A modified couple stress theory for buckling analysis of S-FGM nanoplates embedded in Pasternak elastic medium

Abstract Based on a modified couple stress theory, a model for sigmoid functionally graded material (S-FGM) nanoplates on elastic medium is developed. The two main advantages of the modified couple stress theory over the classical couple stress theory are the inclusion of asymmetric couple stress tensor and the involvement of only one material length scale parameter. Analytical solution for buckling analysis of S-FGM nanoplates on elastic medium is presented. The present models contain one material length scale parameter and can capture the size effect, and two-constituent material variation through the plate thickness. The governing equations are derived from minimum total potential energy principle based on a modified couple stress theory, and the power law variation of the material through the thickness of the plate. Material properties of functionally graded plate are assumed to vary according to two power law distribution of the volume fraction of the constituents. It is assumed that the elastic medium is modeled as Pasternak elastic medium. Buckling response of rectangular S-FGM nanoplates is derived, and the obtained results are compared well with reference solutions. The effects of power law index, small scale coefficient, aspect ratio, side-to-thickness ratio, loading types, and elastic medium parameter on the buckling load of S-FGM nanoplates have been discussed.

[1]  Seung-Eock Kim,et al.  Closed-form solution for buckling analysis of thick functionally graded plates on elastic foundation , 2013 .

[2]  J. Reddy,et al.  Analytical solutions for bending, vibration, and buckling of FGM plates using a couple stress-based third-order theory , 2013 .

[3]  J. Reddy.  MICROSTRUCTURE-DEPENDENT COUPLE STRESS THEORIES OF FUNCTIONALLY GRADED BEAMS , 2011 .

[4]  Abdelouahed Tounsi,et al.  Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes , 2013 .

[5]  Yiming Fu,et al.  Modeling and analysis of microtubules based on a modified couple stress theory , 2010 .

[6]  J. N. Reddy,et al.  A non-classical Mindlin plate model based on a modified couple stress theory , 2011 .

[7]  Sung-Cheon Han,et al.  Non-linear analysis of laminated composite and sigmoid functionally graded anisotropic structures using a higher-order shear deformable natural Lagrangian shell element , 2009 .

[8]  P. L. Pasternak.  On a new method of analysis of an elastic foundation by means of two foundation constants , 1954 .

[9]  Gang Bao,et al.  Multiple cracking in functionally graded ceramic/metal coatings , 1995 .

[10]  R. D. Mindlin.  MICROSTRUCTURE IN LINEAR ELASTICITY , 1999 .

[11]  Liao-Liang Ke,et al.  Size effect on dynamic stability of functionally graded microbeams based on a modified couple stress theory , 2011 .

[12]  P. Tong,et al.  Couple stress based strain gradient theory for elasticity , 2002 .

[13]  Reza Masoomi,et al.  Deflection and stress analysis of thin FGM skew plates on Winkler foundation with various boundary conditions using extended Kantorovich method , 2013 .

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

[15]  M. Asghari,et al.  A size-dependent model for functionally graded micro-plates for mechanical analyses , 2013 .

[16]  M. Bodaghi,et al.  Stability analysis of functionally graded rectangular plates under nonlinearly varying in-plane loading resting on elastic foundation , 2011 .

[17]  Glaucio H. Paulino,et al.  Transient thermal stress analysis of an edge crack in a functionally graded material , 2001 .

[18]  Abdolreza Ohadi,et al.  Three-dimensional free vibration of variable thickness thick circular and annular isotropic and functionally graded plates on Pasternak foundation , 2011 .

[19]  Wanji Chen,et al.  A modified couple stress model for bending analysis of composite laminated beams with first order shear deformation , 2011 .

[20]  Sritawat Kitipornchai,et al.  Free vibration of size-dependent Mindlin microplates based on the modified couple stress theory , 2012 .

[21]  N. Fleck,et al.  Strain gradient plasticity , 1997 .

[22]  Huu-Tai Thai,et al.  SIZE-DEPENDENT FUNCTIONALLY GRADED KIRCHHOFF AND MINDLIN PLATE MODELS BASED ON A MODIFIED COUPLE STRESS THEORY , 2013 .

[23]  Yen-Ling Chung,et al.  MECHANICAL BEHAVIOR OF FUNCTIONALLY GRADED MATERIAL PLATES UNDER TRANSVERSE LOAD-PART I: ANALYSIS , 2006 .

[24]  Sung-Cheon Han,et al.  MECHANICAL VIBRATION AND BUCKLING ANALYSIS OF FGM PLATES AND SHELLS USING A FOUR-NODE QUASI-CONFORMING SHELL ELEMENT , 2008 .

[25]  Reza Ansari,et al.  Dynamic stability analysis of functionally graded higher-order shear deformable microshells based on the modified couple stress elasticity theory , 2013 .

[26]  R. D. Mindlin.  Micro-structure in linear elasticity , 1964 .

[27]  Abdullah H. Sofiyev,et al.  Torsional vibration and buckling of the cylindrical shell with functionally graded coatings surrounded by an elastic medium , 2013 .

[28]  M. Asghari,et al.  The modified couple stress functionally graded Timoshenko beam formulation , 2011 .

[29]  S. K. Park,et al.  Bernoulli–Euler beam model based on a modified couple stress theory , 2006 .

[30]  T. Hirano,et al.  Multi paradigm expert system architecture based upon the inverse design concept , 1988, Proceedings of the International Workshop on Artificial Intelligence for Industrial Applications.

[31]  Jie Yang,et al.  Nonlinear free vibration of size-dependent functionally graded microbeams , 2012 .

[32]  E. Aifantis.  On the Microstructural Origin of Certain Inelastic Models , 1984 .

[33]  M. Eslami,et al.  An exact solution for thermal buckling of annular FGM plates on an elastic medium , 2013 .

[34]  F. Erdogan,et al.  The crack problem for a nonhomogeneous plane , 1983 .

[35]  S. C. Pradhan,et al.  Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory , 2010 .

[36]  M. Ghayesh,et al.  Nonlinear dynamics of a microscale beam based on the modified couple stress theory , 2013 .

[37]  K. Liew,et al.  PREDICTING NANOVIBRATION OF MULTI-LAYERED GRAPHENE SHEETS EMBEDDED IN AN ELASTIC MATRIX , 2006 .

[38]  Mohsen Asghari,et al.  Geometrically nonlinear micro-plate formulation based on the modified couple stress theory , 2012 .

[39]  M. Asghari,et al.  On the size-dependent behavior of functionally graded micro-beams , 2010 .

[40]  M. Shariyat,et al.  Three-dimensional non-linear elasticity-based 3D cubic B-spline finite element shear buckling analysis of rectangular orthotropic FGM plates surrounded by elastic foundations , 2014 .

[41]  Yen-Ling Chung,et al.  Mechanical behavior of functionally graded material plates under transverse load—Part II: Numerical results , 2006 .

[42]  Huu-Tai Thai,et al.  A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation , 2012 .

[43]  George C. Tsiatas,et al.  A new Kirchhoff plate model based on a modified couple stress theory , 2009 .

[44]  W. T. Koiter.  Couple-stresses in the theory of elasticity , 1963 .

[45]  J. N. Reddy,et al.  A microstructure-dependent Timoshenko beam model based on a modified couple stress theory , 2008 .