Energy inequalities and error estimates for axisymmetric torsion of thin elastic shells of revolution

The problem motivating this investigation is that of pure axisymmetric torsion of an elastic shell of revolution. The analysis is carried out within the framework of the three-dimensional linear theory of elastic equilibrium for homogeneous, isotropic solids. The objective is the rigorous estimation of errors involved in the use of approximations based on thin shell theory.

The underlying boundary value problem is one of Neumann type for a second order elliptic operator. A systematic procedure for constructing pointwise estimates for the solution and its first derivatives is given for a general class of second-order elliptic boundary-value problems which includes the torsion problem as a special case.

The method used here rests on the construction of “energy inequalities” and on the subsequent deduction of pointwise estimates from the energy inequalities. This method removes certain drawbacks characteristic of pointwise estimates derived in some investigations of related areas.

Special interest is directed towards thin shells of constant thickness. The method enables us to estimate the error involved in a stress analysis in which the exact solution is replaced by an approximate one, and thus provides us with a means of assessing the quality of approximate solutions for axisymmetric torsion of thin shells.

Finally, the results of the present study are applied to the stress analysis of a circular cylindrical shell, and the quality of stress estimates derived here and those from a previous related publication are discussed.

Length-weight relationships of Cuban marine fishes

A total of 140 sets of parameters (a and b) of the length-weight relationships (LWR) of the form W=aL super(b) are presented for fishes caught in Cuban waters. These parameters cover 94 species of fish belonging to 43 families. Most of the parameters were compiled from 107 sets of published and unpublished studies. Twenty-five sets of parameters were from personal communications through colleagues in Cuba, while the remaining eight sets were estimated by the authors from unpublished data.

Selection properties of the baited hooks used in the Cuban longline fishery of Campeche Bank, Gulf of Mexico

A description of the Cuban set longline fishery on Campeche Bank, Gulf of Mexico is given, with emphasis on the effects of different species of pelagic fishes used as bait. The target species is the red grouper Epinephelus morio, with incidental species consisting of other epinephelids (13%), lutjanids (5.4%) and sparids (1.6%).

Growth parameters of marine fishes in Cuban waters

A total of 73 sets of growth parameters for 34 species belonging to 12 families of marine fish caught in Cuban waters are presented. These parameters are compiled from existing studies (58 sets) or derived from data obtained in the original literature (15 sets).

Reconstruction of surfaces of revolution from single uncalibrated views

This paper addresses the problem of recovering the 3D shape of a surface of revolution from a single uncalibrated perspective view. The algorithm introduced here makes use of the invariant properties of a surface of revolution and its silhouette to locate the image of the revolution axis, and to calibrate the focal length of the camera. The image is then normalized and rectified such that the resulting silhouette exhibits bilateral symmetry. Such a rectification leads to a simpler differential analysis of the silhouette, and yields a simple equation for depth recovery. It is shown that under a general camera configuration, there will be a 2-parameter family of solutions for the reconstruction. The first parameter corresponds to an unknown scale, whereas the second one corresponds to an unknown attitude of the object. By identifying the image of a latitude circle, the ambiguity due to the unknown attitude can be resolved. Experimental results on real images are presented, which demonstrate the quality of the reconstruction. © 2004 Elsevier B.V. All rights reserved.