On Locking-free Methods for Isogeometric Large Deformation Analysis of Geometrically Exact 3D Timoshenko Beams

Abstract

In this thesis the geometrically exact 3D shear-flexible beam model is discretized with the Lagrangian and the NURBS basis functions, and has been used as a basis to develop a family of locking-free NURBS-based elements. This beam model has no restrictions with respect to the size of displacements, rotations and deformations, and is thus well accommodated for large deformation analyses.

In the C0-continuous Lagrange element, numerical locking is overcome by reduced integration. However, for the higher continuous NURBS elements, there exists at the present time no element-by-element Gaussian quadrature rule which effectively alleviates locking. Instead, by a patch-wise approach a selective reduced integration rule has been proposed, and the resulting elements are free for transverse shear and membrane locking.

The performance is evaluated on a range of numerical tests and compared to the conventional reduced integration rule. For comparison, also the standard Lagrange interpolated elements have been tested in parallel.