a fracture criterion is met. The main advantage of such 3-D meshfree continuum approach is its simplicity in both formulation and implementation as compared to shell theory approach, or degenerated continuum approach. Moreover, it is believed that the… More >

B. Chandrasekhar¹

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.3, pp. 243-268, 2008, DOI:10.3970/cmes.2008.033.243

Abstract In this work, a novel numerical technique, based on method of moments solution, is presented to solve the Combined layer formulation (CLF) to insure unique solution to the exterior acoustic scattering problem at all frequencies. A new set of basis functions, namely, Node based basis functions are used to represent the source distribution on the surface of rigid body and the same functions are used as testing functions as well. Combined layer formulation (CLF) is defined by linearly combining the Single layer formulation (SLF) and Double layer formulation (DLF) with complex coupling parameter. The matrix equations for the SLF and… 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 firstly proposed. The so-called \emph… More >

B. Chrasekhar¹, Sadasiva. M. Rao²

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.2, pp. 199-214, 2008, DOI:10.3970/cmes.2008.033.199

Abstract In this work, the acoustic scattering problem based on double layer formulation is solved with a novel numerical technique using method of moment's solution. A new set of basis functions, namely, Edge based Adaptive Basis Functions (EABF) are defined in the method of moment's solution procedure. The geometry of the body is divided into triangular patches and basis functions are defined on the edges. Since the double layer formulation involves the evaluation of the hyper-singular integral, the edge based adaptive basis functions are used to make the solution faster. The matrix equations are derived for the double layer formulation. The… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.2, pp. 179-198, 2008, DOI:10.3970/cmes.2008.033.179

Abstract Dirichlet boundary value problem of quasilinear elliptic equation is numerically solved by using a new concept of fictitious time integration method (FTIM). We introduce a fictitious time coordinate t by transforming the dependent variable u(x,y) into a new one by (1+t)u(x,y) =: v(x,y,t), such that the original equation is naturally and mathematically equivalently written as a quasilinear parabolic equation, including a viscous damping coefficient to enhance stability in the numerical integration of spatially semi-discretized equation as an ordinary differential equations set on grid points. Six examples of Laplace, Poisson, reaction diffusion, Helmholtz, the minimal surface, as well as the explosion… More >