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R. Heuer:
"Dynamic BEM Analysis of Moderately Thick Plates";
in: "Proceedings of WCCM V - Fifth World Congress on Computational Mechanics", H.A. Mang, F. G. Rammerstorfer, J. Eberhardsteiner (ed.); issued by: 5th World Congress on Computational Mechanics; Vienna University of Technology, Vienna, Austria, 2002, ISBN: 3-9501554-0-6.

A numerical routine based on the best suitable direct BEM of frequency domain analysis of moderately thick, transversely isotropic plates under rather general boundary conditions is developed. First-order shear-deformation theory of the Reissner-Mindlin-type is considered. A step forward in efficiency is obtained if the Green's function of the rectangular, simply supported base plate of same stiffness is applied. The time reduced equations of hard hinged polygonal plates reduce to those of a background Kirchhoff plate, which has effective (frequency dependent) mass, and is loaded by effective lateral and in-plane forces and by imposed fictitious "thermal-type" curvatures. This analogy holds even for the shear forces and bending moments if inertia is negligible. Furthermore, it can be shown that in the static case these stress resultants for certain groups of Reissner-type shear-deformable plates are identical with those resulting from the Kirchhoff theory of the background. Since the above mentioned analogy is restricted to hard hinged supports of straight edges, it becomes necessary to apply, e.g., the direct boundary element method of analysis to the plate of general planform and boundary conditions. Efficiently, the Green's function of the hard-hinged rectangular shear deformable plate, with rotatory inertia neglected and no in-plane forces considered for simplicity sake, enters the general formulation. The main effort is thus to study the properties and effective representations of these Green's functions and, quite important, the singularities, which must be subjected to proper integration. Likewise to results for the Kirchhoff plates, the strong singularity of the infinite domain is identified for the rectangular plate and subjected to indirect integration. The resulting direct BEM proves to be efficient, robust and in connection with proper pre- and post processors becomes an effective tool of engineering analyses just within the limits given by the first two of the three spectral branches.

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