Stability of thin micro-periodic cylindrical shells; extended tolerance modelling

Abstract Stability of Kirchhoff-Love-type circular cylindrical shells having geometrical, elastic and inertial properties densely and periodically varying in circumferential direction (uniperiodic shells) is considered. In order to take into account the effect of a cell size on the global stability behaviour of such shells (the length-scale effect), a new mathematical averaged model is formulated. This so-called the general non-asymptotic tolerance model is derived by applying a certain extended version of the well known tolerance modelling technique. This version is based on a new notion of weakly slowly-varying functions being an extension of the known more restrictive concept of slowly-varying functions occurring in the classical tolerance approach. Governing equations of the proposed model have constant coefficients depending also on a microstructure size, contrary to starting shell equations with periodic, non-continuous and oscillating coefficients. As examples, two special length-scale stationary stability problems will be analysed in the framework of the proposed model. It will be shown that within this model not only fundamental cell-independent but also the new additional cell-dependent critical forces can be derived and analysed.