Akademik Veri Yönetim Sistemi
JOURNAL OF COMPUTATIONAL AND THEORETICAL NANOSCIENCE, cilt.8, sa.10, ss.2006-2012, 2011 (SCI-Expanded)
On the face of difficulty of employing the nonlocal constitutive relations in the form of integral equation, researchers started to seek alternative forms of the nonlocal constitutive relations. The Greens function formalism has become the most popular one for this purpose. The nonlocal constitutive equation in differential equation form allows employing stress potentials, such as Airys stress functions to solve boundary value problems in nonlocal elasticity. For the nonlocality kernel of exponential form, the differential equation for Airy's functions in nonlocal elasticity can be obtained by introducing the strains into the compatibility condition. In this work Airy's stress functions for plane stress problems in nonlocal elasticity are studied. Appropriate function forms for the Airys stress function are considered and are applied to solve transversely sinusoidal loaded cantilever beam bending problems. The solutions are compared with their classical counterparts. The results are given in a series of figures and tables. The results indicate that the influence of nonlocal effect becomes stronger as the wave length of sinusoidal loading come near to the length of beam which can not comment by experiments and nonlocal elasticity has more potential to represent the mechanical behavior of nanostructures and nonlocal effects could be significant in nanotechnology.