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Rectangular membrane under shear

This and the next 2 images are from:
Satish Kumar, S.H. Upadhyay and Anil C. Mathur,

“Wrinkling simulation of membrane structures under tensile and shear loading”, Columbia International Publishing, Journal of Vivbration Analysis, Measurement, and Control, Vol. 3, No. 1, pp 17-33, 2015, DOI: 10.7726/jvamc.2015.1002

ABSTRACT: This paper presents a detailed Finite Element Analysis study of the formation and evolution of wrinkle pattern that observed in stretched thin membranes. The model problem is set up under the various load conditions. As a precondition for wrinkling, development of compressive stresses in the transverse direction is found to depend on both the length-to-width aspect ratio & thickness of the rectangular membrane. Shape and size of wrinkle also depends on applied tensile strain and shear strain. The analysis has been done in two parts; in first part we see the effect of thickness of membrane and number of element variation on number of wrinkles and eigenvalue frequency. In second part, two-dimensional stress analysis is performed under the plane-stress condition to finding out stretch-induced stress distribution patterns in the elastic membrane. The analysis has been carried out on the rectangular membrane with tensile loading with assuming imperfections in the structure with the ABAQUS a commercially available finite element package. Wrinkling patterns are presented to show how wrinkle formation with increasing shear loads, tensile loads, membrane thickness and number of elements.

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