Time‐Dependent Response of Three‐Filament Cord
Publication: Journal of Engineering Mechanics
Volume 119, Issue 4
Abstract
A method is presented in which the time‐dependent creep response of a three‐filament cord, constrained by a no‐end rotation boundary condition, may be predicted. This method is an initial attempt to describe the viscoelastic response of the cord by incorporating the stress‐relaxation data for a linearly viscoelastic construction material. The particular material used in this paper is polymethyl methacrylate (PMMA). The stress relaxation for PMMA is modeled analytically by utilizing the Schapery collocation method that determines the constant coefficient values for the elements of a Wiechert response model. The geometric effects of the cord are then combined with the time‐dependent analytical solution for the Wiechert model to develop a system of convolution integrals that satisfy the equilibrium and imposed boundary conditions for the cord construction. The solutions for these integrals are approximated numerically using a modified Newton's iterative method combined with a linear time‐step approximation technique.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bland, D. R. (1960). The theory of linear viscoelasticity. Pergamon Press, New York, N.Y.
2.
Costello, G. A. (1990). Theory of wire rope. Springer‐Verlag, New York, N.Y.
3.
Hearle, J. W. S., Grosberg, P., and Backer, S. (1969). Structural mechanics of fibers, yarns, and fabrics. John Wiley and Sons, New York, N.Y.
4.
Huang, N. C. (1978). “On the finite extension of a viscoelastic two‐ply filament yarn.” Textile Res. J., 48(Feb.), 61–67.
5.
Lee, E. H., and Rogers, T. G. (1963). “Solution of viscoelastic stress analysis problems using measured creep or relaxation functions.” J. Appl. Mech., 33(March), 127–133.
6.
Prakash, A., Conway, T. A., and Costello, G. A. (1992). “Compression of a cord.” J. Appl. Mech., 59(2), S213.
7.
Tschoegl, N. W. (1989). The phenomenological theory of linear viscoelastic behavior. Springer‐Verlag, New York, N.Y.
8.
Wilson, K. (1979). A history of textiles. Westview Press, Boulder, Colo.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 119 • Issue 4 • April 1993
Pages: 833 - 849
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Dec 2, 1991
Published online: Apr 1, 1993
Published in print: Apr 1993
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.