Isogeometric galerkin methods for gradient-elastic bars, beams, membranes and plates

Abstract

Isogeometric Galerkin methods are used to analyse plate and beam bending problems as well as membrane and bar models based on Mindlin's strain gradient elasticity theory for generalized continua. The current strain gradient models include higher-order displacement gradients combined with length scale parameters enriching the strain and kinetic energies of the classical elasticity and hence resulting in higher-order partial differential equations with corresponding non-standard boundary conditions. The problems are first formulated within appropriate higher-order Sobolev space settings and then discretized by utilizing Galerkin methods with isogeometric NURBS basis functions providing appropriate higher-order continuity properties. Example benchmark problems illustrate the convergence properties of the methods.