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TECHNICAL PAPERS

# Hygrothermal Stresses in Unsymmetric Laminates Disturbed by Elliptical Holes

[+] Author and Article Information
M. C. Hsieh

Institute of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan, R.O.C

Chyanbin Hwu

Institute of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan, R.O.Cchwu@mail.ncku.edu.tw

J. Appl. Mech 73(2), 228-239 (Jun 28, 2005) (12 pages) doi:10.1115/1.2074708 History: Received March 23, 2005; Revised June 28, 2005

## Abstract

Since the composite laminates are now in widespread use, many coupling phenomena within the composite laminates are widely focused in the world. One of those is the problem of stretching-bending coupling under hygrothermal environment. Because of the hygrothermal stress concentration, the understanding of hygrothermal effects on holes in laminates becomes important for the practical engineering design. However, due to mathematical infeasibility, most of the analytical solutions presented in literature are for two-dimensional problems or just for mechanical loading conditions, not for general composite laminates under hygrothermal environment. In order to establish a systematic analytical approach, in this study by extending the Stroh formalism for two-dimensional linear anisotropic elasticity and the Stroh-like formalism for coupled stretching-bending analysis of composite laminates, we develop an extended Stroh-like formalism for the coupled stretching-bending analysis under hygrothermal environment. By using the extended Stroh-like formalism developed in this paper, the explicit solutions for an unbounded laminate, symmetric or unsymmetric, disturbed by an elliptical hole subjected to uniform heat flow and moisture transfer in the $x1-x2$ plane or $x3$ direction are now obtained. With these solutions three typical numerical examples are illustrated and compared by ANSYS finite element software package.

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## Figures

Figure 1

Unsymmetric laminate weakened by an elliptical hole subjected to uniform heat flow and moisture transfer in x1-x2 plane

Figure 2

Resultant hoop stress Ns around the circular hole boundary when the laminate is subjected to uniform temperature change

Figure 3

Resultant tractions around the hole boundary when the laminate is subjected to uniform temperature changes (a) Nn∕Ns (b) Nns∕Ns

Figure 4

Resultant hoop stress Ns around the circular hole boundary when the laminate is subjected to uniform heat flow q̂2=q̂ in the positive x2 direction

Figure 5

Resultant tractions around the hole boundary in ANSYS simulation when the laminate is subjected to uniform heat flow q̂2=q̂ in the positive x2 direction

Figure 6

Forces and moments around the elliptical hole in an unsymmetric laminate when the laminate is subjected to uniform heat flow q̂1=q̂ in x1-x2 plane

Figure 7

Temperature distribution around the hole when the laminate is subjected to uniform heat flow q̂1=q̂ in x1-x2 plane

Figure 8

Resultant hoop stress Ns around the circular hole boundary when the laminate is subjected to heat flow in x3 direction

Figure 9

Resultant tractions around the hole boundary in ANSYS simulation when the laminate is subjected to uniform heat flow in x3 direction

Figure 10

Forces and moments around the elliptical hole in an unsymmetric laminate when the laminate is subjected to uniform heat flow in x3 direction (Tu=100°C on the upper surface and Tl=0°C on the lower surface)

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