Restricted accessResearch articleFirst published online 1992-09
Geometrically Non-Linear Analysis of Doubly Curved Laminated and Sandwich Fibre Reinforced Composite Shells with a Higher Order Theory and C° Finite Elements
An isoparametric C° finite element formulation based on a higher order displacement model for linear and geometrically non-linear analysis (that accounts for large displacements in the sense of von Karman) of doubly curved laminated composite and sandwich shells under transverse loads is presented. The displacement model ac counts for cubic and constant variation of tangential and transverse displacement compo nents respectively through the shell thickness. The assumed displacement model elimi nates the use of shear correction coefficients. The discrete element chosen is a nine-noded quadrilateral element with nine degrees of freedom per node. The accuracy of the for mulation is then established by comparing the present results with the available analytical closed-form solutions, three-dimensional elasticity solutions and other finite element solu tions.
Get full access to this article
View all access options for this article.
References
1.
Allen, H.G.1969Analysis and Design of Structural Sandwich Panels. London: Pergamon Press.
2.
Ambartsumyam, S.A.1964. "Theory of Anisotropic Shells," NASA-TT: F-118.
3.
Bert, C.W.1980. "Analysis of Shells," in Analysis and Performance of Composites , L. J. Broutman, ed., New York: Wiley International Edition, pp. 207-258.
4.
Bhimaraddi, A. and L.K. Stevens.1986. "On the Higher Order Theories in Plates and Shells," Int. J. Solids and Struct. , 6:35-50.
5.
Chandrasekhara, K.1985. "Geometrically Non-Linear Analysis of Laminated Composite Plates and Shells," Ph.D. thesis, Virginia Polytechnic Institute and State University.
6.
Chang, T.Y. and K. Sawamiphakdi .1981. "Large Deformation Analysis of Laminated Shells by Finite Element Method," Comput. Struct. , 13:331-341.
7.
Chao, W.C. and J.N. Reddy.1983 "Geometrically Non-Linear Analysis of Layered Composite Shells," in Mech of Composite Materials, G. J Dvorak, ed., AMD, New York: ASME, 58:19-31.
8.
Dennis, S.T. and A.N. Plazotto.1991. "Laminated Cylindrical Bending, Two Dimensional Approach vs. Exact," AIAA J., 29:647-650.
9.
Dong, S.B. and F.K.W. Tso.1972. "On a Laminated Orthotropic Shell Theory Including Transverse Shear Deformation," ASME J. Appl. Mech. , 39:1091-1097.
10.
Hildebrand, F.B., E. Reissner and G.B. Thomas.1949. "Notes on the Foundations of Small Displacements of Orthotropic Shells," NACA: TN-1833.
11.
Horngome, G. and P.G. Bergan.1976. "Incremental Variational Principles and Finite Element Models for Non-Linear Problems," Comput. Meth. Appl Mech. and Engg. , 7:201-217
12.
Kabir, H.R.H.1990. "Static and Dynamic Analysis of Laminated Finite Double Curved Shells," Ph.D. thesis, Dept. of Civil Engg., Univ. of Utah.
13.
Kant, T.1976. "Thick Shells of Revolution-Some Studies," Ph.D. thesis, Dept. of Civil Engg., Indian Institute of Technology, Bombay.
14.
Kant, T.1981a. "A Higher-Order General Shell Theory," Res Rep. C/R/391/81 , Civil Engg. Dept., Swansea, Univ. of Wales.
15.
Kant, T.1981b. "A Higher-Order General Laminated Shell Theory," Res. Rep. C/R/395/81, Civil Engg. Dept., Swansea, Univ. of Wales .
16.
Kant, T.1982. "On Finite Element Discretization of a Higher Order Shell Theory," in Mathematics of Finite Elements and Applications , J. R. Whiteman, ed. , LondonAcademic Press, pp. 209-217.
17.
Kant, T. and B.P. Kulkarni.1986. "A C° Continuous Linear Beam/Bilinear Plate Flexure Element," Comput. Struct. , 22:413-425.
18.
Kant, T. and D. Datye.1989. "Finite Elements Available for the Analysis of Curved Thin Walled Structures," in Finite Element Applications to Thin Walled Structures, J. W. Bull, ed., London: Elsevier Publishers, pp. 1-40.
19.
Kant, T. and Mallikarjuna.1989. "Transient Dynamics of Composite Sandwich Plates Using 4,8,9 Noded Isoparametric Quadrilateral Elements," Finite Elements in Analysis and Design, 6:307-318.
20.
Kant, T. and Mallikarjuna.1991. "Non-Linear Dynamics of Laminated Plates with a Higher Order Theory and C° Finite Elements," Int. J. Non-Linear Mech. , 26:335-343
21.
Kant, T. and B.S. Manjunatha .1988. 'An Unsymmetric FRC Laminate C° Finite Element Model with 12 Degrees of Freedom per Node," Engineering Computations, 5:300-308.
22.
Kant, T. and M.P. Menon.1989. "Higher Order Theories for Composite and Sandwich Cylindrical Shells with C° Finite Elements," Comput. Struct., 33.1191-1204.
23.
Kant, T. and M.P. Menon.1990. "Refined Multi Layered Composite Cylindrical Shell Elements," in Advances in Structural Testing, Analysis and Design, V. S. Arunachalam et al , eds., New Delhi: Tata McGraw Hill, pp. 533-538.
24.
Kant, T. and M.P. Menon.1991. "Estimation of Interlaminar Stresses in Fibre Reinforced Composite Cylindrical Shells," Comput. Struct., 38:131-147.
25.
Kant, T. and B.N. Pandya.1988. "A Simple Finite Element Formulation of a Higher-Order Theory for Unsymmetrically Laminated Composite Plates," Comput. Struct. , 9:215-246.
26.
Kant, T. and S. Patil.1990. "Transient/Pseudo Transient Finite Element Small/Large Deformation Analysis of Two Dimensional Problems," Comput. Struct. , 36:421-427.
27.
Kant, T. and C.K. Ramesh.1976. 'Analysis of Thick Orthotropic Shells ," Proc., I.A.S.S. World Congress on Space Enclosures, Montreal, Canada, pp. 401-409.
28.
Kim, Y.H. and S.W. Lee.1988. "A Solid Element Formulation for Large Deflection Analysis of Composite Shell Structures," Comput. Struct. , 30:269-274.
29.
Liu, C.F.1985. "Geometrically Non-Linear Analysis of Composite Laminates Using a Refined Shear Deformation Shell Theory," Ph.D thesis, Dept. of Engg. Mech., Virginia Polytechnic and State Univ.
30.
Mallikarjuna andT. Kant.1989. "Finite Element Formulation of a Higher Order Theory for Dynamic Response of Laminated Composite Plates," Engineering Computations, 6:198-208.
31.
Mallikarjuna and T. Kant.1990. 'Analysis of Anisotropic Composite/Sandwich Shells Using a New Displacement Model with the Super-Parametric Element," Journal of Structural Engineering, 17:91-100.
32.
Mallikarjuna and T. Kant. "A General Fibre Reinforced Composite Shell Element Based on a Refined Shear Deformation Theory ," Comput. Struct. , 42:381-388.
33.
Murty, A.V.K. and T.S.R. Reddy.1986. "A Higher Order Theory for Laminated Composite Cylindrical Shells," J. Aero. Society of India, pp. 161-171.
34.
Naghdi, P.M.1956. "A Survey of Recent Progress in the Theory of Elastic Shells," Appl. Mech. Reviews, 9:365-368.
35.
Naghdi, P.M.1957. "On the Theory of Thin Elastic Shells," Quart. Appl. Math. , 14:369-380.
36.
Noor, A.K. and S.J. Hartley.1977. "Non-Linear Shell Analysis via Mixed Isoparametric Elements," Comput. Struct. , 7:615-626.
37.
Pagano, N.J.1970. "Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates," J. Compos. Mater., 4:20-31.
38.
Pandya, B.N.1987. "Higher Order Theories and Finite Element Evaluations for Multilayer Composite Plates," Ph.D. thesis, Dept. of Civil Engg., Indian Institute of Technology, Bombay .
39.
Pandya, B.N. and T. Kant.1988. "Finite Element Analysis of Laminated Composite Plates Using a Higher Order Displacement Model," Compos. Sci. Tech., 32:137-155.
40.
Reddy, J.N.1984. "Exact Solutions of Moderately Thick Laminated Shells ," ASCE J. Engg. Mech., 110:794-809.
41.
Reddy, J.N. and K. Chandrasekhara .1985a. "Non-Linear Analysis of Laminated Shells Including Transverse Shear Strains," AIAA J., 23:440-441.
42.
Reddy, J.N. and K. Chandrasekhara .1985b. "Non-Linear Finite Element Models of Laminated Plates and Shells," in Finite Elements in Computational Mechanics, Vol. 1, T. Kant , ed., London: Pergamon Press , pp. 189-209.
43.
Reddy, J.N. and C.F. Liu.1985. "A Higher Order Shear Deformation Theory of Laminated Elastic Shells," Int. J. Eng. Sci. , 23:319-330.
44.
Reissner, E.1950. "On a Variational Theorem in Elasticity," J. Math. and Physics, 29:90-95.
45.
Ren, J.G.1987. "Exact Solutions for Laminated Cylindrical Shells in Cylindrical Bending," Compos. Sci. Tech., 29:169-187.
46.
Sanders, J.L.1959. 'An Improved First Approximation Theory for Thin Shells ," NASA: TR-24.
47.
Stricklin, A., W.E. Haisler and W. A. von Reiseman .1973. "Evaluation of Solution Procedures for Material and/or Geometrical Non-Linear Structural Analysis," AIAA J., 11:292-299.
48.
Varadan, T.K. and K. Bhaskar.1991. "Bending of Laminated Orthotropic Cylindrical Shells-An Elasticity Approach," Compos. Sci. Tech., 17:141-156.
49.
Whitney, J.M. and C.T. Sun.1974. "A Refined Theory for Laminated Anisotropic Cylindrical Shells," ASME J. Appl. Mech. , 41:471-476.
50.
Widera, G.E.O. and D.L. Logan.1980. "Refined Theories for Non-Homogeneous Anisotropic Cylindrical Shells," ASCE J. of Engg. Mech. , 106:1053-1090.
51.
Wunderlich, W.1977. "Incremental Formulations for Geometrically Non-Linear Problems," m Formulations and Computational Algorithms in Finite Element Analysis, K. J. Bathe, J. T. Oden and W. Wunderlich , eds., Cambridge, MA: MIT Press , pp. 193-239
