Abstract
In this paper, mixed formulations are presented in the framework of isogeometric Reissner–Mindlin plates and shells with the aim of alleviating membrane and shear locking. The formulations are based on the Hellinger-Reissner functional and use the stress resultants as additional unknowns, which have to be interpolated in appropriate approximation spaces. The additional unknowns can be eliminated by static condensation. In the framework of isogeometric analysis static condensation is performed globally on the patch level, which leads to a high computational cost. Thus, two additional local approaches to the existing continuous method are presented, an approach with discontinuous stress resultant fields at the element boundaries and a reconstructed approach which is blending the local control variables by using weights in order to compute the global ones. Both approaches allow for a static condensation on the element level instead of the patch level. Various numerical examples are investigated in order to verify the accuracy and effectiveness of the different approaches and a comparison to existing elements that include mechanisms against locking is carried out.
Highlights
Isogeometric Analysis (IGA) was introduced by Hughes et al [1] with the aim of unifying the design and analysis process
A displacement-stress mixed method is presented in the framework of an isogeometric Reissner– Mindlin shell formulation in order to alleviate membrane and shear locking
Several numerical examples were investigated in order to test the accuracy and efficiency of the different approaches
Summary
Isogeometric Analysis (IGA) was introduced by Hughes et al [1] with the aim of unifying the design and analysis process. As it was often stated in these works, the Bmethod within the framework of isogeometric analysis leads to a linear system where a matrix defined on the patch level has to be inverted and the resulting stiffness matrix is fully populated, which increases the computational cost This led to the introduction of local Bformulations, where the B -projection is applied locally and the global variables are obtained from the local ones using reconstruction algorithms. The second approach is based on the reconstruction algorithm used by Greco et al [35,39] in the framework of a Bmethod It is reformulated for the mixed method with the stress resultants as additional unknowns and is extended to the case of Reissner–Mindlin plates and shells where membrane and transverse shear locking occur.
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