Buckling analysis of stiffened variable angle tow panels

Variable angle tow (VAT) laminates have previously shown enhanced buckling performance compared to conventional straight fibre laminates. In this study, an analytical method is developed for the buckling analysis of a novel blade stiffened VAT panel to allow this potential to be more fully exploited. The prebuckling and buckling analysis, performed on a representative section of a blade stiffened VAT panel, are based on a generalised Rayleigh–Ritz procedure. The buckling analysis includes a first order shear deformation theory by introducing additional shape functions for transverse shear and is therefore applicable to structures with thick skins relative to characteristic length. Modelling of the stiffener is achieved with two approaches; idealisation as a beam attached to the skin’s midplane and as a rigidly attached plate. Comparing results with finite element analysis (Abaqus) for selected case studies, local buckling errors for the beam model and plate model were found to be less than 3% and 2% respectively, whilst the beam model error for global buckling was between 3% and 10%. The analytical model provides an accurate alternative to the computationally expensive finite element analysis and is therefore suitable for future work on the design and optimisation of stiffened VAT panels.

[1]  Grant P. Steven,et al.  Buckling mode transition in hat-stiffened composite panels loaded in uniaxial compression , 1997 .

[2]  Jeom Kee Paik,et al.  Buckling strength of steel plating with elastically restrained edges , 2000 .

[3]  László P. Kollár,et al.  Local buckling of fiber reinforced plastic composite structural members with open and closed cross sections , 2003 .

[4]  C. Bisagni,et al.  Analytical formulation for local buckling and post-buckling analysis of stiffened laminated panels , 2009 .

[5]  Christian Mittelstedt,et al.  Closed-form analysis of the buckling loads of uniaxially loaded blade-stringer-stiffened composite plates considering periodic boundary conditions , 2007 .

[6]  Paul M. Weaver,et al.  Optimization of Long Anisotropic Laminated Fiber Composite Panels with T-Shaped Stiffeners , 2007 .

[7]  M. W. Hyer,et al.  Use of curvilinear fiber format in composite structure design , 1991 .

[8]  Paul M. Weaver,et al.  Comparison of Variational, Differential Quadrature, and Approximate Closed-Form Solution Methods for Buckling of Highly Flexurally Anisotropic Laminates , 2013 .

[9]  Michael W. Hyer,et al.  Innovative design of composite structures: The use of curvilinear fiber format to improve buckling resistance of composite plates with central circular holes , 1990 .

[10]  E. Reissner ON THE THEORY OF BENDING OF ELASTIC PLATES , 1944 .

[11]  Layne T. Watson,et al.  Improved Genetic Algorithm for the Design of Stiffened Composite Panels , 1994 .

[12]  W. R. Dean On the Theory of Elastic Stability , 1925 .

[13]  F. Williams,et al.  Optimum design features of VICONOPT, an exact buckling program for prismatic assemblies of anisotropic plates , 1990 .

[14]  J. Reddy Energy and variational methods in applied mechanics : with an introduction to the finite element method , 1984 .

[15]  鷲津 久一郎 Variational methods in elasticity and plasticity , 1982 .

[16]  Paul M. Weaver,et al.  Approximate analysis for buckling of compression loaded long rectangular plates with flexural/twist anisotropy , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[17]  Charles Libove,et al.  A general small-deflection theory for flat sandwich plates , 1948 .

[18]  Raphael T. Haftka,et al.  Buckling and failure characteristics of compression-loaded stiffened composite panels with a hole , 1994 .

[19]  Paul Seide The effect of longitudinal stiffeners located on one side of a plate on the compressive buckling stress of the plate-stiffener combination , 1953 .

[20]  Paul Seide,et al.  Compressive buckling of simply supported plates with longitudinal stiffeners , 1949 .

[21]  Christos Kassapoglou,et al.  Design and Analysis of Composite Structures: With Applications to Aerospace Structures , 2010 .

[22]  Samuel T. IJsselmuiden,et al.  Design of variable-stiffness composite panels for maximum buckling load , 2009 .

[23]  Chiara Bisagni,et al.  Buckling Analysis and Optimization of Stiffened Composite Flat and Curved Panels , 2012 .

[24]  D. J. Dawe,et al.  Rayleigh-Ritz vibration analysis of Mindlin plates , 1980 .

[25]  Damodar R. Ambur,et al.  Buckling of arbitrary quadrilateral anisotropic plates , 1994 .

[26]  Paul M. Weaver,et al.  A 2D equivalent single-layer formulation for the effect of transverse shear on laminated plates with curvilinear fibres , 2013 .

[27]  Zafer Gürdal,et al.  Tailoring for strength of composite steered-fibre panels with cutouts , 2010 .

[28]  Michael P. Nemeth,et al.  A Treatise on Equivalent-Plate Stiffnesses for Stiffened Laminated-Composite Plates and Plate-Like Lattices , 2013 .

[29]  Paul M. Weaver,et al.  Buckling analysis and optimisation of variable angle tow composite plates , 2012 .

[30]  Paul M. Weaver,et al.  Prebuckling and buckling analysis of variable angle tow plates with general boundary conditions , 2012 .

[31]  Eivind Steen Elastic buckling and postbuckling of eccentrically stiffened plates , 1989 .

[32]  Mark A. Bradford,et al.  Numerical convergence of simple and orthogonal polynomials for the unilateral plate buckling problem using the Rayleigh-Ritz method , 1999 .

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

[34]  David Bushnell,et al.  PANDA2: Program for Minimum Weight Design of Stiffened, Composite, Locally Buckled Panels , 1987 .

[35]  Paul M. Weaver,et al.  Buckling of variable angle tow plates: from concept, to experiment , 2009 .

[36]  Z. Gürdal,et al.  In-plane response of laminates with spatially varying fiber orientations - Variable stiffness concept , 1993 .

[37]  Martin M. Mikulas,et al.  Buckling of eccentrically stiffened orthotro- pic cylinders , 1965 .

[38]  Paul M. Weaver,et al.  An enhanced single-layer variational formulation for the effect of transverse shear on laminated orthotropic plates , 2010 .

[39]  Zafer Gürdal,et al.  Optimization of Variable-Stiffness Panels for Maximum Buckling Load Using Lamination Parameters , 2010 .

[40]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[41]  L. Kollár,et al.  Mechanics of Composite Structures , 2003 .

[42]  Frank Diederich,et al.  Buckling Strength Of Metal Structures , 2016 .

[43]  Julio F. Davalos,et al.  LOCAL BUCKLING OF COMPOSITE FRP SHAPES BY DISCRETE PLATE ANALYSIS , 2001 .

[44]  Zhangming Wu,et al.  Buckling of VAT plates using energy methods , 2012 .

[45]  Murray L. Scott,et al.  The analysis of skin-to-stiffener debonding in composite aerospace structures , 2002 .

[46]  M. Stein,et al.  BUCKLING BEHAVIOR AND STRUCTURAL EFFICIENCY OF OPEN-SECTION STIFFENED COMPOSITE COMPRESSION PANELS , 1976 .

[47]  William L. Ko,et al.  Combined Compressive and Shear Buckling Analysis of Hypersonic Aircraft Structural Sandwich Panels. , 1991 .

[48]  Christian Mittelstedt,et al.  Closed-form buckling analysis of compressively loaded composite plates braced by omega-stringers , 2009 .