Div. of Appl. Mech., Dept. of Mech. Eng., Stanford Univ., Stanford, CA 94305-4040
Peter M. Pinsky
Stanford Univ., Stanford, CA 94305-4020
The design and analysis of new finite element methods for the steady-state response of fluid-loaded Reissner--Mindlin plates is presented. In this study, new methods are developed that are more accurate than standard finite element methods in their ability to represent wave propagation for coupled problems in structural acoustics. Generalized Galerkin least-squares (GGLS) finite element methods have been employed previously to enhance the accuracy of the finite element approximation for the uncoupled structural problem [K. Grosh and P. M. Pinsky, in Proc. Second Int. Conf. Math. and Numer. Aspects of Wave Propagation, edited by R. Kleinman et al. (June 1993)] and the uncoupled acoustic problem [I. Harari and T. J. R. Hughes, Comput. Methods Appl. Mech. Eng. 87 (1991)]. Complex wave-number dispersion analysis is used both to design the new methods and characterize their accuracy. Results comparing the finite element dispersion relations to the analytic dispersion relations for the fluid-loaded Reissner--Mindlin plate demonstrate the enhanced accuracy of these new GGLS methods over the standard Galerkin finite element implementation.