Abstract
The investigation aims at: (i) constructing a modified higher-order shear deformation theory in which Kirchhoff's hypotheses are relaxed, to allow for shear deformations; (ii) validating the present 5-parameter-smeared-laminate theory by comparing the results with exact solutions; and (iii) applying the theory to a specific problem of the postbuckling behavior of a flat stiffened fiber-reinforced laminated composite plate under compression.
The first part of this paper is devoted mainly to the derivation of the pertinent displacement field which obviates the need for shear correction factors. The present displacement field compares satisfactorily with the exact solutions for three layered cross-ply laminates. The distinctive feature of the present smeared laminate theory is that the through-the-thickness transverse shear stresses are calculated directly from the constitutive equations without involving any integration of the equilibrium equations.
The second part of this paper demonstrates the applicability of the present modified higher-order shear deformation theory to the post-buckling analysis of stiffened laminated panels under compression. to accomplish this, the finite strip method is employed. A C 2-continuity requirement in the displacement field necessitates a modification of the conventional finite strip element technique by introducing higher-order polynomials in the direction normal to that of the stiffener axes. The finite strip formulation is validated by comparing the numerical solutions for buckling problems of the stiffened panels with some typical experimental results.
Similar content being viewed by others
References
Anderson, M. S.; Stroud, W. J. (1979): A general panel sizing computer code and its application to composite structural panels. AIAA J. 17, 892–897
Bert, C. W. (1984): A critical evaluation of new plate theories applied to laminated composites. Compos. Struct. 2, 329–347
Cheung, Y. K. (1976). Finite strip method in structural analysis. New York: Pergamon
Chia, C. Y. (1988): Geometrically non-linear behavior of composite plates: A review. Appl. Mech. Rev. 41, 439–451
Clarke, M. J.; Hancock, G. J. (1990): A study of incremental-iterative strategies for nonlinear analysis. Int. J. Num. Meth. Eng. 26, 1365–1391
Graves-Smith, T. R.; Sridharan, S. (1978): A finite strip method for the post-locally buckled analysis of plate structures. Int. J. Mech. Sci. 20, 833–842
Jones, R. M. (1975). Mechanics of composite materials. New York: McGraw-Hill
Kant, T.; Owen, D. R. J.; Zienkiewicz, O. C. (1982): A refined higher-order C° plate bending element. Compos. Struct. 15, 177–183
Kant, T.; Pandya, B. N. (1988): A simple finite element formulation of a higher-order theory for unsymmetrically laminated composite plates. Compos. Struct. 9, 215–246
Khdeir, A. A.; Reddy, J. N.; Librescu, L. (1987): Analytical solution of a refined shear deformation theory for rectangular composite plates. Int. J. Solids Struct. 23, 1447–1463
Kouri, J. V. (1991): Improved finite element analysis of thick laminated composite plates by the predictor corrector technique and approximation of C' continuity with a new least squares element. Ph.D. thesis. Georgia Institute of Technology
Krishnamurthy, A. V. (1987): Flexure of composite plates. Compos. Struct. 7, 161–177
Krishnamurthy, A. V.; Vellaichamy, S. (1987): On higher order deformation theory of laminated composite panels. Compos. Struct. 8, 247–270
Longyel, P.; Cusens, A. R. (1983): A finite strip method for the geometrically nonlinear analysis of plate structures. Int. J. Num. Meth. Eng. 19, 331–340
Levinson, M. (1980): An accurate, simple theory of the statics and dynamics of elastic plates. Mechanics Research Communications. 7, 343–350
Librescu, L.; Reddy, J. N. (1989): A few remarks concerning several refined theories of anistropic composite laminated plates. Int. J. Eng. Sci. 27, 515–527
Lo, K. H.; Christensen, R. M.; Wu, E. M. (1977): A high-order theory of plate deformation, Part 1: Homogeneous plates, Part 2: Laminated plates. J. Appl. Mech. 44, 663–676
Mindlin, R. D. (1985): Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. J. Appl. Mech. 73, 31–38
Murthy, M. V. V. (1981): An improved transverse shear deformation theory for laminated anisotropic plates. NASA Technical Paper 1903
Noor, A. K.; Burton, W. S. (1989): Assessment of shear deformation theories for multilayered composite plates. Appl. Mech. Rev. 42, 1–12
Noor, A. K.; Peters, J. (1989): Buckling and postbuckling analyses of laminated anisotropic structures. Int. J. Num. Meth. Eng. 27, 383–401
Noor, A. K.; Burton, W. S. (1990): Assessment of computational models for multilayered anisotropic plates. Compos. Struct. 14, 233–265
Pagano, N. J. (1969): Exact solutions for composite laminates in cylindrical bending. J. Comp. Mat. 3, 398–411
Pagano, N. J. (1970): Exact solutions for rectangular bidirectional composites and sandwich plates. J. Comp. Mat. 4, 20–34
Pandya, B. N.; Kant, T. (1987): A consistent refined theory for a symmetric laminate. Mechanics Research Communications. 14, 107–113
Pandya, B. N.; Kant, T. (1988): Finite element analysis of laminated composite plates using s higher-order displacement model. Compos. Sci. & Tech. 32, 137–155
Phan, N. D.; Reddy, J. N. (1985): Analysis of laminated composite plates using a higher order shear deformation theory. Int. J. Num. Meth. Eng. 21, 2201–2219
Reddy, J. N. (1984): A simple higher-order theory for laminated composite plates. J. Appl. Mech. 51, 745–752
Reddy, J. N. (1985): A review of the literature on finite-element modeling of laminated composite plates. Shock & Vib. Digest. 17, 3–8
Reddy, J. N. (1990): A review of refined theories of laminated composite plates. Shock & Vib. Digest. 22, 3–17
Reissner, E. (1945): The effect of transverse shear deformation on the bending of elastic plates. J. Appl. Mech. 12, 69–77
Reissner, E.; Stavsky, Y. (1961): Bending and stretching of certain types of heterogeneous aeolotropic elastic plates. J. Appl. Mech. 28, 402–408
Reissner, E. (1975): On transverse bending of plates, including the effects of transverse shear deformation. J. Appl. Mech. 11, 569–573
Ren, J. G. (1986): A new theory of laminated plates. Compos. Sci. Tech. 26, 225–239
Rhodes, J.; Harvey, J. M. (1977): Examination of plate post-buckling behavior. ASCE. EM3 103, 461–477
Riks, E. (1972): The application of Newton's method to the problem of elastic stability. J. Appl. Mech. 39, 1060–1066
StarnesJr., J. H.; KnightJr., N. F.; Rouse, M. (1985): Postbuckling behavior of selected flat stiffened graphite-epoxy panels loaded in compression. AIAA J. 23, 1236–1246
Toledano, A.; Murakami, M. (1987): A high-order laminated plate theory with improved in-plane response. Int. J. Solids Struct. 23, 111–131
Touratiev, M. (1988): A refined theory for thick composite plates. Mech. Res. Comm. 15, 229–236
Valisetty, R. R.; Rehfield, L. W. (1985): A theory for stress analysis of composite laminates. AIAA J. 23, 1111–1117
Vijayakumar, K.; Krishnamurthy, A. V. (1988): Iterative modeling for stress analysis of composite laminates. Compos. Sci. Tech. 32, 165–181
Wempner, G. A. (1991): Discrete approximations related to nonlinear theories of solids. Int. J. Solids Struct. 7, 1581–1599
Whitney, J. M.; Pagano, N. J. (1970): Shear deformation in heterogeneous anisotropic plates. J. Appl. Mech. 37, 1031–1036
Yang, P. C.; Norris, C. M.; Stavsky, Y. (1966): Elastic wave propagation in heterogeneous plates. Int. J. Solids Struct. 2, 665–684
Yin, W.-L. (1985): Axisymmetric buckling and growth of a circular delamination in a compressed laminate. Int. J. Solids Struct. 21, 503–514
Zhang, J. D.; Atluri, S. N. (1988): Postbuckling analysis of shallow shells by the field-boundary-element method. Int. J. Num. Meth. Eng. 26, 571–587
Author information
Authors and Affiliations
Additional information
Communicated by G. Yagawa, September 13, 1991
Rights and permissions
About this article
Cite this article
Yoda, T., Atluri, S.N. Postbuckling analysis of stiffened laminated composite panels, using a higher-order shear deformation theory. Computational Mechanics 9, 390–404 (1992). https://doi.org/10.1007/BF00364005
Issue Date:
DOI: https://doi.org/10.1007/BF00364005