Explicit solutions for the coupled stretching–bending problems of holes in composite laminates

Abstract

Although the classical lamination theory was developed long time ago, it is still not easy to apply this theory to find the analytical solutions for the curvilinear boundary value problems especially when the stretching and bending are coupled each other. To overcome the difficulties, recently we developed a Stroh-like formalism for the general composite laminates. By using this formalism, most of the relations for the coupled stretching–bending problems can be organized into the forms of Stroh formalism for two-dimensional anisotropic elasticity problems. With this newly developed Stroh-like formalism, it becomes easier to obtain an analytical solution for the coupled stretching–bending problems of holes in composite laminates. Because the Stroh-like formalism is a complex variable formalism, the analytical solutions for the whole field are expressed in complex form. Through the use of some identities derived in this paper, the resultant forces and moments around the hole boundary are obtained explicitly in real form. Due to the lack of analytical solutions for the general cases, the comparison is made with the existing analytical solutions for some special cases. In addition, to show the generality of our analytical solutions, several numerical examples are presented to discuss the coupling effect of the laminates and the shape effect of the holes.