A variational method to avoid locking—independent of the discretization scheme. (6th February 2018)

• Record Type: Journal Article
• Authors: Bieber, Simon; Oesterle, Bastian; Ramm, Ekkehard; Bischoff, Manfred
• Is Part Of: International journal for numerical methods in engineering. Volume 114:Number 8(2018)
• Page Start: 801
• Page End: 827
• Publication Date: 2018-02-06
• Subjects: finite elements -- isogeometric -- locking -- meshless -- mixed formulation; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5766
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: We present a variational method for problems in solid and structural mechanics that is designed to be intrinsically free from locking when using equal‐order interpolation for all involved fields. The specific feature of the formulation is that it avoids all geometrical locking effects (as opposed to material locking effects, for instance Poisson locking) for any type of structural or solid model, independent of the underlying discretization scheme. The possibility of employing equal‐order interpolation for all involved fields circumvents the task of finding particular function spaces to remove locking and avoid artificial stress oscillations. This is particularly attractive, for instance, for isogeometric analysis using unstructured meshes or T‐splines. Comprehensive numerical tests underline the promising behavior of the proposed method for geometrically linear and nonlinear problems in terms of displacements and stress resultants using standard finite elements, isogeometric finite elements, and a meshless method.