Nonlocal Continuum Modeling of Curved Nanostructures

Nanobeams are widely used as a structural element for nanodevices and nanomachines. The development of nanosized machines depends on proper understanding of mechanical behavior of these nanosized beam elements. In this chapter, the static and dynamic behavior of a curved planar nanobeam having variable curvature and cross-section is investigated. The nonlocal constitutive equations of Eringen are written in cylindrical coordinates and then implemented into the classical beam equations. Analytical exact solutions for static problems are obtained by using the initial value method. The equations of free vibration are derived by means of d'Alembert principle. The nonlocal theory and the equations presented in this chapter form the basis for the study of static and dynamic analysis of nanobeams. Instead of using classical beam theory, using nonlocal elasticity theory reveals the size effects, which is significant to understand the mechanical behavior of nanobeams.