A Simple Co-rotational Geometrically Non Linear Membrane Finite Element Wrinkling Analysis

Thin pre-tensioned membranes are often used in civil architecture as well as in marine and space technologies. Lacking in-plane compression stiffness, membranes will wrinkle at certain states of stress. This paper presents a geometrically nonlinear analysis of membranes in the presence of wrinkling using a unique incremental formulation that accounts for equilibrium in the deformed state and the current wrinkling state by iterations. The membranes with wrinkling are simulated by a geometrically nonlinear upgraded version of the constant strain triangular (CST) membrane finite element. Each load step is comprised of two iteration cycles: the geometrically nonlinear cycle that ensures equilibrium in the deformed sate using the Newton–Raphson iterations and the wrinkling cycle that identifies the location and direction of the wrinkles and redistributes stresses accordingly. Finally, validation and verification of the proposed analysis is made by comparing the present results with those existing for the benchmark examples.