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Research Papers

# The Analytical Solutions of Incompressible Saturated Poroelastic Circular Mindlin’s Plate

[+] Author and Article Information
P. H. Wen

School of Engineering and Materials Science, Queen Mary,  University of London, London E1 4NS, UKp.h.wen@qmul.ac.uk

J. Appl. Mech 79(5), 051009 (Jun 29, 2012) (7 pages) doi:10.1115/1.4006254 History: Received February 25, 2009; Revised January 10, 2012; Posted March 03, 2012; Published June 28, 2012; Online June 29, 2012

## Abstract

In this paper the fundamental solutions for an infinite poroelastic moderately thick plate and analytical solutions for a circular plate saturated by a incompressible fluid are derived in the Laplace transform domain. In order to obtain the solutions in the time domain, the Durbin’s Laplace transform inverse method has been used with high accuracy. The formulations using the boundary integral equation method can be derived directly with these fundamental solutions. In addition, the analytical solutions for a circular plate can be used to validate the accuracy of numerical algorithms such as the boundary element method and the method of fundamental solution. The deflection, moment, and equivalent moment in the time domain for a circular plate, subjected to uniform load and a concentrated force are presented, respectively. The analytical solutions demonstrate that interaction between the solid and flow is significant.

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## Figures

Figure 5

Variation of the normalized moments M11 and M22 with time for a built-in circular plate saturated by a fluid subjected to concentrated force P0H(t) at the center of plate when r/a=1 for different values of K¯

Figure 4

Built-in circular plate saturated by a fluid subjected to concentrated force P0H(t) at the center of plate when r/a=0.5 and h/a=0.1; dashed line: K¯=0; solid line: K¯=10; thick solid line: K¯=30. (a) Normalized deflection w3; (b) normalized moment M11; and (c) normalized equivalent moment M22.

Figure 3

Built-in circular plate saturated by a fluid subjected to uniform load q0H(t): (a) normalized deflection at the center of plate w3; (b) normalized moment at the center of plate M11; and (c) normalized equivalent moment at the center of plate Mp

Figure 2

Simply supported circular plate saturated by a fluid subjected to uniform load q0H(t): (a) normalized deflection at the center of plate w3; (b) normalized moment at the center of plate M11; and (c) normalized equivalent moment at the center of plate Mp. The dashed line is the result given by the method of fundamental solution when h/a=0.1.

Figure 1

Sign convention for the displacement and internal forces

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