Appropriate boundary conditions for nonlocal elastic beams

Abstract

This study is concerned with the boundary conditions of elastic beams within the framework of nonlocal elasticity theory. The general solutions of the plane stress problem are, firstly, discussed. Through which and by employing the decaying analysis technique proposed by Gregory and Wan, a set of necessary conditions on the edge-data, other than the pure displacement one, for the existence of a decaying solution are formulated. A novel method in constructing the auxiliary regular state is also demonstrated, which is different from that we used before. Finally, the appropriate boundary conditions for the interior solution are obtained, which are not altered by the nonlocal parameter and take the form as these for their local elastic counterparts. © (2013) Trans Tech Publications, Switzerland.