On the analysis of microbeams

• Published in: International journal of engineering science Vol. 121; pp. 14 - 33
• Main Authors: Demir, Çiğdem, Civalek, Ömer
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.12.2017; Elsevier BV
• Subjects: Beam; Beam theory (structures); Beamforming; Bending; Bending moments; Boundary conditions; Cantilever beams; Deflection; Enhanced Eringen differential model; Euler-Bernoulli beams; Eulers equations; Load distribution (forces); Materials elasticity; Microbeams; Nonlocal elasticity; Singularity function; Stress concentration; Studies; Beam; Singularity function; Bending; Enhanced Eringen differential model
• ISSN: 0020-7225; 1879-2197
• DOI: 10.1016/j.ijengsci.2017.08.016

The most widely used theory in the analysis of nanostructures is Eringen's nonlocal elasticity theory. But many researchers have mentioned that this theory has a paradox for the cantilever boundary condition. In order to overcome this paradox, different methods of mathematical complications have been applied. By adding additional parameters to Eringen's nonlocal elasticity theory, enhanced Eringen differential model was developed as an alternative solution method without the necessity of these complications. In this paper, bending of nano/micro beams under the concentrated and distributed loads has been investigated by using Euler Bernoulli beam theory via the enhanced Eringen differential model. Singularity function method is used to calculate the deflection of concentrated and distributed loaded beam. Various types of boundary conditions are considered for the beam such as cantilever, clamped, propped cantilever and simply supported. In each case of boundary conditions, closed form solutions for the bending of the beam are presented for various loading locations. Deflection, bending moment and shear force are presented comparatively for variable loadings in figures and tables.