New Analytical and Numerical Methods in Structural Analysis of Nonlinear Two-Dimensional Curved Membranes.

Abstract

Membranes have many engineering applications due to their light weight and low construction cost, as well as their flexibility. As a specific example, optimal design of seal and skirt system in Air Cushion Vehicles (ACVs) is essential to achieve higher speed and stability, and lower fuel consumption. Previously developed methods have considered elastic and hyperelastic membranes, as well as membranes with flexural rigidity. However, some membranes are inextensible, and have no or negligible bending stiffness. This dissertation proposes a number of methods to analyze structural behavior of membranes which can be effectively applied to membranes with complex geometries, those that are extensible or inextensible, as well as membranes with or without resistance to bending.

In particular, this dissertation presents: • An analytical method to investigate the deformation and internal forces in circular semi-submerged inextensible massless membranes, • A numerical method to predict the hydrodynamic pressure applied to bow seal membranes based upon their mechanical properties and forces involved, • A Finite Element (FE) method to model both weightless and weighted inextensible curved membranes under a variety of forces, and • A numerical method based on Isogeometric Analysis capable of analyzing a wide range of membranes.

The analytical method is a powerful, easy and precise method for a weightless membrane with specific geometry subjected to varying normal pressure. The first FE method considers weighted and weightless membranes under shear and normal pressure. Although there are some limitations in the range of applied forces this method can analyze, constant radius arc elements provide a good representation for curved membranes and very accurate results ideal for simple geometries by relatively faster analysis. The method based on the Isogeometric Analysis overcomes the limitations in the FE method; nonetheless it has potential for improvement in cases such as modeling low curvature membranes, by choosing higher degree Bezier curves or B-Spline base functions. This method, especially if improved, provides more accurate result for more complex geometries. The methods presented in this dissertation set the stage for Fluid Structure Interaction (FSI) problems that involve membranes. Large displacements are assumed in all analyses.