A variational approach for large deflection of ends supported nanorod under a uniformly distributed load, using intrinsic coordinate finite elements

Abstract This paper presents a variational formulation that can be used for large deflection analysis of ends supported nanorod including the coupled effects of nonlocal elasticity and surface stress under a uniformly distributed load. The variational formulation involving the strain energy due to bending of nonlocal elasticity including the surface stress effect and virtual work done by a uniformly distributed load, is expressed in terms of the intrinsic coordinates. The Lagrange multiplier technique is applied to impose the boundary conditions which accomplished in the formulation. The validity of the variational approach is ensured by Euler's equation, which identical to the one derived by the force equilibrium consideration of an infinitesimal nanorod segment. The finite element method and Newton–Raphson iterative procedure based on the variational formulation are used to solve a system of nonlinear equations. Moreover, the very large deflection configurations of ends supported nanorod are highlighted in this study.