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Intrinsically locking‐free formulations for isogeometric beam, plate and shell analysis
Author(s) -
Oesterle Bastian,
Bieber Simon,
Sachse Renate,
Ramm Ekkehard,
Bischoff Manfred
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800399
Subject(s) - discretization , timoshenko beam theory , mathematics , galerkin method , isogeometric analysis , beam (structure) , boundary value problem , interpolation (computer graphics) , kinematics , mathematical analysis , finite element method , classical mechanics , physics , motion (physics) , optics , thermodynamics
In this contribution a class of formulations for beams, plates and shells is presented, which intrinsically avoids locking, independent of the utilized discretization scheme. The key idea is the reparametrization of the kinematic equations to avoid locking on theory level – prior to discretization. Thus, the resulting formulations are locking‐free for any equal‐order interpolation. As demonstrator, we present both mixed and primal concepts for Timoshenko beams in both weak and strong form, as well as their theoretical relationships. Besides a weak form Galerkin‐type solution using B‐Splines, we show the generality of the presented concepts by employing isogeometric collocation based on the corresponding Euler‐Lagrange equations of the boundary value problem. The quality of both stress resultants and displacements is investigated. Although the underlying concept addresses beams, plates and shells, the present contribution illustrates the methodology for the Timoshenko beam.