A new Fourier-related double scale analysis for instability phenomena in sandwich structures

Abstract In this paper, we present a new Fourier-related double scale analysis to study instability phenomena of sandwich structures. By using the technique of slowly variable Fourier coefficients, a zig–zag theory based microscopical sandwich model is transformed into a macroscopical one that offers three numerical advantages. Firstly, only the envelopes of instability patterns are evaluated and this leads to a significant improvement on computational efficiency, especially when dealing with high wavenumber wrinkling phenomena. Secondly, the proposed macroscopical model allows one to select modal wavelength, which makes easy to control non-linear calculations. Thirdly, in contrast to Landau–Ginzburg envelope equations, it may also remain valid away from the bifurcation point and the coupling between global and local instabilities can be accounted for. The established non-linear system is solved by asymptotic numerical method (ANM), which is more reliable and less time consuming than other iterative classical methods. The proposed double scale analysis yields accurate results with a significant reduced computational cost.

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