Postbuckling analysis of stiffened laminated composite panels, using a higher-order shear deformation theory

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 C2-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.

[1]  N. Pagano,et al.  Exact Solutions for Composite Laminates in Cylindrical Bending , 1969 .

[2]  C. Chia,et al.  Geometrically Nonlinear Behavior of Composite Plates: A Review , 1988 .

[3]  Ahmed K. Noor,et al.  Assessment of Shear Deformation Theories for Multilayered Composite Plates , 1989 .

[4]  J. N. Reddy A review of the literature on finite-element modeling of laminated composite plates , 1985 .

[5]  Liviu Librescu,et al.  Analytical solution of a refined shear deformation theory for rectangular composite plates , 1987 .

[6]  A. V. Krishna Murty,et al.  On higher order shear deformation theory of laminated composite panels , 1987 .

[7]  Tarun Kant,et al.  Finite element analysis of laminated composite plates using a higher-order displacement model , 1988 .

[8]  Lawrence W. Rehfield,et al.  A theory for stress analysis of composite laminates , 1985 .

[9]  Liviu Librescu,et al.  A few remarks concerning several refined theories of anisotropic composite laminated plates , 1989 .

[10]  E. Reissner,et al.  Bending and Stretching of Certain Types of Heterogeneous Aeolotropic Elastic Plates , 1961 .

[11]  Ahmed K. Noor,et al.  Assessment of computational models for multilayered anisotropic plates , 1990 .

[12]  Yin Wan-Lee,et al.  Axisymmetric buckling and growth of a circular delamination in a compressed laminate , 1985 .

[13]  J. Reddy A Simple Higher-Order Theory for Laminated Composite Plates , 1984 .

[14]  G. Wempner Discrete approximations related to nonlinear theories of solids , 1971 .

[15]  S. Atluri,et al.  Post‐buckling analysis of shallow shells by the field‐boundary‐element method , 1988 .

[16]  Y. K. Cheung,et al.  FINITE STRIP METHOD IN STRUCTURAL ANALYSIS , 1976 .

[17]  J. N. Reddy,et al.  Analysis of laminated composite plates using a higher‐order shear deformation theory , 1985 .

[18]  R. D. Mindlin,et al.  Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates , 1951 .

[19]  M. V. V. Murthy,et al.  An improved transverse shear deformation theory for laminated antisotropic plates , 1981 .

[20]  Y. Stavsky,et al.  Elastic wave propagation in heterogeneous plates , 1966 .

[21]  K. Vijayakumar,et al.  Iterative modelling for stress analysis of composite laminates , 1988 .

[22]  M. Anderson,et al.  A general panel sizing computer code and its application to composite structural panels , 1978 .

[23]  J. Ren,et al.  A new theory of laminated plate , 1986 .

[24]  E. Reissner,et al.  On transverse bending of plates, including the effect of transverse shear deformation☆ , 1975 .

[25]  Jasbir S. Arora,et al.  On implementation of computational algorithms for optimal design 1: Preliminary investigation , 1988 .

[26]  T. R. Graves Smith,et al.  A finite strip method for the post-locally-buckled analysis of plate structures , 1978 .

[27]  J. H. Starnes,et al.  Postbuckling behavior of graphite-epoxy panels , 1984 .

[28]  O. C. Zienkiewicz,et al.  A refined higher-order C° plate bending element , 1982 .

[29]  M. Levinson,et al.  An accurate, simple theory of the statics and dynamics of elastic plates , 1980 .

[30]  J. N. Reddy,et al.  A review of refined theories of laminated composite plates , 1990 .

[31]  Charles W. Bert,et al.  A critical evaluation of new plate theories applied to laminated composites , 1984 .

[32]  E. Riks The Application of Newton's Method to the Problem of Elastic Stability , 1972 .

[33]  N. Pagano,et al.  Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates , 1970 .

[34]  M. J. Clarke,et al.  A study of incremental-iterative strategies for non-linear analyses , 1990 .

[35]  J. Whitney,et al.  Shear Deformation in Heterogeneous Anisotropic Plates , 1970 .

[36]  W. Jefferson Stroud,et al.  General Panel Sizing Computer Code and Its Application to Composite Structural Panels , 1979 .

[37]  Maurice Touratier,et al.  A refined theory for thick composite plates , 1988 .

[38]  R. Christensen,et al.  A HIGH-ORDER THEORY OF PLATE DEFORMATION, PART 1: HOMOGENEOUS PLATES , 1977 .

[39]  James M. Harvey,et al.  Examination of Plate Post-Buckling Behavior , 1977 .

[40]  A. V. Krishna Murty,et al.  Flexure of composite plates , 1987 .

[41]  Tarun Kant,et al.  A Simple Finite Element Formulation of a Higher-order Theory for Unsymmetrically Laminated Composite Plates , 1988 .

[42]  A. R. Cusens,et al.  A finite strip method for the geometrically nonlinear analysis of plate structures , 1983 .

[43]  Ahmed K. Noor,et al.  Buckling and postbuckling analyses of laminated anisotropic structures , 1989 .

[44]  Tarun Kant,et al.  A CONSISTENT REFINED THEORY FOR FLEXURE OF A SYMMETRIC LAMINATE , 1987 .

[45]  Hidenori Murakami,et al.  A high-order laminated plate theory with improved in-plane responses☆ , 1987 .

[46]  E. Reissner The effect of transverse shear deformation on the bending of elastic plates , 1945 .