Histological structure of the cancellous bone layer in Bothriolepis canadensis (Antiarchi, Placodermi)

The Placodermi are extinct basal gnathostomes which had extensive dermal and perichondral bone, but which lacked the endochondral bone which characterizes the more derived bony fishes. Thin sections of bone from a specimen of the antiarch placoderm Bothriolepis canadensis, from the Escuminac Formation ( Frasnian, Upper Devonian), Quebec, Canada, reveal that part of the cancellous layer in its dermal and endoskeletal bone formed from perichondral bone trabeculae growing around cartilage spheres. The resultant structure mimics that of osteichthyan endochondral bone. The layout and dimensions of this polygonal mosaic patterning of the bone trabeculae and flattened cartilage spheres resemble those of the prismatic layers of calcified cartilage in chondrichthyans. If the lack of endoskeletal bone in chondrichthyans is a derived character, then the structure identified in B. canadensis could represent a 'template' for the formation of prismatic calcified cartilage in the absence of bone.

Exact eigenvalue correspondences between laminated plate theories via membrane vibration

Based on Reddy's third-order theory, the first-order theory and the classical theory, exact explicit eigenvalues are found for compression buckling, thermal buckling and vibration of laminated plates via analogy with membrane vibration, These results apply to symmetrically laminated composite plates with transversely isotropic laminae and simply supported polygonal edges, Comprehensive consideration of a Winkler-Pasternak elastic foundation, a hydrostatic inplane force, an initial temperature increment and rotary inertias is incorporated. Bridged by the vibrating membrane, exact correspondences are readily established between any pairs of buckling and vibration eigenvalues associated with different theories. Positive definiteness of the critical hydrostatic pressure at buckling, the thermobukling temperature increment and, in the range of either tension loading or compression loading prior to occurrence of buckling, the natural vibration frequency is proved. (C) 2000 Elsevier Science Ltd. All rights reserved.