A Reissner’s Mixed Variational Theorem Applied to Vibration Analysis of Multilayered Shell

[+] Author and Article Information
E. Carrera

Department of Aeronautics and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy

J. Appl. Mech 66(1), 69-78 (Mar 01, 1999) (10 pages) doi:10.1115/1.2789171 History: Received April 01, 1998; Revised June 17, 1998; Online October 25, 2007


A comprehensive model of anisotropic multilayered double curved shells fulfilling a priori the interlaminar continuity requirements for the transverse shear and transverse normal stress as well as the static conditions on the bounding surfaces of the shell is developed in this paper. To this end, Reissner’s mixed variational theorem is employed to derive the equations governing the dynamic equilibrium and compatibility of each layer, while the interlaminar continuity conditions are used to drive the equations at the multilayered level. No assumptions have been made concerning the terms of type thickness to radii shell ratio h/R . Classical displacement formulations and related equivalent single layer equations have been derived for comparison purposes. Comparison of frequency predictions based upon the presented structural model with a number of results spread throughout the specialized literature and obtained via other models reveals that this advanced model provides results in excellent agreement with the ones based on three-dimensional elasticity theory, and better as compared to the ones violating the interlaminar stress continuity requirements and/or transverse normal stress and related effects.

Copyright © 1999 by The American Society of Mechanical Engineers
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