Closed form analysis of wrinkled membranes with linear stress–strain relation

 This paper considers the wrinkling phenomenon of membranes for the special case of a linear relationship between membrane forces and strains. Beginning from basic equations of regular wrinkling, the problem is treated analytically. An application of the theory to simple examples will be given. Received: 10 September 2002 / Accepted: 11 November 2002     

Wrinkling analysis of membranes with elastic–plastic material behavior

This paper concerns membrane wrinkling in conjunction with inelastic effects. A method will be presented, able to treat wrinkling in membranes with elastic–plastic material behavior. Some effort is spent to obtain a suitable initial guess for the internal wrinkling algorithm iteration, which improves the reliability of the method. The wrinkling algorithm is implemented into a FE–program and applied to structural analysis. Numerical and experimental results are discussed.     

On the elastic membrane in a potential flow

Methods for the calculation of potential flow around thin bodies are well known and can be found in several publications. According to these publications the vortex lattice method (VLM) combined with the quasi-continuous-method (QCM) is most effective for membrane-like bodies with no aerodynamical thickness. The possible flow around edges of a membrane causes singularities which are considered using a cosine-spaced vortex lattice. The structural membrane analysis with the finite element method (FEM) is also well known and has been applied to several problems of engineering. If the same mesh is used for both methods it is easy to combine the QCM and the FEM. However, a cosine-spaced FE-mesh makes no sense because it is not FEM problem-orientated. Therefore, until now, equidistant or nearly equidistant vortex lattices have been used to calculate the interacting flow and structure. They also cause unacceptable errors because they are not optimal for the VLM problem. This paper describes a new method to reduce the errors of combined calculations of flow and structure. A FEM problem-orientated mesh out of improved finite elements is combined with a cosine-spaced vortex lattice. The method is called quasi-continuous-continuous (QCC) because the discrete forces of the VLM are transformed into a continuous membrane load. A set of numerical examples shows the excellent numerical performance of the QCC and the reduction of errors. © 1998 John Wiley & Sons, Ltd.     

Wrinkling of nonlinear membranes

 Membranes are stiff under tension but switch over to wrinkling when compression occurs. Roddeman proposed a kinematic model to handle this phenomenon under finite deformation conditions. The wrinkling conditions of Roddeman are transformed into the reference configuration. This results in a more simple nonlinear formulation. For application in a finite element code a consistent linearization was carried out. Numerical examples for linear and nonlinear orthotropic constitutive equations are discussed. Received 21 December 2001 / Accepted 10 April 2002