Abstract
Thin linearly elastic Kirchhoff–Love-type circular cylindrical shells of periodically micro-inhomogeneous structure in circumferential and axial directions (biperiodic shells) are investigated. The aim of this contribution is to formulate and discuss a new averaged nonasymptotic model for the analysis of selected stability problems for these shells. This, so-called, general nonasymptotic tolerance model is derived by applying a certain extended version of the known tolerance modelling procedure. Contrary to the starting exact shell equations with highly oscillating, noncontinuous and periodic coefficients, governing equations of the tolerance model have constant coefficients depending also on a cell size. Hence, the model makes it possible to investigate the effect of a microstructure size on the global shell stability (the length-scale effect).
Highlights
Thin linearly elastic Kirchhoff–Love-type circular cylindrical shells with a periodically micro-inhomogeneous structure in circumferential and axial directions are objects of consideration
We restrict our consideration to those biperiodic cylindrical shells, which are Communicated by Andreas Öchsner
The asymptotic procedures are usually restricted to the first approximation, which leads to homogenized models neglecting the effect of a periodicity cell size on the overall shell behaviour
Summary
The mechanical problems of periodic structures (shells, plates, beams) are described by partial differential equations with periodic, highly oscillating and discontinuous coefficients. The main aim of this contribution is to formulate and discuss a new mathematical averaged general tolerance model for the analysis of selected stability problems for the biperiodic cylindrical shells under consideration. This model makes it possible to investigate stationary stability and dynamic stability as well as parametric vibrations. Contrary to the starting exact equations of the shell stability with periodic, highly oscillating and discontinuous coefficients, governing equations of the proposed averaged model have constant coefficients depending on a cell length dimensions. It has to be emphasized that the general tolerance model of stability problems for thin linearly elastic Kirchhoff–Love-type circular cylindrical shells having a periodically micro-inhomogeneous structure in the circumferential direction and a constant structure in the axial direction (uniperiodic shells), which is proposed by Tomczyk et al [13], cannot be applied to the analysis of stability problems for biperiodic shells considered here
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