Locking-free variational formulations and isogeometric analysis for the Timoshenko beam models of strain gradient and classical elasticity

The Timoshenko beam bending problem is formulated in the context of strain gradient elasticity for both static and dynamic analysis. Two non-standard variational formulations in the Sobolev space framework are presented in order to avoid the numerical shear locking effect pronounced in the strain gradient context. Both formulations are shown to be reducible to their locking-free counterparts of classical elasticity. Conforming Galerkin...