Postbuckling of shear deformable FGM cylindrical shells surrounded by an elastic medium

Abstract This paper presents a study on the postbuckling response of a shear deformable functionally graded cylindrical shell of finite length embedded in a large outer elastic medium and subjected to axial compressive loads in thermal environments. The surrounding elastic medium is modeled as a tensionless Pasternak foundation that reacts in compression only. The postbuckling analysis is based on a higher order shear deformation shell theory with von Karman–Donnell-type of kinematic nonlinearity. The thermal effects due to heat conduction are also included and the material properties of functionally graded materials (FGMs) are assumed to be temperature-dependent. The nonlinear prebuckling deformations and the initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the postbuckling response of the shells and an iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region between the shell and the elastic medium. Numerical solutions are presented in tabular and graphical forms to study the postbuckling behavior of FGM shells surrounded by an elastic medium of tensionless Pasternak foundation, from which the postbuckling results for FGM shells with conventional elastic foundations are also obtained for comparison purposes. The results reveal that the unilateral constraint has a significant effect on the postbuckling responses of shells subjected to axial compression in thermal environments when the foundation stiffness is sufficiently large.

[1]  Hui‐Shen Shen,et al.  Thermomechanical postbuckling of unilaterally constrained shear deformable laminated plates with temperature-dependent properties , 2006 .

[2]  Hui-Shen Shen,et al.  Thermal postbuckling behavior of shear deformable FGM plates with temperature-dependent properties , 2007 .

[3]  D. N. Paliwal,et al.  Free vibrations of circular cylindrical shell on Winkler and Pasternak foundations , 1996 .

[4]  Hui‐Shen Shen.  Thermal postbuckling behavior of functionally graded cylindrical shells with temperature-dependent properties , 2004 .

[5]  Hui‐Shen Shen.  Postbuckling of axially loaded FGM hybrid cylindrical shells in thermal environments , 2005 .

[6]  G. G. Sheng,et al.  Thermal Vibration, Buckling and Dynamic Stability of Functionally Graded Cylindrical Shells Embedded in an Elastic Medium , 2008 .

[7]  Jin-Guang Teng,et al.  Postbuckling analysis of unilaterally constrained laminated thin plates , 2004 .

[8]  Y. Shimizu,et al.  Buckling Strength of Lining Shells of Pressure Vessels , 1992 .

[9]  沈惠申.  Kármán-type equations for a higher-order shear deformation plate theory and its use in the thermal postbuckling analysis , 1997 .

[10]  Shaker A. Meguid,et al.  Thermomechanical postbuckling analysis of moderately thick functionally graded plates and shallow shells , 2005 .

[11]  Jie Yang,et al.  Postbuckling of internal pressure loaded FGM cylindrical shells surrounded by an elastic medium , 2010 .

[12]  K. Tanaka,et al.  Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .

[13]  Michael J. Forrestal,et al.  Buckling of a long cylindrical shell surrounded by an elastic medium , 1965 .

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

[15]  Y. S. Touloukian.  THERMOPHYSICAL PROPERTIES OF HIGH TEMPERATURE SOLID MATERIALS. , 1967 .

[16]  H. C. Chan,et al.  The stabilisation of the steel liner of a prestressed concrete pressure vessel , 1966 .

[17]  J. N. Reddy,et al.  A higher-order shear deformation theory of laminated elastic shells , 1985 .

[18]  Hui-Shen Shen,et al.  Nonlinear thermal bending response of FGM plates due to heat conduction , 2007 .

[19]  Naotake Noda,et al.  Thermal Stresses in Materials with Temperature-Dependent Properties , 1991 .

[20]  Buckling of Soil-Surrounded Tubes , 1971 .

[21]  Paulo B. Gonçalves,et al.  Nonlinear analysis of structural elements under unilateral contact constraints by a Ritz type approach , 2008 .

[22]  Paulo B. Gonçalves,et al.  Postbuckling Analysis of Plates Resting on a Tensionless Elastic Foundation , 2003 .

[23]  Yoshinobu Tanigawa,et al.  SOME BASIC THERMOELASTIC PROBLEMS FOR NONHOMOGENEOUS STRUCTURAL MATERIALS , 1995 .

[24]  R. Hill.  A self-consistent mechanics of composite materials , 1965 .

[25]  Hui‐Shen Shen,et al.  Postbuckling of FGM cylindrical shells under combined axial and radial mechanical loads in thermal environments , 2005 .

[26]  Jie Yang,et al.  FREE AND FORCED VIBRATION OF REISSNER–MINDLIN PLATES WITH FREE EDGES RESTING ON ELASTIC FOUNDATIONS , 2001 .

[27]  Ian D. Moore,et al.  Simplified theory for the behaviour of buried flexible cylinders under the influence of uniform hoop compression , 1985 .

[28]  James G.A. Croll,et al.  Buckling of cylindrical tunnel liners , 2001 .

[29]  N. Ganesan,et al.  Buckling and free vibration analysis of functionally graded cylindrical shells subjected to a temperature-specified boundary condition , 2006 .

[30]  J. N. Reddy,et al.  THERMOMECHANICAL ANALYSIS OF FUNCTIONALLY GRADED CYLINDERS AND PLATES , 1998 .

[31]  S. L. Fok,et al.  Analysis of the buckling of long cylindrical shells embedded in an elastic medium using the energy method , 2002 .

[32]  M. Eslami,et al.  Thermal Buckling of Simply Supported Piezoelectric FGM Cylindrical Shells , 2007 .

[33]  Flexible buried cylinders: Part III—Buckling behaviour , 1971 .

[34]  Ohseop Song,et al.  Thin-Walled Beams Made of Functionally Graded Materials and Operating in a High Temperature Environment: Vibration and Stability , 2005 .

[35]  Herzl Chai,et al.  Contact buckling and postbuckling of thin rectangular plates , 2001 .

[36]  Hui‐Shen Shen,et al.  THERMOMECHANICAL POSTBUCKLING OF SHEAR DEFORMABLE LAMINATED CYLINDRICAL SHELLS WITH LOCAL GEOMETRIC IMPERFECTIONS , 2002 .

[37]  M. Ashby,et al.  The mechanical properties of natural materials. II. Microstructures for mechanical efficiency , 1995, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[38]  M. R. Eslami,et al.  THERMAL BUCKLING OF FUNCTIONALLY GRADED CYLINDRICAL SHELL , 2003 .

[39]  P. Gonçalves,et al.  Numerical methods for analysis of plates on tensionless elastic foundations , 2001 .

[40]  Buckling of a Short Cylindrical Shell Surrounded by an Elastic Medium , 2000 .

[41]  On the existence of post-buckling solutions of shallow shells under a certain unilateral constraint , 1982 .

[42]  Hui‐Shen Shen.  Thermal Postbuckling of Shear Deformable FGM Cylindrical Shells with Temperature-Dependent Properties , 2007 .

[43]  Lanhe Wu,et al.  Thermoelastic stability of functionally graded cylindrical shells , 2005 .

[44]  Hui‐Shen Shen.  Postbuckling analysis of axially-loaded functionally graded cylindrical shells in thermal environments , 2002 .