This is a review paper containing the governing equations and analytical solutions of classical shear deformation theories functionally graded straight beams. The classical, first-order, third-order account for through-thickness variation two-constituent material, modified couple stress (i.e., strain gradient), von Kármán nonlinearity. Analytical bending linear theories, some which are not read...

The main goal of this research is to study the postbuckling behavior nonlocal functionally graded beams. Eringen’s differential model used evaluate influence material length scale in bending response. An improved shear deformation beam theory with five independent parameters utilized, which suitable for use 3D constitutive equations. A finite element derived spectral high-order interpolation fu...

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...

In this paper, a unified beam theory is developed and applied to study the buckling response of two types of functionally graded sandwich beams. In the first type (Type A), the sandwich beam has a hardcore whereas in the second type (Type B), the sandwich beam has a softcore. In both the type of beams, face sheets are made up of functionally graded material. The material properties of face shee...

This study presents the effect of porosity on mechanical behaviors of a power distribution functionally graded beam. The Euler-Bernoulli beam is assumed to describe the kinematic relations and constitutive equations. Because of technical problems, particle size shapes and micro-voids are created during the fabrication which should be taken into consideration. Two porosity models are proposed. T...