Static and buckling analysis of functionally graded Timoshenko nanobeams

• Published in: Applied mathematics and computation Vol. 229; pp. 283 - 295
• Main Authors: Eltaher, M.A., Khairy, A., Sadoun, A.M., Omar, Fatema-Alzahraa
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 25.02.2014
• Subjects: Beams (structural); Bending; Buckling; Differential equations; Equilibrium equations; Finite element method; Functionally graded; Functionally gradient materials; Mathematical models; Nanostructure; Neutral axis; Static-buckling analysis; Timoshenko beams; Timoshenko nanobeam; Finite element method; Timoshenko nanobeam; Static-buckling analysis; Functionally graded; Neutral axis
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2013.12.072

Investigation of static and buckling behaviors of nonlocal functionally graded (FG) Timoshenko nanobeam is the main objective of this paper. Eringen nonlocal differential constitutive equation is exploited to describe the size dependency of nanostructure beam. The material properties of FG nanobeam are assumed to vary through the thickness direction by power-law. The kinematic assumption of beam is assumed by Timoshenko theory, which accommodates for thin and moderated thick beam, and hence, considers the shear effect. The equilibrium equations are derived using the principle of the minimum total potential energy. A finite element method is proposed to obtain a numerical solution of equilibrium equations. Model validation is presented and compared with peer works. The results show and address the significance of the material distribution profile, size-dependence, and boundary conditions on the bending and buckling behavior of nanobeams. Also, the significant effects of neutral axis position on static and buckling behaviors are figured out.