In the present investigation, the geometrically nonlinear analysis of laminated doubly curved shells in a hygrothermal environment is presented using the finite element method. The laminated composite shells may be exposed to moisture and temperature during their service life. Hygrothermal effects induce residual stresses and the laminated shell may undergo large bending deformation. The shell geometry used in the formulation is derived using the orthogonal curvilinear coordinate system. Based on the principle of virtual work the nonlinear finite element equations are derived. A total Lagrangian approach associated to the arc-length method is implemented to solve the equilibrium equations. The present results are found to compare well with those available in the open literature and parametric studies are performed to analyze the nonlinear deflections of [0°/±45°/90°]s laminated spherical, cylindrical and conoidal shell panels under hygrothermal condition.
Whitney, J.M. and Ashton, J.E. (1971). Effects of Environment on the Elastic Response of Layered Composite Plates, AIAA Journal, 9(9): 1708—1713.
2.
Bathe, K.J., Ramm, E. and Wilson, E.L. (1975). Finite Element Formulations for Large Deformation Dynamic Analysis, International Journal of Numerical Methods in Engineering, 9(2): 353—386.
3.
Pica, A., Wood, R.D. and Hinton, E. (1980). Finite Element Analysis of Geometrically Nonlinear Plate Behaviour Using a Mindlin Formulation, Computers & Structures, 11(3): 203—215.
4.
Pipes, R.B., Vinson, J.R. and Chou, T.W. (1976). On the Hygrothermal Response of Laminated Composite Systems, J. Compos. Mater., 10(2): 129—148.
5.
Huang, N.N. and Tauchert, T.R. (1988). Large Deformation of Antisymmetric Angle-ply Laminates Resulting Nonuniform Temperature Loadings, J. Thermal Stresses , 11(3): 287—297.
6.
Lee, S.Y. and Yen, W.J. (1989). Hygrothermal Effects on the Stability of Cylindrical Composite Shell Panel, Computers & Structures, 33(2): 551—559.
7.
Huang, N.N. and Tauchert, T.R. (1991). Large Deformations of Laminated Cylindrical and Doubly Curved Panels under Thermal Loading, Computers & Structures, 41(2): 303—312.
8.
Chang, J.S. and Huang, N.N. (1991). Nonlinear Analysis of Composite Antisymmetric Angle Ply Under Uniform Temperature Field, Computers & Structures, 40(4): 857—869.
9.
Sai Ram, K.S. and Sinha, P.K. (1991). Hygrothermal Effects on the Bending Characteristics of Laminated Composite Plates, Computers & Structures, 40(4): 1009—1015.
10.
Basi, S., Rogers, T.G. and Spencer, A.J.M. (1991). Hygrothermoelastic Analysis of Anisotropic Inhomogeneous and Laminated Plates, Journal of the Mechanics andPhysics of Solids, 39(1): 1—22.
11.
Birman, V. and Bert, C.W. (1993). Buckling and Post Buckling of Composite Plates and Shells Subjected to Elevated Temperature, ASME, J. Appl. Mech., 60(2): 514—519.
12.
Chandrashekhara, K. and Tenneti, R. (1994). Nonlinear Static and Dynamic Analysis of Heated Laminated Plates: a Finite Element Approach, Composites Science and Technology, 51(1): 85—94.
13.
Chandrashekhara, K. and Bhimaraddi, A. (1994). Thermal Stress Analysis of Laminated Doubly Curved Shells using a Shear Flexible Finite Element, Computers & Structures, 52(5): 1023—1030.
14.
Marques, S.P.C. and Creus, G.J. (1994). Geometrically Nonlinear Finite Element Analysis of Viscoelastic Composite Materials Under Mechanical and Hygrothermal Loads, Computers & Structures, 53(2): 449—456.
15.
Patel, B.P. , Ganapathi, M. and Makhecha, D.P. (2002). Hygrothermal Effects on the Structural Behaviour of Thick Composite Laminates using Higher-order Theory, Composite Structures, 56(1): 25—34.
16.
Teng, J.G. and Hong, T. (1998). Nonlinear Thin Shell Theories for Numerical Buckling Predictions, Thin-Walled Structures, 31(1—3): 89—115.
17.
Kundu, C. K. and Sinha, P.K. (2006). Nonlinear Transient Analysis of Laminated Composite Shells. Journal of Reinforced Plastics and Composites, 25(11): 1129—1147.
18.
Kundu, C.K. and Sinha, P.K. (2005). Post Buckling Analysis of Laminated Composite Shells, Composite Structures, 78(3): 316—324.
19.
Jha, A.K. and Inman, D.J. (2004). Importance of Geometric Nonlinearity and Follower Pressure Load in the Dyncamic Analysis of a Gossamer Structure, Journal of Sound and Vibration, 278(1—2): 207—231.
20.
Riks, E. (1979). An Incremental Approach to the Solution of Snapping and Buckling Problems, International Journal of Solids and Structures, 15(7): 529—551.
21.
Crisfield, M.A. (1981). A Fast Incremental Iterative Solution Procedure that Handles Snap Through, Computers & Structures, 13(1—3): 55—62.
22.
Kraus, H. (1967). Thin Elastic Shells, John Wiley and Sons, Inc., New York, pp. 3—18.
23.
Boley, B.A. and Weiner, J.H. (1960). Theory of Thermal Stresses, Wiley, New York.
24.
Jones, R. (1999). Mechanics of Composite Materials, Taylor and Francis, Philadelphia, pp. 195—198.
25.
Saada, A.S. (1974). Elasticity: Theory and Applications, Pergamon Press, New York, pp. 129—137.
26.
Zienckiewicz, O.C. and Taylor, R.L. (1989). The Finite Element Method, Vol-1, McGraw Hill International Edition, Singapore, pp. 150—170.
27.
Cook, R.D., Malkus, D.S. and Plesha, M.E. (1989). Concepts and Applications of Finite Element Analysis , Wiley, New York.
