Isogeometric analysis of thin Reissner–Mindlin shells: locking phenomena and B-bar method

Abstract

We propose a local type of B-bar formulation, addressing locking in degenerated Reissner-Mindlin plate and shell formulations in the context of isogeometric analysis. Parasitic strain components are projected onto the physical space locally, i.e. at the element level, using a least-squares approach.The formulation allows the flexible utilization of basis functions of different order as the projection bases. The present formulation is much cheaper computationally than the classicalB method. We show the numerical consistency of the scheme through numerical examples, moreover they show that the proposed formulation alleviates locking and yields good accuracy even for slenderness ratios of 1 × 10 5 , and has the ability to capture deformations of thin shells using relatively coarse meshes. In addition it can be opined that the proposed method is less sensitive to locking and mesh distortion.

High‐fidelity tensor‐decomposition based matrix formation for isogeometric buckling analysis of laminated shells with solid‐shell formulation

“…The researchers have shown that the problem can be solved or alleviated by using higher-order finite-element methods or adding special locking treatments to lower-order methods. The typical locking treatment approaches, which may not be restricted to solid-shell elements, include assumed natural strains (ANS), 18,19 enhanced assumed strain (EAS), 20 discrete strain gap (DSG), 21 B-method, [22][23][24][25] mixed formulations, 22,[26][27][28] selective/reduced integration, 26,[29][30][31] and projection techniques based on the moving least square (MLS). 32 Extensive literatures have reported that shells are studied by kinds of numerical methods: the finite element method (FEM), [33][34][35] the meshfree method, [36][37][38][39] and analytical 40,41 or semianalytical 42,43 methods and so forth.…”

“…The researchers have shown that the problem can be solved or alleviated by using higher‐order finite‐element methods or adding special locking treatments to lower‐order methods. The typical locking treatment approaches, which may not be restricted to solid‐shell elements, include assumed natural strains (ANS), 18,19 enhanced assumed strain (EAS), 20 discrete strain gap (DSG), 21 ‐method, 22–25 mixed formulations, 22,26–28 selective/reduced integration, 26,29–31 and projection techniques based on the moving least square (MLS) 32 …”

Two-field formulations for isogeometric Reissner–Mindlin plates and shells with global and local condensation

“…There the local variables are directly interpolated with local B-spline functions without a Bézier projection and transformation to the Bernstein basis. Local B formulations where the locking strains or stresses are projected onto interpolation spaces with the lowest possible order for each element leading to different projection spaces for the inner, corner and boundary elements are presented in Hu et al [40,41]. Antolin et al [42,43] used discontinuous polynomial spaces for the projection of the strains.…”

Skew-symmetric Nitsche’s formulation in isogeometric analysis: Dirichlet and symmetry conditions, patch coupling and frictionless contact

“…In boundary element method (BEM), this translates into the ability to solve directly from the field variables at the control points defining the geometry [78,77,74,59,10,60,58,68]. In FEM, a 3D parameterization of the volume is still necessary [87,88], except when solving shell-like problems [53,13,14,38,49]. The present paper focuses on two following issues.…”