Zhongming Hu^1,*, Leilei Chen¹, Delei Yang¹, Jichao Zhang¹, Youyang Xin¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.27, No.4, pp. 1-3, 2023, DOI:10.32604/icces.2023.09340

Abstract Functionally graded materials (FGMs), a kind of composite materials, were proposed to satisfy the requirements of thermal barrier materials initially [1-3]. Compared with traditional composites, the microstructure and mechanical characteristics of FGMs change continuously which make them present excellent performance in deformation resistance or toughness under extreme mechanical and thermal loadings [4]. Therefore, FGMs have been paid much attention and experienced rapid developments in the last decade. Nowadays, various structural components manufactured by FGMs have been used in extensive applications, such as aerospace, bioengineering, nuclear industries, civil constructions etc. [5-7]
While, FG Euler-Bernoulli beams maybe suffer damage in practical… More >

Chih-Wen Chang^*

CMC-Computers, Materials & Continua, Vol.73, No.1, pp. 433-451, 2022, DOI:10.32604/cmc.2022.027021

Abstract We retrieve unknown nonlinear large space-time dependent forces burdened with the vibrating nonlinear Euler-Bernoulli beams under varied boundary data, comprising two-end fixed, cantilevered, clamped-hinged, and simply supported conditions in this study. Even though some researchers used several schemes to overcome these forward problems of Euler-Bernoulli beams; however, an effective numerical algorithm to solve these inverse problems is still not available. We cope with the homogeneous boundary conditions, initial data, and final time datum for each type of nonlinear beam by employing a variety of boundary shape functions. The unknown nonlinear large external force can be recuperated via back-substitution of the… More >

Zhenghao Yang, Erkan Oterkus^*, Selda Oterkus

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.2, pp. 527-544, 2020, DOI:10.32604/cmes.2020.010804

Abstract In this study, a new state-based peridynamic formulation is developed for functionally graded Euler-Bernoulli beams. The equation of motion is developed by using Lagrange’s equation and Taylor series. Both axial and transverse displacements are taken into account as degrees of freedom. Four different boundary conditions are considered including pinned support-roller support, pinned support-pinned support, clamped-clamped and clamped-free. Peridynamic results are compared against finite element analysis results for transverse and axial deformations and a very good agreement is observed for all different types of boundary conditions. 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 >

K.G. Vinod¹, S. Gopalakrishnan¹, R. Ganguli¹

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.3, pp. 197-208, 2006, DOI:10.3970/cmes.2006.016.197

Abstract A spectral finite element formulation for a rotating beam subjected to small duration impact is presented in this paper. The spatial variation in centrifugal force is modeled in an average sense. Spectrum and dispersion plots are obtained as a function of rotating speed. It is shown that the flexural wave tends to behave non-dispersively at very high rotation speeds. The numerical results are simulated for two rotating waveguides of different dimensions. The results show that there is a steep increase in responses with the response peaks and the reflected signals almost vanishing at higher rotating speeds. The solution obtained in… More >

C. R. A. Silva¹, H. P. Azikri de Deus¹, G.E. Mantovani², A.T. Beck³

CMES-Computer Modeling in Engineering & Sciences, Vol.67, No.2, pp. 119-150, 2010, DOI:10.3970/cmes.2010.067.119

Abstract In this paper, the Askey-Wiener scheme and the Galerkin method are used to obtain approximate solutions to stochastic beam bending on Winkler foundation. The study addresses Euler-Bernoulli beams with uncertainty in the bending stiffness modulus and in the stiffness of the foundation. Uncertainties are represented by parameterized stochastic processes. The random behavior of beam response is modeled using the Askey-Wiener scheme. One contribution of the paper is a sketch of proof of existence and uniqueness of the solution to problems involving fourth order operators applied to random fields. From the approximate Galerkin solution, expected value and variance of beam displacement… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.39, No.2, pp. 125-154, 2009, DOI:10.3970/cmes.2009.039.125

Abstract We propose a new numerical method for solving the boundary value problems of ordinary differential equations (ODEs) under multipoint boundary conditions specified at t = T_i, i = 1,...,m, where T₁ < ... < T_m. The finite difference scheme is used to approximate the ODEs, which together with the m-point boundary conditions constitute a system of nonlinear algebraic equations (NAEs). Then a Fictitious Time Integration Method (FTIM) is used to solve these NAEs. Numerical examples confirm that the new approach is highly accurate and efficient with a fast convergence. The FTIM can also be used to find the periods of… More >

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 >

Cheng-Hung Huang^1,2, Chih-Chun Shih¹

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.3, pp. 239-254, 2007, DOI:10.3970/cmes.2007.021.239

Abstract An inverse forced vibration problem, based on the Conjugate Gradient Method (CGM), (or the iterative regularization method), is examined in this study to estimate simultaneously the unknown time-dependent applied force and moment for an Euler-Bernoulli beam by utilizing the simulated beam displacement measurements. The accuracy of this inverse problem is examined by using the simulated exact and inexact displacement measurements. The numerical experiments are performed to test the validity of the present algorithm by using different types of applied force and moment, sensor locations and measurement errors. Results show that excellent estimations on the applied force and moment can be… More >

U. Andreaus^1,3, R.C. Batra², M. Porfiri^{2, 3}

CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.2, pp. 111-132, 2005, DOI:10.3970/cmes.2005.009.111

Abstract Structural health monitoring techniques based on vibration data have received increasing attention in recent years. Since the measured modal characteristics and the transient motion of a beam exhibit low sensitivity to damage, numerical techniques for accurately computing vibration characteristics are needed. Here we use a Meshless Local Petrov-Galerkin (MLPG) method to analyze vibrations of a beam with multiple cracks. The trial and the test functions are constructed using the Generalized Moving Least Squares (GMLS) approximation. The smoothness of the GMLS basis functions requires the use of special techniques to account for the slope discontinuities at the crack locations. Therefore, a… More >