Finite element formulations based generally on classical beam theories such as Euler-Bernoulli or Timoshenko. Sometimes, these two formulations could be problematic expressed in terms of restrictions of Euler-Bernoulli beam theory, in case of thicker beams due to non-consideration of transverse shear; phenomenon that is known as shear locking characterized the Timoshenko beam theory, in case of...

A homogenization methodology for the construction of effective Cosserat substitution media heterogeneous materials is proposed, combining a variational principle in linear elasticity with extended Hill-Mandel lemma accounting introduced generalized kinematics. The proposed method general and can be applied to wide class architected composites prone such micropolar effects. microscopic displacem...

In this research the sensitivity analysis of the geometric parameters such as: length, thickness and width of a single link flexible manipulator on maximum deflection (MD) of the end effector and vibration energy (VE) of that point are conducted. The equation of motion of the system is developed based on Gibbs-Appel (G-A) formulation. Also for modeling the elastic property of the system the ass...

A complete investigation on the free vibration and stability analysis of beams made of functionally graded materials (FGMs) containing open edge cracks utilizing four beam theories, Euler-Bernoulli, Rayleigh, shear and Timoshenko, is performed in this research. It is assumed that the material properties vary along the beam thickness exponentially and the cracked beam is modeled as two segments ...

In this paper, we study the flexural vibration behavior of single-walled carbon nanotubes (SWCNTs) for the assessment of Timoshenko beam models. Extensive molecular dynamics (MD) simulations based on second-generation reactive empirical bond-order (REBO) potential and Timoshenko beam modeling are performed to determine the vibration frequencies for SWCNTs with various length-todiameter ratios, ...

in this article, the bending and free vibration analysis of functionally graded (fg) nanocomposites timoshenko beam model reinforced by single-walled boron nitride nanotube (swbnnt) using micro-mechanical approach embedded in an elastic medium is studied. the modified coupled stress (mcst) and nonlocal elasticity theories are developed to take into account the size-dependent effect. the mechani...

In this paper an overview of functionally graded materials and constitutive relations of electro elasticity for three-dimensional deformable  solids is presented, and  governing equations of the Bernoulli–Euler and Timoshenko beam theories which account for through-thickness power-law variation of a two-constituent material and piezoelectric layers are developed  using the  principle  of virtua...

In this study, free vibration analysis of carbon nanotubes is investigated based on Timoshenko beam theory. Discrete singular convolution (DSC) method is used for free vibration problem of numerical solution of carbon nanotubes. Numerical results are presented and compared with that available in the literature. It is shown that reasonable accurate results are obtained. Keywords-Carbon Nanotubes...

Non-prismatic beams have received great attention from engineers due to their capability in optimizing the strength and weight of the structure. In recent years, many researchers have worked on engineering problems related to static and dynamic analysis of either Euler–Bernoulli [1–3] or Timoshenko [4,5] beams. For short thick beams and rotating machineries, the Timoshenko beam theory presents ...

This work presents a method to find the exact solutions for the free vibration analysis of a delaminated beam based on the Timoshenko type with different boundary conditions. The solutions are obtained by the method of Lagrange multipliers in which the free vibration problem is posed as a constrained variational problem. The Legendre orthogonal polynomials are used as the beam eigenfunctions. N...