Kirchhoff–Love shells within strain gradient elasticity : Weak and strong formulations and an H3-conforming isogeometric implementation

Research output: Contribution to journalArticleScientificpeer-review


Original languageEnglish
Pages (from-to)837-857
Number of pages21
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - 1 Feb 2019
MoE publication typeA1 Journal article-refereed


Research units

  • Norwegian University of Science and Technology


A strain gradient elasticity model for shells of arbitrary geometry is derived for the first time. The Kirchhoff–Love shell kinematics is employed in the context of a one-parameter modification of Mindlin's strain gradient elasticity theory. The weak form of the static boundary value problem of the generalized shell model is formulated within an H3 Sobolev space setting incorporating first-, second- and third-order derivatives of the displacement variables. The strong form governing equations with a complete set of boundary conditions are derived via the principle of virtual work. A detailed description focusing on the non-standard features of the implementation of the corresponding Galerkin discretizations is provided. The numerical computations are accomplished with a conforming isogeometric method by adopting Cp−1-continuous NURBS basis functions of order p≥3. Convergence studies and comparisons to the corresponding three-dimensional solid element simulation verify the shell element implementation. Numerical results demonstrate the crucial capabilities of the non-standard shell model: capturing size effects and smoothening stress singularities.

    Research areas

  • Convergence, Isogeometric analysis, Kirchhoff–Love shell, Size effects, Strain gradient elasticity, Stress singularities

ID: 30191997