Buckling of Generic Higher-Order Shear Beam/Columns with Elastic Connections: Local and Nonlocal Formulation

In this paper, the buckling behavior of generic higher-order shear beam models is investigated in a unified framework. This paper shows that most higher-order shear beam models developed in the literature (polynomial, sinusoidal, exponential shear strain distribution assumptions over the cross section) can be classified in a common gradient elasticity Timoshenko theory, whatever the shear strain distribution assumptions over the cross section. The governing equations of the bending/buckling problem are obtained from a variational approach, leading to a generic sixth-order differential equation. Buckling solutions are presented for usual archetypal boundary conditions such as pinned-pinned, clamped-free, clamped-hinge, and clamped-clamped boundary conditions. The results are then extended to general boundary conditions based on generalized linear elastic connection law including vertical and rotational stiffness boundary conditions. Engineering analytical solutions are derived in a dimensionless format. The model valid for macrostructures is generalized for micro-or nanostructures using the nonlocal integral Eringen's model. The nonlocal framework is also developed in a variational consistent framework. Buckling solutions are finally presented for the nonlocal higher-order beam/colum models. (C) 2013 American Society of Civil Engineers.