Bochumer Institut für Technologie (Germany)

An explicit formula for the polyharmonic Green function of any order for the unit disc of the complex plane based on the work of E. Almansi is widely known through I.N. Vekua’s 1967 book. A simple, however, not easy way to prove the formula is by verification of the defining properties. P.R. Garabedian has suggested a constructive way for this function in his 1964 pde book but only has applied it for the biharmonic case. His construction is not smoothly working for higher order as is explained here in the triharmonic case. The general case will demand very concentrated calculations. The procedure should similarly work also for the half plane.

Abstract In order to raise the hardness and strength of the surface layer of mechanical components and induce favorable residual compressive stresses, case‐hardening procedures have become established in the heat treatment of steel. In this work, a calculation concept for the fatigue strength of components that have been case‐hardened through carburizing heat treatment is being developed. The residual stress and the load stresses in complex‐shaped, carburized materials are determined using a finite element (FE) model. The fatigue limit of the components is derived using probabilistic methods and taking into account hardness gradients, residual stresses, and non‐metallic inclusions. The model is validated with available axial bending fatigue test data and then used to predict the rotating bending fatigue limit of samples with various geometries and heat‐treatment conditions. This work demonstrates the capability of combining probabilistic and FE‐based modeling to represent complex interactions between variables that affect the fatigue of heat‐treated components, such as steel cleanliness, notch shape, case‐hardening depth, or loading conditions.

Video capsule endoscopy (VCE) has been applied in the last 15 years in an increasing field of applications. Although many contraindications have been put into perspective, some precautions still have to be considered. Known stenosis of the gastrointestinal tract is a clear contraindication for VCE unless surgery is already scheduled or at least has been considered as an optional treatment modality. In patients with a higher incidence of stenosis, as in an established diagnosis of Crohn’s disease, clinical signs of obstruction, prior radiation or surgical small bowel resection, a preceding test with the self-dissolving patency capsule can override this contraindication. Endoscopic placement of the capsule should be considered in patients with swallowing disorders to avoid aspiration. Esophageal or gastric motility disorders may require endoscopic capsule transport or application of prokinetics if the real-time viewer proofs delayed transit. In pregnant women, VCE should be restricted to urgent cases where diagnosis cannot be postponed after delivery, as data on safety are missing. There is theoretical and clinical evidence that patients with implanted cardiac devices such as a pacemaker, cardioverters or left heart assist devices, can safely undergo VCE in spite of still existing contraindication by manufacturers. Children from the age of 2 years have safely undergone VCE. Although video capsules are not proven safe with magnetic resonance imaging (MRI), first single cases of patients incidentally undergoing MRI with an incorporated capsule have been reported, showing susceptibility artifacts but no signs of clinical harm.

Abstract In case of contact between two colliding bodies various force interactions in the contact area occur. Therefore, the virtual power for contact zones has to comprise impulse or contact in normal direction and friction in tangential direction of the common plane depending on the way of relative movement. Within this paper a sophisticated algorithm for the description of the virtual power in contact zones is presented. Hence, the implementation of this algorithm to the MEPHISTO (Multibody systems with ElasticPlastic HInges and changeable STructure Organization) multibody program code is successfully proved in the particular case of vehicle impact on a safety barrier system.

Measurements were made of parent and branch vessel diameters and of the included angles of branch-points from postmortem human coronary arteriograms to determine the usefulness of theoretical equations predicting the relationships between parent and branch vessel caliber and between arterial caliber and branch-angle. The formulas were based on the concept that blood vessel size and arrangement provided for blood flow with minimum energy loss. Size relationships between parent vessel and its branches were determined for 42 left main and 53 other epicardial coronary artery branch-points in hearts with angiographically normal arteries. Left main coronary artery branch-points were studied in 68 hearts with various degrees of angiographically defined coronary artery disease. Measured diameters (D) of parent and branch vessels corresponded well to the theoretical formula: (DParent)3 = (DBranch1)3 + (DBranch2)3....,in angiographically normal coronary arteries. The exponent, on the average, is less with increasing grades of vascular disease for left main coronary artery branch-points. Mean area ratio, the sum of the cross-sectional area of the branches divided by the area of parent vessel, decreased with greater arteriographic disease. Area ratio varies with changes in the relative calibers of branch vessels. Fifty-seven branch-angles were determined by graphic analysis of postmortem biplane coronary arteriograms. No relationship could be found between branch-angle and vessel caliber. The included angle between branches varied from 32 degrees to 124 degrees without respect to relative or absolute vessel calibers. The results of these postmortem measurements on human coronary arteriogram suggest that coronary artery caliber may adjust to minimize energy loss at the branch-point but that branch-angle is determined by other factors. Restudy of arteriograms suggests that branch-angle may be determined by branch vessel destination.