Proceedings of the 2 nd World Congress on New Technologies (NewTech'16) Budapest, Hungary – August 18 – 19, 2016 Paper No. ICNFA 142 DOI: 10.11159/icnfa16.142 ICNFA 142-1 A Nonlocal Elasticity Approach for the In-Plane Static Analysis of Nanoarches Serhan Aydin Aya, Olcay Oldac, Ekrem Tufekci Istanbul Technical University, Faculty of Mechanical Engineering, Gumussuyu, Istanbul, Turkey ayas@itu.edu.tr; olcay.oldac@tr.kspg.com; tufekcie@itu.edu.tr Abstract - Eringen’s nonlocal elasticity theory is incorporated into classical beam model considering the effects of axial extension and the shear deformation to capture unique static behavior of the nanobeams under continuum mechanics theory. The governing differential equations are obtained for curved beams and solved exactly by using the initial value method. Circular uniform beam with concentrated loads are considered. The effects of shear deformation, axial extension, geometric parameters and small scale parameter on the displacements and stress resultants are investigated. Keywords: Nanoarches, nonlocal elasticity, in-plane statics, exact solution, initial value method. 1. Introduction Nano-sized beam structures have great potential applications in many different fields such as nanoscale actuation, sensing, and detection due to their remarkable mechanical, electronic and chemical properties. The growing interest in nanotechnology has fueled the study of nanostructures such as nanotrusses, nanobeams and nanoshells. Classical continuum mechanics cannot fully describe the mechanical behavior of these structures due to the absence of an internal material length scale in the constitutive law. Eringen’s studies on nonlocal elasticity introduced integro-differential constitutive equations to account for the effect of long-range interatomic forces [1]. This theory states that the stress at a given reference point of a body is a function of the strain field at every point in the body; hence, the theory takes the long range forces between atoms and the scale effect into account in the formulation. Application of nonlocal elasticity for the formulation of nonlocal version of the Euler-Bernoulli beam model is initially proposed by Peddieson et al. [2]. Since then, the nonlocal theory, including nano-beam, plate and shell models were successfully developed using nonlocal continuum mechanics and many researchers reported on bending, vibration, buckling and wave propagation of nonlocal nanostructures [3-5]. Most of these studies focused on straight beam formulation, however, it is known that these structures might not be perfectly straight [6]. As an example, carbon nanotubes are long and bent, the bending being observed in isolated carbon nanotubes between electrodes or composite systems made from carbon nanotubes [7]. The curvature may be originated from buckling of axially loaded straight nanotubes or it is a result of fabrication and waviness affects the material stiffness. Although carbon nanotubes are usually not straight and have some waviness along its length, few investigations are known to be concerned with the vibration of these nanostructures. In the study, in-plane static behavior of a planar curved nanobeam is investigated. Exact analytical solution of in-plane static problems of a circular nanobeam with uniform cross-section is presented. It is known that the size elimination of the nano scale effect may cause a significant deviation in the results. This study aims to overcome t he problem by using Eringen’s nonlocal theory. Initially, the governing differential equations of static behavior of a curved nanobeam are given by using the nonlocal constitutive equations of Eringen. The expressions for components of Laplacian of the symmetrical second order tensor in cylindrical coordinates given by Povstenko [8] are implemented in Eringen’s nonlocal equations in order to obtain the governing equations of a curved beam in Frenet frame. Based on the initial value method, the exact solution of the differential equations is obtained. The displacements, rotation angle about the binormal axis and the stress resultants are obtained analytically. The axial extension and shear deformation effects are considered in the analysis. A parametric study is also performed to point out the effects of the geometric parameters such as slenderness ratio, opening angle, loading and boundary conditions. To the authors’ best knowledge, almost all of the studies on the nonlocal beam theory has been discussed in the context of straight nanobeams. There is very limited number of papers on the curved nanobeams and most