Static Analysis of Gradient Elastic Bars, Beams, Plates and Shells

ABSTRACT

A review on the response of gradient elastic structural components, such as bars, beams, plates and shells, to static loading is provided. The simplified form II gradient elastic theory of Mindlin with just one elastic constant (the gradient elastic modulus) in addition to the two classical elastic moduli is employed to derive the governing equations of equilibrium and buckling of the aforementioned structural components. All possible boundary conditions (classical and non-classical) are obtained with the aid of variational formulations of the problems associated with these components. Thus, well posed boundary value problems are solved analytically and the response of gradient elastic bars, beams, plates and shells to static loading is determined. In all cases, the effect of the microstructure consists of stiffening the structure, which results in decreasing deflections and increasing buckling loads for increasing values of the gradient elastic modulus.