An exact solution of angle-ply laminated cylindrical panels in cylindrical bending with imperfect interfaces

An exact elasticity analysis is presented for the cylindrical bending problem of simply-supported angle-ply laminated cylindrical panels featuring interlaminar bonding imperfections. Alinear spring-layer model is adopted to describe the interfacial imperfections. New physicalvariables are introduced to rewrite the basic equations, and the corresponding state-spaceformulations are established. A variable substitution technique is then employed to transfer the stateequation into the one with constant variables, of which the solution can be obtained exactly. It isshown that the effect of weak interfaces can be easily taken intoconsideration by integrating the so-called interfacial transfer matrix into the global transfer matrix.Numerical comparison is firstly made with other exact solution inliterature for perfect angle-ply laminated cylindrical panels and goodagreement is obtained, thus validating the correctness ofthe algebra as well as program of the present method. For an imperfect cross-ply laminatedcylindrical panel, results are then compared with those obtained by an extended zig-zag shell theory.It is shown that when the compliance constants of weak interfaces increase, the shell theorybecomes more and more inaccurate. Thus, for a laminated shell structure with bondingimperfections, the applicability of various two-dimensional approximate theories as well asnumerical methods should be carefully clarified. The results of an unsymmetric five-layeredcylindrical panel further show that the presence of weak interfaces generally reduces the transverseshear stress level at the interfaces; but for some particular values of compliance constants, thetransverse shear stresses may increase at certain perfect interfaces. This will lead to a dangeroussituation because high transverse shear stress is generally one of the most important causes of theinterlaminar shear failure. Thus, the effect of weak interfaces should be precisely evaluated forpractical laminated structures.