C° finite elements based on a set of higher-order theones are projected to provide reliable predictions for interlaminar stresses in layered composite and sandwich laminates. These theoretical-cum-computational models incorporate laminate deforma tions which account for the effects of transverse shear deformation, transverse normal strain/stress and a nonlinear variation of inplane displacements with respect to the thick ness coordinate, thus eliminating the need for shear correction coefficients. The inplane stresses are evaluated via constitutive relations, while the interlaminar stresses are evalu ated by using the equilibrium equations. 16 and 9 noded Lagrangian selectively integrated isoparametric elements are used in this study. The present results, when compared with available elasticity and closed-form laminate solutions, show good agreement. New results for sandwich laminates are also presented which may serve as a benchmark for future investigations.
Get full access to this article
View all access options for this article.
References
1.
Jones, R.M.1975. Mechanics of Composite Materials. New York: McGraw-Hill.
2.
Reissner, E.1945. "The Effect of Transverse Shear Deformation on the Bending of Elastic Plates," ASME J. Appl. Mech. , 12: A69-A77.
3.
Mindlin, R.D.1951 "Influence of Rotatory Inertia and Shear Deformation on Flexural Motions of Isotropic Elastic Plates," ASME J. Appl. Mech. , 18:31-38.
4.
Reissner, E.1975. "On Transverse Bending of Plates Including the Effect of Transverse Shear Deformation," Int. J. Solids Struct. , 11.569-573.
5.
Lo, K.H. , R.M. Christensen and E.M. Wu.1977. " A Higher Order Theory of Plate Deformation-Part 2: Laminated Plates," ASME J. Appl. Mech. , 44:669-676
Kant, T., D.R.J. Owen and O.C. Zienkiewicz .1982. "A Refined Higher Order C° Plate Bending Element," Comput. Struct. , 15:177-183.
8.
Murthy, M V. V.1981. "An Improved Transverse Shear Deformation Theory for Laminated Anisotropic Plates," NASA Technical Paper-1903.
9.
Reddy, J.N.1984. "A Simple Higher Order Theory for Laminated Composite Plates," ASME J Appl. Mech. , 51:745-752
10.
Phan, N.D. and J.N. Reddy.1985. "Analysis of Laminated Composite Plates Using a Higher Order Shear Deformable Theory," Int. J. Numer. Meth. Engg. , 21:2201-2219.
11.
Pucha, N.S. and J.N. Reddy.1986. "A Refined Mixed Shear Flexible Finite Element for the Non-Linear Analysis of Laminated Plates," Comput. Struct. , 22:529-538.
12.
Pandya, B.N. and T. Kant1987. "A Consistent Refined Theory for Flexure of a Symmetric Laminate," Mech Res. Commun. , 14:107-113.
13.
Pandya, B.N. and T. Kant1988. "Flexure Analysis of Laminated Composites Using Refined Higher Order C° Plate Bending Elements," Comput. Meth Appl. Mech. Engg. , 66:173-198.
14.
Pandya, B.N. and T. Kant.1988. "A Refined Higher Order Generally Orthotropic C° Plate Bending Element," Comput. Struct. , 28:119-133.
15.
Pandya, B.N. and T. Kant.1988. "A Simple Finite Element Formulation of a Higher Order Theory for Unsymmetrically Laminated Composite Plates," Compos. Struct , 9:215-246.
16.
Pandya, B.N. and T. Kant.1988. "Finite Element Stress Analysis of Laminated Composite Plates Using a Higher Order Displacement Model," Compos. Sci. Technol , 32.137-155
17.
Kant, T. and B.N. Pandya.1988. "Finite Element Stress Analysis of Unsymmetrically Laminated Composite Plates Based on a Refined Higher Order Theory," in Composite Materials and Structures, K. A. V. Pandalai and S. K. Malhotra, eds., New Delhi: Tata McGraw-Hill, pp. 373-380.
18.
Pandya, B.N. and T. Kant.1988. "Higher Order Shear Deformable Theories for Flexure of Sandwich Plates-Finite Element Evaluations," Int. J. Solids Struct. , 24(12) 1267-1286.
19.
Kant, T. and B.S. Manjunatha .1988. "An Unsymmetric FRC Laminate C° Finite Element Model with Twelve Degrees of Freedom Per Node," Int. J. Engg. Computat , 5(4):300-308.
Iyengar, K.T.S. and S.K. Pandya.1983. 'Analysis of Orthotropic Rectangular Thick Plates," Fibre Sci. Technol , 18:19-36.
22.
Ren, J.G.1987. "A New Theory of Laminated Plate," Compos. Sci. Technol , 26:225-239.
23.
Pagano, N.J.1970. "Exact Solution for Rectangular Bidirectional Composites and Sandwich Plates," J. Compos. Mater., 4.20-34.
24.
Pagano, N.J.1969. "Exact Solution for Composite Laminates in Cylindrical Bending," J. Compos. Mater., 3:398-411.
25.
Ambartsumyan, S.A.1970. Theory of Anisotropic Plates. Lancaster, PA: Technomic Publishing Co., Inc.
26.
Ren, J.G.1987. "Bending of Simply Supported, Antisymmetrically Laminated Rectangular Plate under Transverse Loading," Compos Sci. Technol. , 28.231-243.
27.
Reissner, E. and Y. Stavsky.1961. "Bending and Stretching of Certain Types of Heterogeneous Aeolotropic Elastic Plates," ASME J. Appl. Mech. , 28:402-408.
28.
Stavsky, Y.1961. "Bending and Stretching of Laminated Aeolotropic Plates," ASCE J. Engg. Mech. , 87:31-56.
29.
Iyengar, K.T.S. and S.K. Pandya.1986. 'Application of the Method of Initial Functions for the Analysis of Composite Laminated Plates ," Ing. Arch. , 56.407-416.
30.
Reddy, J.N. and W.C. Chao.1981. "A Comparison of Closed Form and Finite Element Solutions of Thick Laminated Anisotropic Rectangular Plates," Nucl. Engg. Des., 64.153-167.
31.
Chirns, D.S. and P.A. Lagace.1987. "Thick Composite Plates Subjected to Lateral Loading," ASME J. Appl. Mech. , 54:611-616.
32.
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.
