Stability buckling and bending of nanobeams including cutouts

• Published in: Engineering with computers Vol. 38; no. 1; pp. 209 - 230
• Main Authors: Hamed, Mostafa A., Mohamed, N. A., Eltaher, M. A.
• Format: Journal Article
• Language: English
• Published: London Springer London 01.02.2022; Springer Nature B.V
• Subjects: Atomic interactions; Atomic properties; Beam theory (structures); Bending; Boundary conditions; Buckling; CAE) and Design; Calculus of Variations and Optimal Control; Optimization; Classical Mechanics; Computer Science; Computer-Aided Engineering (CAD; Control; Equilibrium equations; Euler-Bernoulli beams; Math. Applications in Chemistry; Mathematical and Computational Engineering; Mathematical models; Nanoelectromechanical systems; Numerical analysis; Original Article; Perforation; Scale effect; Systems Theory; Timoshenko beams; Nonlocal nanobeams; Bending and stability; Cutout beams; Perforation; Thin and thick beams; Analytical analysis; MEMS/NEMS
• ISSN: 0177-0667; 1435-5663
• DOI: 10.1007/s00366-020-01063-2

This manuscript developed a comprehensive model and numerical studies to illustrate the effect of perforation parameters on critical buckling loads and static bending of thin and thick nanobeams for all boundary conditions, for the first time. Analytical closed-form solutions are presented for buckling loads and static deflections, respectively. Euler–Bernoulli beam theory is exploited for thin beam analysis, and Timoshenko beam theory is proposed to consider a shear effect in case of thick beam analysis. Nonlocal differential form of elasticity theory is included to consider a size scale effect that is missing in case of classical theory and macro-analysis. Geometrical adaptations for perforated beam structures are illustrated in simplest form. Equilibrium equations for local and nonlocal beam are derived in detail. Numerical studies are illustrated to demonstrate influences of long-range atomic interaction, hole perforation size, number of rows of holes and boundary conditions on buckling loads and deflection of perforated nanobeams. The recommended model is helpful in designing nanoresonators and nanoactuators used in NEMS structures and nanotechnology.