Design principles and error analysis for reduced-shear plate-bending finite elements

Summary. In this paper, we consider the problem of designing plate-bending elements which are free of shear locking. This phenomenon is known to afflict several elements for the Reissner-Mindlin plate model when the thickness of the plate is small, due to the inability of the approximating subspaces to satisfy the Kirchhoff constraint. To avoid locking, a “reduction operator” is often applied to the stress, to modify the variational formulation and reduce the effect of this constraint. We investigate the conditions required on such reduction operators to ensure that the approximability and consistency errors are of the right order. A set of sufficient conditions is presented, under which optimal errors can be obtained – these are derived directly, without transforming the problem via a Hemholtz decomposition, or considering it as a mixed method. Our analysis explicitly takes into account boundary layers and their resolution, and we prove, via an asymptotic analysis, that convergence of the finite element approximations will occur uniformly as , even on quasiuniform meshes. The analysis is carried out in the case of a free boundary, where the boundary layer is known to be strong. We also propose and analyze a simple post-processing scheme for the shear stress. Our general theory is used to analyze the well-known MITC elements for the Reissner-Mindlin plate. As we show, the theory makes it possible to analyze both straight and curved elements. We also analyze some other elements. Received June 19, 1995     

Diagnostic performance of low field MRI in acute knee injuries

The diagnostic performance of low field (0.1 T) magnetic resonance imaging (MRI) was studied prospectively and double-blindly among 33 patients with acute knee injuries. The subsequent arthroscopy was the golden standard. For lesions of the medial meniscus low field MR had a sensitivity of 88% and a specificity of 80%; for lesions of the lateral meniscus the sensitivity was 25% and the specificity 97%. For anterior cruciate ligament tears, low field MRI had a sensitivity of 83% and a specificity of 85%. The specificity for posterior cruciate ligament tears was 97%. The performance of low field MRI equalled that reported earlier for high field MRI, the only exception being the sensitivity for lateral meniscus lesions.     

Classes of Quasi-nearly Subharmonic Functions

It is well known and important that if u ≥ 0 is subharmonic on a domain Ω in ℝ ⁿ and p > 0, then there is a constant C(n,p) ≥ 1 such that for each open ball B(x,r) ⊂ Ω. The definition of a relatively new function class, quasi-nearly subharmonic functions, is based on such a generalized mean value inequality. It is pointed out that the obtained function class is natural. It has important and interesting properties and, at the same time, it is large: In addition to nonnegative subharmonic functions, it includes, among others, Hervé’s nearly subharmonic functions, functions satisfying certain natural growth conditions, especially certain eigenfunctions, polyharmonic functions and generalizations of convex functions. Further, some of the basic properties of quasi-nearly subharmonic functions are stated in a unified form. Moreover, a characterization of quasi-nearly subharmonic functions with the aid of the quasihyperbolic metric and two weighted boundary limit results are given.      

MR imaging of fatigue stress injuries to bones: intra- and interobserver agreement

The aim of this study was to determine the validity of MR imaging (MRI) in the assessment of stress-related injuries to bone.MR images of 50 military recruits (8 females and 42 males; 18-27 (mean 20) years of age) were retrospectively evaluated twice for stress injuries to bone by 4 radiologists (2 musculoskeletal radiologists, 2 radiology residents). Coronal T1-weighed (T1W) and STIR images, as well as axial and coronal T2-weighted (T2W) fat-suppressed images were taken using a 1.0T scanner. Rates for sensitivity, specificity, and accuracy of MRI of the stress-related injuries were calculated. Intraobserver and interobserver agreement was determined with kappa statistics.Rates for MRI sensitivity were 27-96%, for specificity 65-100%, and for diagnostic accuracy 58-97%. Lowest rates were seen when reading T1W images and highest when reading STIR images. Readers showed moderate to excellent intraobserver agreement (kappa 0.75-0.95). Interobserver agreement was fair to excellent (kappa 0.41-0.91), and the lowest values were seen in the interpretation of T1W images. Normal findings could be differentiated from various grades of stress injury to bone.MRI is a valid means of revealing the presence of stress injuries to bone and their staging. Observer agreement is good to excellent when using T2W images and STIR images, while T1W images are of lesser value.     

IR-induced processes for allyl alcohol dimers involving an intermolecular OH...π Bond in low-temperature matrices

Sharp peaks were observed in the IR spectra of allyl alcohol dimers in the νOH and τOH regions in low-temperature Ar and N₂ matrices. In Ar a peak at 3587 cm^?1 was found to increase in intensity upon annealing and decrease upon IR irradiation; it is concluded that this peak is due to an OH...π interaction (of a cyclic structure) present in part of the dimers. This is the first time such an interaction and photoprocess have been found for an alcohol in matrices. Also a faster photo-process was found. Confomer changes in the monomers accompany the photoprocess in allyl alcohol dimers.     

Advanced TMAH and TMAAc thermochemolysis–pyrolysis techniques for molecular characterization of size-separated fractions from aquatic dissolved organic matter

The structural similarities and differences between the original DOM and the eight size fractions separated were studied in detail with the pyrolysis technique in combination with gas chromatography and mass spectrometry (Py-GC-MS) using two alkylating reagents: TMAH (tetramethylammonium hydroxide), to find both esterified and free carboxylic acids; and TMAAc (tetramethylammonium acetate), to specify only free carboxylic acids. A statistical analysis of the original multidimensional TMAH and TMAAc pyrograms disclosed that the overall structural compositions of the five most important size fractions, accounting for 84% of the original DOM, greatly resembled each other. The remaining three minor size fractions were not classified as homogeneous associations, but they also contained the same total, covalently bound and free carboxylic acid species as the other size fractions and the original DOM mixture, thus representing some kind of intermediate forms. This fundamental outcome strongly supports the opinion that the native dissolved humic-like macromolecules resemble supramolecular associations of smaller molecular size moieties with similar structural functionalities. The concentrations of free aliphatic and aromatic dicarboxylic acids in the DOM solution were so low that their effects on the potential formation of multiply charged ions in electrospray ionization-MS (ESI-MS) studies are likely insignificant.     

Analysis of ALD-processed thin films by ion-beam techniques

This review introduces the possibilities of ion-beam techniques for the analysis of thin films and thin-film structures processed by atomic layer deposition (ALD). The characteristic features of ALD are also presented. The analytical techniques discussed include RBS, NRA and ERDA with its variants, viz. the TOF-ERDA and HI-ERDA. The thin film examples are taken from flat-panel display technology (TFEL structures) and the semiconductor industry (high-k insulators).Dedicated to the memory of Wilhelm Fresenius