A variable-kinematic model for variable stiffness plates: Vibration and buckling analysis

Abstract This paper presents an advanced approximate technique for the vibration and buckling analysis of variable stiffness plates. The formulation is based on a variable-kinematic approach and is developed in the context of a variational framework together with the method of Ritz. Any set of boundary conditions can be accounted for, while loading conditions of pure axial compression are assumed. Results are validated against finite element predictions and solutions available in the literature, demonstrating the accuracy of the proposed method in terms of eigenvalues and modal shape descriptions. A novel set of vibration and buckling results is provided for moderately thick variable stiffness plates, including monolithic and sandwich configurations.

[1]  Asme,et al.  A collection of technical papers : 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference AIAA/ASME Adaptive Structures Forum April 19-22, 1993/LA Jolla, CA , 1993 .

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

[3]  E. Carrera,et al.  Variable-Kinematics Approach for Linearized Buckling Analysis of Laminated Plates and Shells , 2010 .

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

[5]  Calvin J. Ribbens,et al.  Analysis of tow placed, parallel fiber, variable stiffness laminates , 1996 .

[6]  M. Hyer,et al.  Innovative design of composite structures: The use of curvilinear fiber format in composite structure design , 1990 .

[7]  Erasmo Carrera,et al.  Analysis of thick isotropic and cross-ply laminated plates by radial basis functions and a Unified Formulation , 2011 .

[8]  J. Reddy.  Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

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

[10]  Paul A. Lagace,et al.  Buckling and postbuckling of laminated composite plates with ply dropoffs , 1989 .

[11]  H. Akhavan,et al.  Natural modes of vibration of variable stiffness composite laminates with curvilinear fibers , 2011 .

[12]  António J.M. Ferreira,et al.  A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates , 2003 .

[13]  Paul M. Weaver,et al.  Buckling analysis, design and optimisation of variable-stiffness sandwich panels , 2016 .

[14]  L. Dozio,et al.  Exact refined buckling solutions for laminated plates under uniaxial and biaxial loads , 2015 .

[15]  Paul M. Weaver,et al.  Buckling analysis of stiffened variable angle tow panels , 2014 .

[16]  Z. Gürdal,et al.  Design of variable stiffness composite panels for maximum fundamental frequency using lamination parameters , 2007 .

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

[18]  E. Carrera,et al.  Thermo-Mechanical Buckling Analysis of Anisotropic Multilayered Composite and Sandwich Plates by Using Refined Variable-Kinematics Theories , 2013 .

[19]  Chiara Bisagni,et al.  Single-Stringer Compression Specimen for the Assessment of Damage Tolerance of Postbuckled Structures , 2011 .

[20]  Zafer Gürdal,et al.  Buckling response of laminates with spatially varying fiber orientations , 1993 .

[21]  Erasmo Carrera,et al.  Vibration Analysis of Anisotropic Simply Supported Plates by Using Variable Kinematic and Rayleigh-Ritz Method , 2011 .

[22]  Z. Gürdal,et al.  Design of variable-stiffness conical shells for maximum fundamental eigenfrequency , 2008 .

[23]  E. Carrera.  Theories and finite elements for multilayered, anisotropic, composite plates and shells , 2002 .

[24]  Yoshihiro Narita,et al.  Vibration design of laminated fibrous composite plates with local anisotropy induced by short fibers and curvilinear fibers , 2011 .

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

[26]  Zafer Gürdal,et al.  Design Tailoring for Pressure Pillowing Using Tow-Placed Steered Fibers , 2008 .

[27]  Jerzy Warminski,et al.  A review on the mechanical behaviour of curvilinear fibre composite laminated panels , 2014 .

[28]  Z. Gürdal,et al.  Variable stiffness composite panels : Effects of stiffness variation on the in-plane and buckling response , 2008 .

[29]  Arthur W. Leissa,et al.  Vibration and buckling of rectangular composite plates with variable fiber spacing , 1990 .

[30]  R. N. Jorge,et al.  Buckling analysis of sandwich plates with functionally graded skins using a new quasi‐3D hyperbolic sine shear deformation theory and collocation with radial basis functions , 2012 .

[31]  E. Carrera,et al.  Advanced variable kinematics Ritz and Galerkin formulations for accurate buckling and vibration analysis of anisotropic laminated composite plates , 2011 .

[32]  E. Carrera,et al.  Higher-order theories and radial basis functions applied to free vibration analysis of thin-walled beams , 2016 .

[33]  Srinivas Kodiyalam,et al.  Optimization of tow fiber paths for composite design , 1995 .

[34]  L. Dozio.  Exact vibration solutions for cross-ply laminated plates with two opposite edges simply supported using refined theories of variable order , 2014 .

[35]  Lorenzo Dozio,et al.  Ritz analysis of vibrating rectangular and skew multilayered plates based on advanced variable-kinematic models , 2012 .

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

[37]  R. Olmedo,et al.  Composite laminates with spatially varying fiber orientations - 'Variable stiffness panel concept' , 1992 .

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

[39]  Chiara Bisagni,et al.  Two-step procedure for fast post-buckling analysis of composite stiffened panels , 2013 .

[40]  Erasmo Carrera.  A class of two-dimensional theories for anisotropic multilayered plates analysis , 1995 .

[41]  E. Carrera,et al.  Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique , 2013 .

[42]  C. Bisagni,et al.  Single-mode solution for post-buckling analysis of composite panels with elastic restraints loaded in compression , 2012 .

[43]  Ahmed K. Noor,et al.  Assessment of continuum models for sandwich panel honeycomb cores , 1997 .

[44]  Nicholas Fantuzzi,et al.  Higher-order theories for the free vibrations of doubly-curved laminated panels with curvilinear reinforcing fibers by means of a local version of the GDQ method , 2015 .

[45]  J. Reddy,et al.  Buckling analysis of isotropic and laminated plates by radial basis functions according to a higher-order shear deformation theory , 2011 .

[46]  Paul M. Weaver,et al.  Postbuckling analysis of variable angle tow composite plates under shear load , 2013 .

[47]  J. Reddy,et al.  Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory , 1985 .

[48]  Chiara Bisagni,et al.  Fast Tool for Buckling Analysis and Optimization of Stiffened Panels , 2009 .