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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