Finite-element Modeling for Analysis of Isotropic and Orthotropic Beams Using First Order Shear Deformation Theory
New Ideas Concerning Science and Technology Vol. 10,
17 March 2021
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.
- Finite element method
- Timoshenko beam theory
- composite materials mechanics
- static and dynamic analysis of beams