Postbuckling analysis of nonlocal functionally graded beams

Abstract

The main goal of this research is to study the postbuckling behavior of nonlocal functionally graded beams. Eringen's nonlocal differential model is used to evaluate the influence of the material length scale in the bending response. An improved shear deformation beam theory with five independent parameters is utilized, which is suitable for the use of 3D constitutive equations. A finite element model is derived with spectral highorder interpolation functions to avoid shear locking. The formulation is verified by comparing the present results with the ones found in the literature. Functionally graded beams with different boundary conditions, nonlocal parameters, and power law indices are analyzed. It is shown that the present model can accurately predict the behavior of nonlocal beams due to the use of high-order terms in the displacement field in comparison with classical beam formulations. Finally, new benchmark problems are analyzed to show the capabilities of the present model to evaluate the effect of the nonlocal parameter and the power law index on postbuckling beam behavior.

Nonlinear Transient Dynamic Behavior of Functionally Graded Beams

“…Finally, corresponding to the last variable 𝛙 = 𝜓 𝑖 (𝑥 𝑖 , 𝑡)𝐞 𝐢 is the transversal quadratic deformation vector for stretching. It is important to note that 3D constitutive equations are required in accordance with the authors [20].…”

“…This expression is known as effective stiffness, in the same way for the force vector, both masses are multiplied by coefficients (20) that generate stability and accuracy to the method. In addition, the velocity and acceleration expressions are shown, which are updated at each time step.…”

Studying the Critical Buckling Load of FG Beam Using ANSYS

“…In this work, the critical mechanical buckling loads are calculated for Fixed-Free and Fixed-Fixed FG beams, while the critical thermal buckling loads are calculated for Fixed-Fixed and Pinned-Pinned FG beams. In order to generalize the results of mechanical load, the nondimension critical buckling load is calculated using the following equation [22]:…”

“…al. [22] used finite element method to investigate the geometrically non-linear bending behavior of FG beam under buckling load. They derived finite element formulation using principle of virtual work and improving first-order shear deformation theory to study the volume fraction effect on the response of FG beam made of ceramics and metals.…”