Highly accurate nonlinear three-dimensional finite element elasticity approach for biaxial buckling of rectangular anisotropic FGM plates with general orthotropy directions

Abstract Buckling of the orthotropic FGM plates has not been investigated so far. In the present paper, a highly accurate nonlinear three-dimensional energy-based finite element elasticity formulation is developed for buckling investigation of anisotropic functionally graded plates with arbitrary orthotropy directions. The material properties are assumed to have in-plane orthotropy and transverse heterogeneity. The formulation and results cover uniaxial compression and compression and tension–compression biaxial loading conditions. The governing equations are developed based on the principle of minimum total potential energy and solved based on finite element orthogonal integral equations. To achieve most accurate results, a full compatible Hermitian element with 168 degrees of freedom, which satisfies continuity of the strain and stress components at the mutual edges and nodes of the element a priori, is employed. A variety of loading combinations, orthotropy directions, and aspect ratios is considered and discussed in the results section to draw practical conclusions. Results reveal that when the external loads are exerted in the principal directions of the materials, higher strengths may be achieved.

[1]  Glaucio H. Paulino,et al.  T-stress in orthotropic functionally graded materials: Lekhnitskii and Stroh formalisms , 2004 .

[2]  A. Ugural.  Stresses in Beams, Plates, and Shells , 2009 .

[3]  Qiusheng Li,et al.  Postbuckling of shear deformable laminated plates resting on a tensionless elastic foundation subjected to mechanical or thermal loading , 2004 .

[4]  P. Camanho,et al.  Three-dimensional failure criteria for fiber-reinforced laminates , 2013 .

[5]  L. Sudak,et al.  Three-dimensional analysis of multi-layered functionally graded anisotropic cylindrical panel under thermomechanical loading , 2008 .

[6]  L. Donnell,et al.  Beams, plates and shells , 1976, Finite Element Analysis.

[7]  S. Dag.  Thermal fracture analysis of orthotropic functionally graded materials using an equivalent domain integral approach , 2006 .

[8]  T. Zeng,et al.  The dynamic response of an edge crack in a functionally graded orthotropic strip , 2005 .

[9]  M. R. Eslami,et al.  Buckling of thick functionally graded plates under mechanical and thermal loads , 2007 .

[10]  F. Erdogan,et al.  Interface crack problems in graded orthotropic media: Analytical and computational approaches , 2004 .

[11]  A. Naderi,et al.  An accurate approach for finding the critical buckling stress of thick orthotropic plates , 2013 .

[12]  Senthil S. Vel,et al.  An exact solution for the steady-state thermoelastic response of functionally graded orthotropic cylindrical shells , 2006 .

[13]  M. Shariyat.  A nonlinear double-superposition global–local theory for dynamic buckling of imperfect viscoelastic composite/sandwich plates: A hierarchical constitutive model , 2011 .

[14]  M. Eslami,et al.  Vibration of thermo-electrically post-buckled rectangular functionally graded piezoelectric beams , 2013 .

[15]  Zheng Zhong,et al.  Three-dimensional exact analysis of a simply supported functionally gradient piezoelectric plate , 2003 .

[16]  Z. Karaca,et al.  The vibration and buckling of laminated non-homogeneous orthotropic conical shells subjected to external pressure , 2009 .

[17]  A. Waas,et al.  Modeling the response, strength and degradation of 3D woven composites subjected to high rate loading , 2012 .

[18]  N. Kuruoglu,et al.  Buckling analysis of nonhomogeneous orthotropic thin-walled truncated conical shells in large deformation , 2013 .

[19]  M. Shariyat.  Non-linear dynamic thermo-mechanical buckling analysis of the imperfect sandwich plates based on a generalized three-dimensional high-order global–local plate theory , 2010 .

[20]  Stephen R Hallett,et al.  Effect of fabric compaction and yarn waviness on 3D woven composite compressive properties , 2011 .

[21]  Baozhong Sun,et al.  FEM simulation of 3D angle-interlock woven composite under ballistic impact from unit cell approach , 2010 .

[22]  M. Shariyat.  A generalized high-order global–local plate theory for nonlinear bending and buckling analyses of imperfect sandwich plates subjected to thermo-mechanical loads , 2010 .

[23]  M. Eslami,et al.  Non-linear thermal stability analysis of temperature dependent FGM beams supported on non-linear hardening elastic foundations , 2013 .

[24]  E. Pan,et al.  Exact Solution for Functionally Graded Anisotropic Elastic Composite Laminates , 2003 .

[25]  Yoshihiro Ootao,et al.  Three-dimensional solution for transient thermal stresses of an orthotropic functionally graded rectangular plate , 2007 .

[26]  M. Shariyat,et al.  A Technique to Distinguish the Primary and Secondary Stresses , 1995 .

[27]  Bhavani V. Sankar,et al.  Effect of Z-yarns on the stiffness and strength of three-dimensional woven composites , 2009 .

[28]  M. Shariyat,et al.  Dynamic buckling and post-buckling of imperfect orthotropic cylindrical shells under mechanical and thermal loads, based on the three-dimensional theory of elasticity , 1999 .

[29]  Hui‐Shen Shen.  Postbuckling of shear deformable laminated plates under biaxial compression and lateral pressure and resting on elastic foundations , 2000 .

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

[31]  O. C. Zienkiewicz,et al.  The Finite Element Method: Its Basis and Fundamentals , 2005 .

[32]  Tarun Kant,et al.  A critical review of recent research on functionally graded plates , 2013 .

[33]  M. Shariyat,et al.  Thermal buckling analysis of rectangular composite plates with temperature-dependent properties based on a layerwise theory , 2007 .

[34]  Soheil Mohammadi,et al.  XFEM fracture analysis of orthotropic functionally graded materials , 2013 .

[35]  Frederic Ward Williams,et al.  Biaxial buckling and post-buckling of composite laminated plates on two-parameter elastic foundations , 1997 .

[36]  Huu-Tai Thai,et al.  An efficient and simple refined theory for buckling analysis of functionally graded plates , 2012 .

[37]  Hui‐Shen Shen.  Postbuckling of Reissner—Mindlin plates under biaxial compression and lateral pressure and resting on elastic foundations , 1999 .

[38]  Vladimir Sladek,et al.  Three‐dimensional analysis of functionally graded plates , 2011 .

[39]  Agnieszka Sabik,et al.  Large thermo-elastic displacement and stability FEM analysis of multilayered plates and shells , 2013 .

[40]  K. Huebner.  The finite element method for engineers , 1975 .

[41]  Bahar Uymaz,et al.  Three dimensional mechanical buckling of FG plates with general boundary conditions , 2013 .

[42]  Xian‐Fang Li,et al.  Elastic analysis of rotating functionally graded polar orthotropic disks , 2012 .

[43]  M. Shariyat,et al.  Vibration and dynamic buckling control of imperfect hybrid FGM plates with temperature-dependent material properties subjected to thermo-electro-mechanical loading conditions , 2009 .

[44]  M. Shariyat,et al.  Dynamic buckling of imperfect laminated plates with piezoelectric sensors and actuators subjected to thermo-electro-mechanical loadings, considering the temperature-dependency of the material properties , 2009 .

[45]  K. Bilisik.  Multiaxis 3D Woven Preform and Properties of Multiaxis 3D Woven and 3D Orthogonal Woven Carbon/Epoxy Composites , 2010 .

[46]  J. N. Reddy,et al.  Postbuckling analysis of functionally graded plates subject to compressive and thermal loads , 2010 .

[47]  S. Pinho,et al.  An experimental study of failure initiation and propagation in 2D woven composites under compression , 2011 .

[48]  S. Pinho,et al.  Analytical modelling of the compressive and tensile response of woven composites , 2012 .

[49]  M. Shariyat.  A double-superposition global–local theory for vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates: a complex modulus approach , 2011 .