Variational eigenvalue approximation of non-coercive operators with application to mixed formulations in elasticity

We present an abstract framework for the eigenvalue approximation of a class of non-coercive operators. We provide sufficient conditions to guarantee the spectral correctness of the Galerkin scheme and to obtain optimal rates of convergence. The theory is applied to the convergence analysis of mixed finite element approximations of the elasticity and Stokes eigensystems.

A Case of Brainstem Anesthesia after Retrobulbar Block for Globe Rupture Repair

Purpose. To present a rare case of brainstem anesthesia from retrobulbar block and discuss evidence-based methods for reducing the incidence of this complication. Case. A 72-year-old female, was given a retrobulbar block of 5 mL of bupivacaine 0.5% for postoperative pain management, after a globe rupture repair under general anesthesia. Prior to injection, the patient was breathing spontaneously via the anesthesia machine circuit and had not received any additional narcotics/muscle relaxants for 2.5 hr (with full recovery of neuromuscular blocking agent after anesthetic reversal). Over 7 min, however, there was a steady increase in ETCO2 and the patient became apneic, consistent with brainstem anesthesia. She remained intubated and was transported to the postanesthesia care unit for prolonged monitoring, with eventual extubation. Discussion. Brainstem anesthesia is an important complication to recognize as it can lead to apnea and death. The judicious use of anesthetic volume, shorter needle tips, and mixed formulations can help reduce the chance of brainstem anesthesia. Observation of the contralateral eye 5–10 minutes after injection for pupillary dilation, and prior to surgical draping, can help identify early CNS involvement.

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

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.

Deformation and Stress Analysis of Catenary Shell of Revolution

The catenary shells of revolution are widely used in constructions due to their unique mechanics' feature. However, no publications on this type of shells can be found in the literature. To have a better understanding of the deformation and stress of the catenary shells of revolution, we formulate the principal radii for two kinds of catenary shells of revolution and their displacement type governing equations. Numerical simulations are carried out based on both Reissner-Meissner mixed formulations and displacement formulations. Our investigations show that both deformation and stress response of elastic catenary shells of revolution are sensitive to its geometric parameter $c$, and reveal that the mechanics of the catenary shells of revolution does much better than the spherical shells. Two complete codes in Maple are provided.