Presented here is a new total-Lagrangian displacement-based finite-element formulation for plates and shells undergoing large displacements and rotations. The theory fully accounts for geometric nonlinearities, general initial curvatures, and extensionality by using Jaumann stress and strain measures, an exact coordinate transformation, and orthogonal virtual rotations. Moreover, transverse shear deformations are accounted for by using a first-order shear deformation theory with shear correction factors obtained by matching the shear strain energy and stress resultants with those of a general layerwise higher-order shear deformation theory. Large static deformations of several different plates and shells under different loading and boundary conditions are obtained. Comparison with available results in the literature reveals that the finite-element model is accurate in predicting large deformations of highly flexible two-dimensional structures.
Jenkins, C. H. M.Gossamer Spacecraft: Membrane and Inflatable Structures Technology for Space Applications, AIAA, 2001.
2.
Salama, M., Lou, M., and Fang, H.Deployment of inflatable space structures: A review of recent developments, AIAA-2000-1730, AIAA, New York, (2000).
3.
Damle, S. V., Joshi, M. N., Sreenivasan, S. and Subba Rao, J. V.Development of cost effective balloon design and fabrication methods, AIAA International Balloon Technology Conference (San Francisco, CA, June 3–5), 1997.
4.
Hedgepeth, J. M.Interaction between an inflated lenticular reflector and its rim support, AIAA-95-1510-CP (1995).
5.
Greschik, G.The unfolding deployment of a shell parabolic reflector, AIAA-95-1278-CP (1995).
6.
Szyszkowski, W., Youck, D. and Johnson, D. W.The dynamics of deployment of a satellite boom with self-locking joints, in 15th CANCAM (University of Victoria, Victoria, BC, Canada, May 28–June 1), 1995.
7.
Greschik, G. and Park, K. C.The deployment of curved closed tubes, AIAA-95-1395-CP (1995).
8.
Palisoc, A. L.Inflatable reflector development program, L'Garde Technical Report LTR-94-AP-008 (1994).
9.
Pai, P. F., Wen, B., Schulz, M. J. and Naser, A. S.Nonlinear vibration suppression of cantilever beams using bimoments induced by PZT actuators. AIAA-97-1357-CP, (1997).
10.
Anderson, M. S.Design of panels having postbuckling strength, AIAA-97-1240-CP (1997).
11.
Nayfeh, A. H. and Pai, P. F.Linear and Nonlinear Structural Mechanics. Wiley, New York, 2004.
12.
Pai, P. F. and Nayfeh, A. H.A nonlinear composite plate theory. Nonlinear Dynamics, 2, 445–477 (1991).
13.
Pai, P. F. and Nayfeh, A. H.Fully nonlinear model of cables. AIAA Journal, 30, 2993–2996 (1992).
14.
Pai, P. F. and Nayfeh, A. H.A fully nonlinear theory of curved and twisted composite rotor blades accounting for warpings and three-dimensional stress effects. International Journal of Solids and Structures, 31, 1309–1340 (1994).
15.
Pai, P. F. and Nayfeh, A. H.A unified nonlinear formulation for plate and shell theories. Nonlinear Dynamics, 6, 459–500 (1994).
16.
Pai, P. F. and Palazotto, A. N.Polar decomposition theory in nonlinear analyses of solids and structures. Journal of Engineering Mechanics, 121, 568–581 (1995).
17.
Pai, P. F. and Palazotto, A. N.Nonlinear displacement-based finite-element analyses of composite shells—A new total Lagrangian formulation. International Journal of Solids and Structures, 32, 3047–3073 (1995).
18.
Greer, J. M. and Palazotto, A. N.Nonlinear finite element analysis of isotropic and composite shells by a total Lagrangian decomposition scheme. Mechanics of Composite Materials and Structures, 3, 241–271 (1996).
19.
Pai, P. F.A new look at shear correction factors and warping functions of anisotropic laminates. International Journal of Solids and Structures, 32, 2295–2313 (1995).
20.
Washizu, K.Variational Methods in Elasticity and Plasticity, 3rd edn, Pergamon, New York, 1982.
21.
Cook, R. D., Malkus, D. S. and Plesha, M. E.Concepts and Applications of Finite Element Analysis, 3rd edn, Wiley, New York, 1989.
22.
Palazotto, A. N. and Dennis, S. T.Nonlinear Analysis of Shell Structures., AIAA, New York, 1992.
23.
Riks, E.An incremental approach to the solution of snapping and buckling problems. International Journal of Solids and Structures, 15, 524–551 (1979).
24.
Lee, S. H.MSC/NASTRAN Handbook for Nonlinear Analysis, Version 67, The MacNeal-Schwendler Corporation, (1992).
25.
Sabir, A. B. and Lock, A. C.The application of finite elements to the large deflection geometrically nonlinear behaviour of cylindrical shells, in Variational Methods in Engineering, ed. C. A. Brebbia and H. Tottenham, Southampton Press, London, 1972.
26.
Rankin, C. C., Stehlin, P. and Brogan, F. A.Enhancements to the STAGS Computer Code, NASA CR-4000, 1986.
27.
Nayfeh, A. H. and Balachandran, B.Applied Nonlinear Dynamics, Wiley, New York, 1995.
28.
Pai, P. F. and Lee, S. Y.Three-dimensional postbuckling analysis of curved beams. International Journal of Computational Engineering Science, 3, 305–338 (2002).
29.
Simo, J. C., Fox, D. D. and Rifai, M. S.On a stress resultant geometrically exact shell model: Part III. Computational aspects of the nonlinear theory. Computer Methods in Applied Mechanics and Engineering, 79, 21–70 (1990).
