Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Locking-free hp-discontinuous Galerkin methods for Timoshenko beams

Fatih Celikera,*, Bernardo Cockburna, Henryk K. Stolarskib, Kumar K. Tammac
aSchool of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA bDepartment of Civil Engineering, University of Minnesota, Minneapolis, MN 55455, USA cDepartment of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
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ABSTRACT
With the ultimate goal of eliminating a long history of issues that have plagued the structural mechanics community such as the locking phenomenon, we analyze a family of discontinuous Galerkin methods for the Timoshenko beam problem. We prove that the rate of convergence in the energy seminorm is p + 1/2 when polynomials of degree p are employed to approximate the unknowns. The estimate is sharp and independent of the thickness-to-length ratio of the beam, which shows that the method is free from shear locking.

Keywords:  Shear locking; Timoshenko beams; Discontinuous Galerkin method
* Corresponding author. Tel.: +1 612 624 2329; Fax: +1 612 626 2017; E-mail: celiker@math.umn.edu