Numerical Drape Behavior of Circular Fabric Sheets Over Circular Pedestals

Abstract

Draping of circular fabric sheets over a circular pedestal is a typical large displacement/ rotation post-buckling deformation problem. Different deformed shapes or drape patterns may appear when repeating the same draping experiment for the same piece of fabric. This paper explores the possibility of using numerical techniques to reproduce this complicated but interesting fabric drape behavior. A recently developed geometrically nonlinear finite-volume method is deployed here in the numerical simulation. An initially flat circular fabric sheet is first subdivided into a number of structured finite volumes (or control volumes) by mesh lines along the warp and weft directions, resulting in rectan gular internal volumes and triangular or quadrilateral boundary volumes. Each control volume contains one grid node. The strains and curvatures and hence the out-of-plane bending and in-plane membrane strain energies of a typical volume can be evaluated using the global coordinates of its grid node and several neighbors surrounding it. The equi librium equations of the fabric sheet are derived by employing the principle of stationary total potential energy. The full Newton-Raphson iteration method with line searches is used to solve the nonlinear algebraic equations resulting from the formulation. Numerical results of two circular fabric pieces of different sizes and materials are presented. The predicted symmetrically deformed shape of the first fabric sheet is compared with existing experimental results, demonstrating good agreement between the two approaches. Several other asymmetrical drape patterns for each fabric sheet are presented, demonstrating that the proposed finite-volume method is capable of predicting not only the basic deformed shape of a circular fabric sheet, but also other possible drape patterns in a real experiment.