Xiaojun Huang¹, Liaojun Zhang^2,*, Hanbo Cui¹, Gaoxing Hu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.140, No.2, pp. 1647-1668, 2024, DOI:10.32604/cmes.2024.049124 - 20 May 2024

Abstract This study proposes an effective method to enhance the accuracy of the Differential Quadrature Method (DQM) for calculating the dynamic characteristics of functionally graded beams by improving the form of discrete node distribution. Firstly, based on the first-order shear deformation theory, the governing equation of free vibration of a functionally graded beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam axial displacement, transverse displacement, and cross-sectional rotation angle by considering the effects of shear deformation and rotational inertia of the beam cross-section. Then, ignoring the shear deformation of the… More >

Yang Xia^*, Luting Deng, Jian Zhao

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.2, pp. 605-626, 2020, DOI:10.32604/cmes.2020.010204 - 20 July 2020

Abstract Geometric fitting based on discrete points to establish curve structures is an important problem in numerical modeling. The purpose of this paper is to investigate the geometric fitting method for curved beam structure from points, and to get high-quality parametric model for isogeometric analysis. A Timoshenko beam element is established for an initially curved spacial beam with arbitrary curvature. The approximation and interpolation methods to get parametric models of curves from given points are examined, and three strategies of parameterization, meaning the equally spaced method, the chord length method and the centripetal method are considered.… 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 More >

Vinita Chellappan¹, S. Gopalakrishnan¹ and V. Mani¹

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.2, pp. 131-174, 2014, DOI:10.3970/cmes.2014.097.131

Abstract The paper discusses the frequency domain based solution for a certain class of wave equations such as: a second order partial differential equation in one variable with constant and varying coefficients (Cantilever beam) and a coupled second order partial differential equation in two variables with constant and varying coefficients (Timoshenko beam). The exact solution of the Cantilever beam with uniform and varying cross-section and the Timoshenko beam with uniform cross-section is available. However, the exact solution for Timoshenko beam with varying cross-section is not available. Laplace spectral methods are used to solve these problems exactly… More >

A.E. Kampitsis¹, E.J. Sapountzakis²

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.6, pp. 367-409, 2014, DOI:10.3970/cmes.2014.103.367

Abstract In this paper a Boundary Element Method (BEM) is developed for the geometrically nonlinear inelastic analysis of Timoshenko beams of arbitrary doubly symmetric simply or multiply connected constant cross-section, resting on inelastic tensionless Winkler foundation. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading, while its edges are subjected to the most general boundary conditions. To account for shear deformations, the concept of shear deformation coefficients is used. A displacement based formulation is developed and inelastic redistribution 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… More >

A.S Vinod Kumar, Ranjan Ganguli²

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.6, pp. 443-474, 2012, DOI:10.3970/cmes.2012.088.443

Abstract The governing differential equation of a rotating beam becomes the stiff-string equation if we assume uniform tension. We find the tension in the stiff string which yields the same frequency as a rotating cantilever beam with a prescribed rotating speed and identical uniform mass and stiffness. This tension varies for different modes and are found by solving a transcendental equation using bisection method. We also find the location along the rotating beam where equivalent constant tension for the stiff string acts for a given mode. Both Euler-Bernoulli and Timoshenko beams are considered for numerical results. More >

Biao Zhou^1,2,3, Xiong yao Xie^1,2, Yeong Bin Yang⁴, Jing Cai Jiang³

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.4, pp. 321-348, 2012, DOI:10.3970/cmes.2012.086.321

Abstract The vibration-based SHM (Structure Health Monitoring) system has been successfully used in bridge and other surface civil infrastructure. However, its application in operation tunnels remains a big challenge. The reasons are discussed in this paper by comparing the vibration characteristics of the free tunnel structure and tunnel-soil coupled system. It is revealed that all the correlation characteristics of the free tunnel FRFs (Frequency Response Function spectrum) will vanish and be replaced by a coupled resonance frequency when the tunnel is surrounded by soil. The above statement is validated by field measurements. Moreover, the origin of More >

E.J. Sapountzakis¹, J.A. Dourakopoulos¹

CMC-Computers, Materials & Continua, Vol.18, No.2, pp. 121-154, 2010, DOI:10.3970/cmc.2010.018.121

Abstract In this paper a boundary element method is developed for the nonlinear flexural - torsional analysis of Timoshenko beam-columns of arbitrary simply or multiply connected constant cross section, undergoing moderate large deflections under general boundary conditions. The beam-column is subjected to the combined action of an arbitrarily distributed or concentrated axial and transverse loading as well as to bending and twisting moments. To account for shear deformations, the concept of shear deformation coefficients is used. Seven boundary value problems are formulated with respect to the transverse displacements, to the axial displacement, to the angle of… 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 More >