Thermal wrinkling of thin membranes using a Fourier-related double scale approach

• Reduced membrane model equations are recovered from full membrane model equations.
• Only few degrees of freedom needed to recover instability patterns from reduced membrane model.
• Full membrane model and reduced membrane model fit near bifurcation point.
• Boundary conditions influence membrane wrinkling behavior.
• Wrinkles shapes in thin membranes depend on thermal stresses.

The thermal wrinkling behavior of thin membranes is investigated in this paper. Wrinkles often occur at multiple length scales where induced compressive stresses are located during thermal loading. In the present study, the method of double scale Fourier series is used to deduce the macroscopic membrane wrinkling equations. The obtained equations account for the global and local wrinkling modes. Numerical examples are conducted to assess the validity of the approach developed. The present membrane׳s model needs only few degrees of freedom to recover more accurately the post-buckling equilibrium curves and the wrinkling shapes. Different parameters such as membrane׳s aspect ratio, wave number, and pre-stressed membranes are discussed from a numerical point of view and the properties of the wrinkles (critical load, wavelength, size, and location) are presented.