Isogeometric Analysis of Gradient-Elastic 1D and 2D Problems

Abstract

In the present contribution, isogeometric methods are used to analyze the statics and dynamics of rods as well as plane strain and plane stress problems based on a simplified version of the form II of Mindlin’s strain gradient elasticity theory. The adopted strain gradient elasticity models, in particular, include only two length scale parameters enriching the classical energy expressions and resulting in fourth order partial differential equations instead of the corresponding second order ones based on the classical elasticity. The problems are discretized by an isogeometric non-uniform rational B-splines (NURBS) based $C^{p-1}$ continuous Galerkin method. Computational results for benchmark problems demonstrate the applicability of the method and verify the implementation.