Nonlinear 3D numerical computations for the square membrane versus experimental data

This paper presents a discussion on the three-dimensional (3D) mechanical model proposed by Shi et al. for the membrane deformation by comparing the experimental results, and the limitation of this model to predict the behaviors of the membrane structure with large deformations (i.e. geometric nonlinearity). Three nonlinear numerical models, all of which can avoid the limitation, are then established to simulate the membrane’s large deformations, including the membrane model with zero bending stiffness and the shell model with small but nonzero bending stiffness based on the latest Edge-based Smoothed Finite Element Method (ES-FEM) as well as the standard Finite Element Method (FEM). The effects of geometric nonlinearity on the numerical results are carefully checked by comparing the benchmark experimental results, and the effects of different models/methods on the numerical results are also quantitatively examined. Factors, e.g. pressure fluctuations in the experiment and boundary conditions in the numerical models, are discussed to illustrate the differences between the numerical and experimental results, so as to provide some further suggestions on the improvements of the corresponding numerical models.