Localized buckling of laminated cylindrical shells with low reduced shear modulus under non‐uniform axial compression

The problem on buckling of a thin laminated non‐circular cylindrical shell under action of axial compressive forces non‐uniformly distributed along edges is considered. It is assumed that some layers are made of a “soft” material so that the reduced (effective) shear modulus for the entire package is much less than the reduced Young's modulus. The differential equations based on the generalized hypotheses of Timoshenko and including the effect of transverse shears are used to predict the buckling of laminated cylinders regardless a number of layers and their mechanical properties. Using the asymptotic method, the buckling modes are constructed in the form of functions rapidly decaying far away from some generatrix at the reference surface. It is shown that accounting transverse shears strongly effect on the buckling modes and corresponding critical buckling forces. In particular, the preferable buckling form for a medium‐length thin laminated cylinder with a low reduced shear modulus (as compared with the reduced Young's modulus) is found to be a system of small dents in the axial direction, whose amplitudes decay in the circumferential direction without oscillations; whereas the buckling of a shell with a relatively large reduced shear modulus may occur with formation of waves in both the axial and circumferential directions. As an example, the buckling of cylindrical sandwiches assembled from the ABS‐plastic and magnetorheological elastomer with variable shear modulus under different levels of an applied magnetic field is examined