E. Carrera, S. Brischetto¹, M. Cinefra²

CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.3, pp. 259-342, 2010, DOI:10.3970/cmes.2010.065.259

Abstract This paper investigates the problem of free vibrations of multilayered plates and shells embedding anisotropic and thickness polarized piezoelectric layers. Carrera's Unified Formulation (CUF) has been employed to implement a large variety of electro-mechanical plate/shell theories. So-called Equivalent Single Layer and Layer Wise variable descriptions are employed for mechanical and electrical variables;linear to fourth order expansions are used in the thickness direction z in terms of power of z or Legendre polynomials. Various forms are considered for the Principle of Virtual Displacements (PVD) and Reissner's Mixed Variational Theorem (RMVT) to derive consistent differential electro-mechanical governing equations. The effect of electro-mechanical… More >

M.K. Kang¹, E.H. Kim¹, M.S. Rim¹, I. Lee^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.64, No.3, pp. 227-250, 2010, DOI:10.3970/cmes.2010.064.227

Abstract An engineering model for predicting the behavior of shape memory alloy (SMA) wire is presented in this study. Piecewise linear relations between stress and strain at a given temperature are assumed and the mixture rule of Reuss bounds is applied to get the elastic modulus of the SMAs in the mixed phase. Critical stresses and strains of the start and finish of the phase transformation are calculated at a given temperature by means of a linear constitutive equation and a stress-temperature diagram. Transformation conditions based on the critical stresses are translated in terms of critical strains. Martensite volume fraction and… More >

Y. Inoue¹, R. Kobayashi¹, S. Ogata¹, T. Gotoh¹

CMES-Computer Modeling in Engineering & Sciences, Vol.63, No.2, pp. 137-162, 2010, DOI:10.3970/cmes.2010.063.137

Abstract Vibration of a single graphene and a pair of graphenes at micro meter scale induced by air flow is numerically simulated and examined by using a hybrid computational method starting from a microscopic level of description for the graphene. In order to bridge a huge gap in spatial and time scales in their motions, the carbon atoms of the graphene are represented by a small number of coarse grained particles, the fluid motion is described by the lattice Boltzmann equation and the momentum exchange at the boundary is treated by the time averaged immersed boundary method. It is found that… More >

Shueei-Muh Lin¹

CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.1, pp. 95-114, 2010, DOI:10.3970/cmes.2010.060.095

Abstract In this study, the mathematical model of double-beams assembly subjected to the a.c. electrostatic force is established. This is helpful for designing sensors and actuators. The boundary condition of this system is nonlinear and time-dependent. Obviously, this system is very complicated. A new solution method is here developed to derive the analytical solution. Because the a.c. electrostatic force includes the static and harmonic forces, the system is divided into the nonlinear static and dynamic subsystems. The exact static solution is presented. In the other hand, the boundary conditions of the dynamic subsystem are nonlinear and time-dependent. First, using the balanced… More >

Wei-Ming Lee¹, Jeng-Tzong Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.50, No.2, pp. 141-160, 2009, DOI:10.3970/cmes.2009.050.141

Abstract This paper presents the multipole Trefftz method to derive an analytical model describing the free vibration of a circular plate with multiple circular holes. Based on the addition theorem, the solution of multipoles centered at each circle can be expressed in terms of multipoles centered at one circle, where boundary conditions are specified. In this way, a coupled infinite system of simultaneous linear algebraic equations is derived for the circular plate with multiple holes. The direct searching approach is employed in the truncated finite system to determine the natural frequencies by using the singular value decomposition (SVD). After determining the… More >

Shueei-Muh Lin¹

CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.1, pp. 73-90, 2009, DOI:10.3970/cmes.2009.043.073

Abstract In this study, the mathematical model of a moving beam is established. This model is composed of a governing differential equation and three homogenous boundary conditions and one non-homogenous boundary condition including a time-dependent inertia force and a nonlinear active control force. Obviously, a moving mass problem with nonlinear and time dependent boundary condition is very complicated. One solution method is here developed to derive the exact solution for this system. By taking a change of dependent variable with a shifting function the original system is transformed to be a system composed of one non-homogeneous governing differential equation and four… More >

E. Brusa¹, E. Franceschinis², S. Morsut²

CMES-Computer Modeling in Engineering & Sciences, Vol.42, No.2, pp. 75-106, 2009, DOI:10.3970/cmes.2009.042.075

Abstract Electrodes motion and positioning are critical issues of the Electric Arc Furnace (EAF) operation in steelmaking process. During the melting process electrode is exposed to some impulsive and harmonic forces, superimposing to the structure's static loading. Unfortunately, structural vibration may interact with the electric arc regulation, because of the dynamic resonance. Instability in the furnace power supplying and dangerous electrode breakage may occur as a consequence of those dynamic effects. In this paper the dynamic behaviour of a real EAF structure is discussed and some numerical models are proposed. Available experimental data, collected by a monitoring system on a real… More >

C. J. Wu¹, C. Y. Chou¹, C. N. Han¹, K. N. Chiang²

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.1, pp. 49-68, 2009, DOI:10.3970/cmes.2009.041.049

Abstract In this paper, the atomistic-continuum mechanics method (ACM) is applied for carbon nanotube modeling. The atomistic-continuum mechanics is based on the transformation of chemical bonds between atoms in molecular mechanics into appropriate elements in finite element method and continuum mechanics. Spring elements are treated as chemical bonds between carbon atoms in carbon nanotube, whose force-displacement function is determined by the Reactive Empirical Bond Order (REBO) potential model. The advantages and unique feature of ACM method is same analytical model can be used for both tensile and vibration analyses, and most importantly, there are no prior inputs such as Young's Modulus,… More >

Sen Yung Lee¹, Jyh Shyang Wu²

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.2, pp. 133-154, 2009, DOI:10.3970/cmes.2009.040.133

Abstract The three coupled governing differential equations for the in-plane vibrations of curved non-uniform Timoshenko beams are derived via the Hamilton's principle. Three physical parameters are introduced to simplify the analysis. By eliminating all the terms with the axial displacement parameter, then reducing the order of differential operator acting on the flexural displacement parameter, one uncouples the three governing characteristic differential equations with variable coefficients and reduces them into a sixth-order ordinary differential equation with variable coefficients in term of the angle of the rotation due to bending for the first time. The explicit relations between the axial and the flexural… More >

X.Y. Cui^1,2, G. R. Liu^2,3, G. Y. Li^1,4, G. Zheng¹

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.3, pp. 217-230, 2008, DOI:10.3970/cmes.2008.038.217

Abstract In this paper, a gradient smoothed formulation is proposed to deal with a fourth-order differential equation of Bernoulli-Euler beam problems for static and dynamic analysis. Through the smoothing operation, the C¹ continuity requirement for fourth-order boundary value and initial value problems can be easily relaxed, and C⁰ interpolating function can be employed to solve C¹ problems. In present thin beam problems, linear shape functions are employed to approximate the displacement field, and smoothing domains are further formed for computing the smoothed curvature and bending moment field. Numerical examples indicate that very accurate results can be yielded when a reasonable number… More >