Prediction of Large Deformation Behavior of Fabric Using Galerkin Finite Element Method

In this study, an alternative finite element solution procedure is applied to predict large deformations of fabrics in terms of the boundary and the loading conditions. The element stiffness matrix is obtained by using the Galerkin approach. The generalized displacements are defined in terms of cubic Hermite polynomials with the nodal rotations and the curvatures along the deformed geometry. The resulting non-linear stiffness equations are solved by the Newton-Raphson iteration method. The proposed formulation is verified by comparing deformations results with those published in the literature and the calculated results show excellent agreement with previously published works.

[1]  Kjell Mattiasson,et al.  Numerical results from large deflection beam and frame problems analysed by means of elliptic integrals , 1981 .

[2]  Timothy G. Clapp,et al.  A Comparison of Linear and Non-linear Bending Models for Predicting Fabric Deformation in Automated Handling , 1991 .

[3]  T. Ghosh,et al.  Indirect Measurement of the Moment-Curvature Relationship for Fabrics , 1990 .

[4]  K. E. Bisshopp,et al.  Large deflection of cantilever beams , 1945 .

[5]  George C. Lee,et al.  Finite element solution to an elastica problem of beams , 1970 .

[6]  D. W. Lloyd,et al.  The folding of heavy fabric sheets , 1978 .

[7]  W. L. Wood.  Note on dynamic relaxation , 1971 .

[8]  Discussion of paper† By Yasuo Tada and George and George C. Lee , 1972 .

[9]  B. W. Golley.  The solution of open and closed elasticas using intrinsic coordinate finite elements , 1997 .

[10]  T. Y. Yang,et al.  Matrix displacement solution to elastica problems of beams and frames , 1973 .

[11]  P. Grosberg.  The Mechanical Properties of Woven Fabrics Part II: The Bending of Woven Fabrics , 1966 .

[12]  D. Griffin,et al.  Finite-Element Analysis , 1975 .

[13]  T. Clapp,et al.  Buckling of Woven Fabrics , 1990 .

[14]  F. T. P. B.Sc..  26—THE “HANDLE” OF CLOTH AS A MEASURABLE QUANTITY , 1930 .

[15]  Analyzing Fabric Buckling Based on Nonlinear Bending Properties , 2004 .

[16]  Barnes.  Discussion of the Paper , 1961, Public health papers and reports.

[17]  David R. Buchanan,et al.  Large-deflexion Bending of Woven Fabric for Automated Material-handling , 1990 .

[18]  J. Atkinson,et al.  Large Deformation Modelling of Flexible Materials , 1996 .

[19]  F. Virginia Rohde.  Large deflections of a cantilever beam with uniformly distributed load , 1953 .

[20]  M. Konopasek,et al.  Computational theory of bending curves part I: The initial value problem for the three-dimensional elastic bending curve , 1972 .