Static and Dynamic Analysis of a Simple Model of Explicit Gradient Elasticity

Abstract

Gradient elasticity has developed into an important area of continuum mechanics with numerous applications in engineering mechanics, structural analysis, experimental and computational mechanics. The present thesis is concerned with a simple model of explicit gradient elasticity. The aim is to provide a comprehensive insight into the basic properties of this model, by solving several problems in statics and dynamics. The problems include one - dimensional and two - dimensional (bending) loading conditions. Especially, use is made of a consistent Euler - Bernoulli beam theory and of different versions of Hamilton's principle. Moreover, a method is presented for determining the critical load in buckling problems. The investigations highlight, among others, the effect of non - classical boundary conditions and of non - classical material parameters.