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Studies Relating to the Structural Dynamic Behavior of Laminated Plates and Shells

Author: Dong, Stanley B.
Corporate Author: School of Engineering and Applied Science, University of California Los Angeles
Corporate Report Number: UCLA-ENG-7236
Laboratory: Office of Naval Research
Date of Publication: 1972-05
Pages: 200
Contract: N00014-71-C-0056
AD Number: AD0745336
Original AD Number: AD0745336

In this paper, a number of studies related to structural dynamic behavior of laminated orthotropic plates and shells is reported. The plate or shell structure is composed of an arbitrary number of bonded elastic orthotropic layers, whose principal elastic axes coincide with the coordinate axes. These studies are based on two main approaches to the problem, viz., formulations by shell theory and by linear elastic theory. Generally, shell theory formulations are approximate by virtue that they take special note of the structural geometry and the anticipated deformation characteristics into account in order to arrive at simplified governing equations appropriate for a large class of shell configurations. The role of an elasticity formulation, aside from its inherent capacity to predict frequencies, stresses and deformations over a wide range of wave lengths, is then to delineate the limits of applicability of shell theory formulations. First, attention is directed toward a shell theory formulation, where a constitutive relation including transverse shear deformation is given. This relation involves composite correction factors k211, k222 which are determined by consideration of plane waves in a plate with the same layered construction.  A method is then presented for the setermination of frequencies and modal patterns of plane wave motions in laminated orthotropic plates within the framework of linear elasticity so as to permit evaluation of these composite correction factors.  this elasticity solution can also be used to assess the accuracy of the shell theory when applied to plates.  Next, a method is given for the study of vibrations and waves in laminated orthotropic plates and cylinders using elasticity equations.  Lastly, a finite element formulation for shells of revolution based on the current shell theory is presented.  Conical frustra are employed for the modeling of the shell of revolution.  The displacement field adopted requires, in addition to nodes at the ends, a mid-node in the element.  Along with the determination of frequencies and mode shapes is a calculation of the percentage distribution of strain energies due to extensional, flexural and transverse shear deformations and this information serves to identify the nature of a given vibratory motion.  Comparisons of the present results with known solutions indicate the veracity of the current model.

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