Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 62157, 17 pages
Dynamic Stationary Response of Reinforced Plates by the Boundary Element Method
1Department of Mathematics, Paulista State University, Al. Rio de Janeiro s/n, Ilha Solteira 15385-000, SP, Brazil
2Department of Computational Mechanics, State University of Campinas, Rua Mendeleiev s/n, Campinas 13083-970, SP, Brazil
3Department of Structures, State University of Campinas, Avenida Albert Einstein 951, Campinas 13083-970, SP, Brazil
Received 1 October 2006; Revised 7 February 2007; Accepted 26 February 2007
Academic Editor: José Manoel Balthazar
Copyright © 2007 Luiz Carlos Facundo Sanches et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A direct version of the boundary element method (BEM) is developed to
model the stationary dynamic response of reinforced plate structures, such as
reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary
fundamental solutions of thin plates and plane stress state are used to transform
the governing partial differential equations into boundary integral equations (BIEs).
Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state
(membrane) and for the out-of-plane state (bending). These uncoupled systems
are joined to form a macro-element, in which membrane and bending effects are
present. The association of these macro-elements is able to simulate thin-walled
structures, including reinforced plate structures. In the present formulation, the BIE
is discretized by continuous and/or discontinuous linear elements. Four
displacement integral equations are written for every boundary node. Modal data,
that is, natural frequencies and the corresponding mode shapes of reinforced plates,
are obtained from information contained in the frequency response functions (FRFs).
A specific example is presented to illustrate the versatility of the proposed
methodology. Different configurations of the reinforcements are used to simulate
simply supported and clamped boundary conditions for the plate structures.
The procedure is validated by comparison with results determined by the finite
element method (FEM).