Improved Procedures for Static and Dynamic Analyses of Wrinkled Membranes

[+] Author and Article Information
Amit Shaw

Structures Lab, Department of Civil Engineering, Indian Institute of Science, Bangalore 560012, India

D Roy1

Structures Lab, Department of Civil Engineering, Indian Institute of Science, Bangalore 560012, Indiaroyd@civil.iisc.ernet.in


Author to whom correspondence should be addressed.

J. Appl. Mech 74(3), 590-594 (Apr 10, 2006) (5 pages) doi:10.1115/1.2338057 History: Received May 18, 2005; Revised April 10, 2006

An analysis of large deformations of flexible membrane structures within the tension field theory is considered. A modification of the finite element procedure by Roddeman (Roddeman, D. G., Drukker, J., Oomens, C. W. J., Janssen, J. D., 1987, ASME J. Appl. Mech.54, pp. 884–892) is proposed to study the wrinkling behavior of a membrane element. The state of stress in the element is determined through a modified deformation gradient corresponding to a fictive nonwrinkled surface. The new model uses a continuously modified deformation gradient to capture the location orientation of wrinkles more precisely. It is argued that the fictive nonwrinkled surface may be looked upon as an everywhere-taut surface in the limit as the minor (tensile) principal stresses over the wrinkled portions go to zero. Accordingly, the modified deformation gradient is thought of as the limit of a sequence of everywhere-differentiable tensors. Under dynamic excitations, the governing equations are weakly projected to arrive at a system of nonlinear ordinary differential equations that is solved using different integration schemes. It is concluded that implicit integrators work much better than explicit ones in the present context.

Copyright © 2007 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Actual geometry of membrane in space

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Figure 2

(a) Direction of principal Cauchy frame is indicated by the angle α and (b) triangular element, ξ1, ξ2, and ξ3 material coordinates

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Figure 3

(a) Geometry of the triangular membrane discretized with (b) mesh 0 (2 elements), (c) mesh 1 (6 elements), (d) mesh 2 (10 elements), (e) mesh 3 (14 elements), and (f) Mesh 4 (18 elements)

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Figure 4

(a) Geometry and loading pattern of the triangular membrane; comparison of displacement history at node 3 via MTL-Lagrangian, Newmark (β=0.25, γ=0.5), and Runge-Kutta method for time-varying load, (b) h=0.01s; (c) h=0.05s; (d) h=0.2s



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