J. Kong¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.10, No.2, pp. 57-64, 2009, DOI:10.3970/icces.2009.010.057

Abstract For the analysis of prismatic thin-walled structures, whether single or continuous spanned, the finite strip method is one of the most effective methods developed to date. Significant development of the method has been made, in particular, by adopting various analytical functions in the longitudinal direction to suit various support conditions, including the classical beam vibration functions and the spline functions. In contrast to analytically-defined functions, an alternative finite strip method is presented herein by exploring the use of computed beam vibration functions that takes into consideration explicitly the axial-bending coupling effect of unsymmetrical, cross-ply laminates as well as various combinations… More >

S.Yu. Reutskiy¹

CMC-Computers, Materials & Continua, Vol.2, No.3, pp. 177-188, 2005, DOI:10.3970/cmc.2005.002.177

Abstract In this paper a new meshless method for eigenproblems with Laplace and biharmonic operators in simply and multiply connected domains is presented. The solution of an eigenvalue problem is reduced to a sequence of inhomogeneous problems with the differential operator studied. These problems are solved using the method of fundamental solutions. The method presented shows a high precision in simply and multiply connected domains. The results of the numerical experiments justifying the method are presented. More >

Mena E. Tawfik^{1, 2}, Peter L. Bishay^{3, *}, Edward A. Sadek¹

CMES-Computer Modeling in Engineering & Sciences, Vol.115, No.1, pp. 105-129, 2018, DOI:10.3970/cmes.2018.115.105

Abstract Monte Carlo Simulations (MCS), commonly used for reliability analysis, require a large amount of data points to obtain acceptable accuracy, even if the Subset Simulation with Importance Sampling (SS/IS) methods are used. The Second Order Reliability Method (SORM) has proved to be an excellent rapid tool in the stochastic analysis of laminated composite structures, when compared to the slower MCS techniques. However, SORM requires differentiating the performance function with respect to each of the random variables involved in the simulation. The most suitable approach to do this is to use a symbolic solver, which renders the simulations very slow, although… More >

V. Panchore¹, R. Ganguli², S. N. Omkar³

CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.4, pp. 215-237, 2015, DOI:10.3970/cmes.2015.108.215

Abstract A rotating Timoshenko beam free vibration problem is solved using the meshless local Petrov-Galerkin method. A locking-free shape function formulation is introduced with an improved radial basis function interpolation and the governing differential equations of the Timoshenko beam are used instead of the alternative formulation used by Cho and Atluri (2001). The locking-free approximation overcomes the problem of ill conditioning associated with the normal approximation. The radial basis functions satisfy the Kronercker delta property and make it easier to apply the essential boundary conditions. The mass matrix and the stiffness matrix are derived for the meshless local Petrov-Galerkin method. Results… More >

V. Panchore¹, R. Ganguli², S. N. Omkar³

CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.5, pp. 353-373, 2015, DOI:10.3970/cmes.2015.104.353

Abstract Free vibration problem of a rotating Euler-Bernoulli beam is solved with a truly meshless local Petrov-Galerkin method. Radial basis function and summation of two radial basis functions are used for interpolation. Radial basis function satisfies the Kronecker delta property and makes it simpler to apply the essential boundary conditions. Interpolation with summation of two radial basis functions increases the node carrying capacity within the sub-domain of the trial function and higher natural frequencies can be computed by selecting the complete domain as a sub-domain of the trial function. The mass and stiffness matrices are derived and numerical results for frequencies… More >

Salvatore Brischetto¹

CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.4, pp. 305-327, 2015, DOI:10.3970/cmes.2015.104.305

Abstract This paper proposes the free vibration analysis of Double-Walled Carbon NanoTubes (DWCNTs). A continuum elastic three-dimensional shell model is used for natural frequency investigation of simply supported DWCNTs. The 3D shell method is compared with beam analyses to show the applicability limits of 1D beam models. The effect of van der Waals interaction between the two cylinders is shown for different Carbon NanoTube (CNT) lengths and vibration modes. Results give the van der Waals interaction effect in terms of frequency values. In order to apply the 3D shell continuum model, DWCNTs are defined as two concentric isotropic cylinders (with an… More >

Hao Zuo^1,2, Zhi-Bo Yang^1,2,3, Xue-Feng Chen^1,2, Yong Xie⁴, Xing-Wu Zhang^1,2, Yue Liu⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.6, pp. 477-506, 2014, DOI:10.3970/cmes.2014.100.477

Abstract The application of B-spline wavelet on the interval (BSWI) finite element method for static, free vibration and buckling analysis in functionally graded (FG) beam is presented in this paper. The functionally graded material (FGM) is a new type of heterogeneous composite material with material properties varying continuously throughout the thickness direction according to power law form in terms of volume fraction of material constituents. Different from polynomial interpolation used in traditional finite element method, the scaling functions of BSWI are employed to form the shape functions and construct wavelet-based elements. Timoshenko beam theory and Hamilton’s principle are adopted to formulate… More >

W.L.A. Pereira¹, V.J. Karam², J.A.M. Carrer³, C.S.G. Monteiro¹, W.J. Mansur¹

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.2, pp. 117-130, 2013, DOI:10.3970/cmes.2013.096.117

Abstract In this work, the BEM is applied to obtain the numerical solutions for free vibration analysis of thick square plates with two edges simply supported or clamped, and the other two edges free. A formulation based on Reissner’s theory is used here, which includes the contribution of the additional translational inertia terms to the integral equation of displacements and internal forces. The boundary element method is used to discretize the space, where it is employed the static fundamental solution. In literature, the responses for the kind of problem addressed here are very important in the hydroelastic analysis of very large… More >

S. Brischetto¹

CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.5, pp. 391-430, 2013, DOI:10.3970/cmes.2013.095.391

Abstract This paper gives an exact three-dimensional elastic model for the free vibration analysis of functionally graded one-layered and sandwich simply-supported plates and shells. An exact elasticity solution is proposed for the differential equations of equilibrium written in general orthogonal curvilinear coordinates. The equations consider a geometry for shells without simplifications, and allow the analysis of the cases of spherical shell panels, cylindrical shell panels, cylindrical closed shells and plates. The main novelty is the possibility of a general formulation for these geometries. The coefficients in equilibrium equations depend on the thickness coordinate because of the radii of curvature for the… More >

S.Yu. Reutskiy¹

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.2, pp. 115-142, 2009, DOI:10.3970/cmes.2009.051.115

Abstract In this paper a new numerical technique for problems of free vibrations of arbitrary shaped non-homogeneous membranes:∇²w + k²q(x)w = 0, x∈ Ω⊂R², B[w] = 0, x∈∂Ω is presented. Homogeneous membranes of a complex form are considered as a particular case. The method is based on mathematically modeling of physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the resonant frequencies. Applying the method, one gets a sequence of boundary value problems (BVPs) depending on the spectral parameter k. The eigenvalues are sought as positions of the maxima of… More >