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Research Papers

Composite Circular Plates With Residual Tensile Stress Undergoing Large Deflections

[+] Author and Article Information
Brian Homeijer

 Technology Development Organization, Image and Printing Group, HP, Corvallis, OR 97330brian.homeijer@hp.com

Benjamin A. Griffin, Matthew D. Williams, Bhavani V. Sankar

 Interdisciplinary Microsystems Group, Department of Mech. & Aero. Eng.,  Univ. of Florida, Gainesville, FL 32611-6250

Mark Sheplak1

 Interdisciplinary Microsystems Group, Department of Mech. & Aero. Eng.,  Univ. of Florida, Gainesville, FL 32611-6250sheplak@ufl.edu

1

Corresponding author.

J. Appl. Mech 79(2), 021007 (Feb 24, 2012) (8 pages) doi:10.1115/1.4005534 History: Received January 24, 2011; Received April 28, 2011; Posted January 25, 2012; Published February 13, 2012; Online February 24, 2012

Many micromachined electroacoustic devices use thin plates in conjunction with electrical components to measure acoustic signals. Composite layers are needed for electrical passivation, moisture barriers, etc. The layers often contain residual stresses introduced during the fabrication process. Accurate models of the composite plate mechanics are crucial for predicting and optimizing device performance. In this paper, the von Kármán plate theory is implemented for a transversely isotropic, axisymmetric plate with in-plane tensile stress and uniform transverse pressure loading. A numerical solution of the coupled force-displacement nonlinear differential equations is found using an iterative technique. The results are verified using finite element analysis. This paper contains a study of the effects of tensile residual stresses on the displacement field and examines the transition between linear and nonlinear behavior. The results demonstrate that stress stiffening in the composite plate delays the onset of nonlinear deflections and decreases the mechanical sensitivity. In addition, under high stress the plate behavior transitions to that of a membrane and becomes insensitive to the composite nature of the plate. The results suggest a tradeoff between mechanical sensitivity and linearity.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Cross section of an axisymmetric, composite plate with in-plane stress in the second layer

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Figure 2

Linear nondimensional solution for various k *

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Figure 3

Linear nondimensional stresses for various k * when the plate is loaded with P * = 1

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Figure 4

Nonlinear nondimensional solution for various pressure loadings (k* = 0). Finite element results are marked by a circle.

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Figure 5

Nonlinear nondimensional stresses for various k* when the plate is loaded with P* = 1

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Figure 6

Mechanical sensitivity versus uniform transverse load for various values of in-plane tension. Finite element results are marked by a circle.

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Figure 7

Maximum transverse loading for linear deflections versus in-plane tension

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