Improved numerical integration for locking treatment in isogeometric structural elements, Part I: Beams

A NURBS based hybrid collocation–Galerkin method for the analysis of boundary represented solids

“…However, from Fig. 6(a)-(d), it demonstrates that poor convergence is obtained for lower polynomial degrees p C , a behavior which clearly indicates the presence of locking, see e.g., [19][20][21].…”

Developments of the mixed grid isogeometric Reissner–Mindlin shell: Serendipity basis and modified reduced quadrature

“…In the higher dimensional case, the quadrature number in an element is the largest one of those determined by each direction. For p ¼ 2 and 3, it will be similar but more conservative than those proposed in paper Adam et al (2015Adam et al ( , 2014, our boundary elements have more quadrature points. We use a ScordeliseLo roof problem with KirchhoffeLove shell to test it.…”

“…When C 0 continuous elements are used, it will be the same as the C 0 FEM. Some relevant phenomena already appeared in literatures, such as the using of reduced quadrature in IGA brought "hourglass" mode (Adam et al, 2015), there are more quadrature points in the patch border elements than in the inner region in optimal quadrature (Adam et al, 2015(Adam et al, , 2014Auricchio et al, 2012), and there exist more quadrature points in the boundary elements in the reduced quadrature scheme proposed in paper Adam et al (2015Adam et al ( , 2014, Schillinger et al (2014).…”

“…Various locking alleviation methods in FEM exist, see Zienkiewicz et al (1971), Pian and Sumihara (1984), Bletzinger et al (2000). Their essential ideas can also be used in the IGA method with some modifications or even intact (Adam et al, 2015(Adam et al, , 2014Bouclier et al, 2012;Elguedj et al, 2008;Cardoso and Cesar de Sa, 2012;Bouclier et al, 2013b;Echter and Bischoff, 2010). Another interesting locking free element technique is strain smoothing, which originated from the mesh-free method, one could read papers .…”

Isogeometric configuration design sensitivity analysis of finite deformation curved beam structures using Jaumann strain formulation

“…In order to alleviate the shear and membrane locking troubles, Bouclier et al [22] extended the selective reduced integration (SRI) andB projection methods to the IGA context. This is further developed in terms of SRI by Adam et al [23], to higher order basis function. Also, Beirão da Veiga et al [24] and Auricchio et al [25] developed locking-free mixed formulations respectively for straight planar and spatial curved Timoshenko beams in the context of isogeometric collocation method.…”