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T. Lidstrom, “An Analytical Energy Expression for Equilibrium Analysis of 3-D Timoshenko Beam Element,” Computers and Structures, Vol. 52, No. 1, 1994, pp. 95 101. doi:10.1016/0045-7949(94)90259-3

has been cited by the following article:

• TITLE: FE Modeling and Analysis of Isotropic and Orthotropic Beams Using First Order Shear Deformation Theory

  AUTHORS: M. Adnan Elshafei

  KEYWORDS: Finite Element Method; Timoshenko Beam Theory; Composite Materials Mechanics; Static and Dynamic Analysis of Beams

  JOURNAL NAME: Materials Sciences and Applications, Vol.4 No.1, January 24, 2013

  ABSTRACT: In the present work, a finite element model is developed to analyze the response of isotropic and orthotropic beams, a common structural element for aeronautics and astronautic applications. The assumed field displacements equations of the beams are represented by a first order shear deformation theory, the Timoshenko beam theory. The equations of motion of the beams are derived using Hamilton’s principle. The shear correction factor is used to improve the obtained results. A MATLAB code is constructed to compute the natural frequencies and the static deformations for both types of beams with different boundary conditions. Numerical calculations are carried out to clarify the effects of the thickness-to-length ratio on both the Eigen values and the deflections of the beams due to the applied mechanical load. The obtained results of the proposed model are compared to the available results of other investigators, good agreement is generally obtained.