ABAQUS-based study of wrinkles in spherical and inflated shell structures

Abstract

Wrinkles are wave like patterns formed over thin-walled structures whenever compressive stresses are induced. It is a non-linear phenomenon. We present stress analysis and study of wrinkles in axis-symmetric stretched thin spherical shell and an internally pressurised inflated thin-walled structure which look like fruit juice pouch available in market.

We performed buckling (eigenvalue) and post-buckle for spherical shell and dynamic explicit analysis for inflatable structure in ABAQUS package with linear elastic isotropic material and consideration of geometric non-linearity.

For thin spherical shell, equal and opposite unidirectional tension is applied on two halves. Under this load, one of the principle stress in spherical coordinate becomes negative in equator region. Due to induced compressive stress, wrinkles are observed in equator region in direction perpendicular to loading. Eigen value analysis for different radius and thickness suggest that the critical buckling load depends on ratio of radius and thickness. For different modes, buckling load is proportional to square of wavenumber. So, at lowest buckling load wavenumber is more than one.  As the load is increased beyond buckling has occurred, the wavenumber starts decreasing. But the wavelength of wrinkles (distance between two peaks) decreases at first and then increases.

Later, we analysed an internally pressurized plane symmetric inflatable structure using dynamic explicit procedure. This structure is made by joining plane sheets in such a way that it takes nearly cylindrical shape after internal pressured in applied. I this structure, wrinkles appears at the sides near joints and in the middle part. In the middle part wrinkle appears in longitudinal direction due to negative longitudinal stress. Also, we have done parametric study by changing the shape of the structure to search for non-negative longitudinal stress in the middle part along a curve in centre plane perpendicular to plane of symmetry.

Formation of wrinkles is an instability problem and under certain boundary and loading condition it occurs in elastic region of stress-strain curve. This causes failure of thin-walled structures under elastic limit hence study of wrinkles is important. Also, it finds application in determination of elastic properties of micro-structures and membrane.

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