Embedded kinematic boundary conditions for thin plate bending by Nitsche's approach

Isaac Harari*, Evgeny Shavelzon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

SUMMARY: A stabilized variational formulation, based on Nitsche's method for enforcing boundary constraints, leads to an efficient procedure for embedding kinematic boundary conditions in thin plate bending. The absence of kinematic admissibility constraints allows the use of non-conforming meshes with non-interpolatory approximations, thereby providing added flexibility in addressing the C 1-continuity requirements typical of these problems. Work-conjugate pairs weakly enforce kinematic boundary conditions. The pointwise enforcement of corner deflections is key to good performance in the presence of corners. Stabilization parameters are determined from local generalized eigenvalue problems, guaranteeing coercivity of the discrete bilinear form. The accuracy of the approach is verified by representative computations with bicubic C 2 B-splines, exhibiting optimal rates of convergence and robust performance with respect to values of the stabilization parameters.

Original languageEnglish
Pages (from-to)99-114
Number of pages16
JournalInternational Journal for Numerical Methods in Engineering
Volume92
Issue number1
DOIs
StatePublished - 5 Oct 2012

Keywords

  • B-splines
  • Kinematic boundary conditions
  • Nitsche's method
  • Thin plate bending

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