Isogeometric analysis of gradient-elastic 1D and 2D problems

Viacheslav Balobanov*, Sergei Khakalo, Jarkko Niiranen

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

5 Citations (Scopus)


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 Cp−1 continuous Galerkin method. Computational results for benchmark problems demonstrate the applicability of the method and verify the implementation.

Original languageEnglish
Title of host publicationGeneralized continua as models for classical and advanced materials
EditorsHolm Altenbach, Samuel Forest
Number of pages9
ISBN (Electronic)978-3-319-31721-2
ISBN (Print)978-3-319-31719-9
Publication statusPublished - 1 Apr 2016
MoE publication typeA3 Part of a book or another research book

Publication series

NameAdvanced Structured Materials
ISSN (Print)1869-8433
ISSN (Electronic)1869-8441


  • Bar
  • Gradient elasticity
  • Isogeometric analysis
  • Plane strain/stress


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