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Abstract
Nonlinear behavior of Functionally Graded Material (FGM) skew plates under in-plane load is investigated here using a shear deformable eight noded iso-parametric plate bending finite element. The material is graded in the thickness direction according to a power-law distribution in terms of volume fractions of the constituents. The effective material properties are estimated using Mori-Tanaka homogenization method. The nonlinear governing equations for the FGM plate under in-plane load are solved by Newton-Raphson technique to obtain the out-of-plane central deflection and in-plane displacement of the loaded edge. The existence of bifurcation-type of buckling for FGM plates is examined for different boundary conditions, constituent gradient index, and skew angle.
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References
- Koizumi M., "The Concept of FGM", Ceramic Transaction: Functionally Graded Material. 1993, 34, pp. 3-10.
- Suresh S. and Mortensen A., "Functionally Graded Metals and Metal-ceramic Composites Part 2. Thermomechanical Behavior" Int. Mat. Rev. 1997, 42, pp. 85-116.
- Birman V., "Buckling of Functionally Graded Hybrid Composite Plates", Proceedings of the 10th Conference on Engineering Mechanics, Boulder, Colorado, 1995, 2, pp.1199-1202.
- Feldman E. and Aboudi J., "Buckling Analysis of Functionally Graded Plates Subjected to Uniaxial Loading", Composite Structures, 1997, 38, pp. 29- 36.
- Javaheri R. and Eslami M. R.,"Buckling of Functionally Graded Plates Under in-plane Compressive Loading", ZAMM, 2002, 82, pp.277-283.
- Chen X. L. and Liew K. M., "Buckling of Rectangular Functionally Graded Material Plates Subjected to Nonlinearly Distributed In-plane Edge Loads", Smart Materials and Structures, 2004, 3, pp.1430- 1437.
- Ganapathi M., Prakash T. and Sundararajan N., "Influence of Functionally Graded Material on Buckling of Skew Plates under Mechanical Loads", Journal of Engineering Mechanics, ASCE, 2006, 132 (8), pp.902-905.
- Najafizadeh M. M. and Eslami, M. R., "Buckling Analysis of Circular Plates of Functionally Graded Materials Under Uniform Radial Compression", Int. J. of Mech. Sci., 2002, 44, pp.2479-2493.
- Sharjat B. A. S., Javaheri R. and Eslami M. R.,"Buckling of Imperfect Functionally Graded Plates Under in-plane Compressive Loading", Thin-Walled Structures, 2005, 43, pp.1020-1036.
- Leissa A.W., "Conditions for Laminated Plates to Remain Flat Under Inplane Loading", Composite Structures, 1986, 6, pp.261-270.
- Qatu M. S. and Leissa A. W., "Buckling or Transverse Deflections of Unsymmetrically Laminated Plates Subjected to In-plane Loads", AIAA Journal, 1993, 31, pp.189-194.
- Ayodogdu M., "Conditions for Functionally Graded Plates to Remain Flat Under In-plane Loads by Classical Plate Theory", Composite Structures, 2007 (in press).
- Liew K. M., Yang J. and Kitipornchai S., "Postbuckling of Piezoelectric FGM Plates Subject to Thermoelectro- mechanical Loading", Int. J. of Solids and Struct. 2003, 40, pp.3869-3892.
- Shen H-S., "Postbuckling of FGM Plates with Piezoelectric Actuators Under Thermo-Electro-Mechanical Loadings", Int. J. of Solids and Struct., 2005, 42, pp.6101-6121.
- Prathap G., Naganarayana B.P. and Somashekar B. R., "A Field Consistency Analysis of the Isoparametric Eight-noded Plate Bending Elements", Computers and Structures, 1988, 29, pp.857-874.
- Ganapathi M., Varadan TK. and Sarma B.S., "Nonlinear Flexural Vibrations of Laminated Orthotropic plates", Computers and Structures, 1991, 39, pp.685- 688.
- Cheng Z-Q. and Batra R. C., "Three Dimensional Thermoelastic Deformations of a Functionally Graded Elliptic Plate. Composites Part B", Engineering, 2000, 31, pp.97-106.
- Mori T. and Tanaka K., "Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions". Acta Metallurgica, 1973, 21, pp.571-574.
- Zienkiewicz O. C. and Taylor R. L., "The Finite Element Method", McGraw-Hill, Singapore, 1989.
- Hinton E. and Huang H. C., "A Family of Quadrilateral Mindlin Plate Elements with Substitute Shear Strain Fields", Computers and Structures, 1986, 23, pp. 409-431.
- Singha M. K., Ramachandra L. S. and Bandyopadhyay J. N., "Thermal Postbuckling Analysis of Laminated Composite Plates", Composite Structures, 2001, 54, pp.453-458.
- Wang S., "Buckling Analysis of Skew Fibre-reinforced Composite Laminates Based on First-order shear Deformation Theory", Composite Structures, 1997, 37, pp.5-19.
- Sundaresan P., Singh G. and Rao G. V., "Buckling and Post-buckling Analysis of Moderately Thick Laminated Rectangular Plates", Computers and Structures, 1996, 61, pp.79-86.
References
Koizumi M., "The Concept of FGM", Ceramic Transaction: Functionally Graded Material. 1993, 34, pp. 3-10.
Suresh S. and Mortensen A., "Functionally Graded Metals and Metal-ceramic Composites Part 2. Thermomechanical Behavior" Int. Mat. Rev. 1997, 42, pp. 85-116.
Birman V., "Buckling of Functionally Graded Hybrid Composite Plates", Proceedings of the 10th Conference on Engineering Mechanics, Boulder, Colorado, 1995, 2, pp.1199-1202.
Feldman E. and Aboudi J., "Buckling Analysis of Functionally Graded Plates Subjected to Uniaxial Loading", Composite Structures, 1997, 38, pp. 29- 36.
Javaheri R. and Eslami M. R.,"Buckling of Functionally Graded Plates Under in-plane Compressive Loading", ZAMM, 2002, 82, pp.277-283.
Chen X. L. and Liew K. M., "Buckling of Rectangular Functionally Graded Material Plates Subjected to Nonlinearly Distributed In-plane Edge Loads", Smart Materials and Structures, 2004, 3, pp.1430- 1437.
Ganapathi M., Prakash T. and Sundararajan N., "Influence of Functionally Graded Material on Buckling of Skew Plates under Mechanical Loads", Journal of Engineering Mechanics, ASCE, 2006, 132 (8), pp.902-905.
Najafizadeh M. M. and Eslami, M. R., "Buckling Analysis of Circular Plates of Functionally Graded Materials Under Uniform Radial Compression", Int. J. of Mech. Sci., 2002, 44, pp.2479-2493.
Sharjat B. A. S., Javaheri R. and Eslami M. R.,"Buckling of Imperfect Functionally Graded Plates Under in-plane Compressive Loading", Thin-Walled Structures, 2005, 43, pp.1020-1036.
Leissa A.W., "Conditions for Laminated Plates to Remain Flat Under Inplane Loading", Composite Structures, 1986, 6, pp.261-270.
Qatu M. S. and Leissa A. W., "Buckling or Transverse Deflections of Unsymmetrically Laminated Plates Subjected to In-plane Loads", AIAA Journal, 1993, 31, pp.189-194.
Ayodogdu M., "Conditions for Functionally Graded Plates to Remain Flat Under In-plane Loads by Classical Plate Theory", Composite Structures, 2007 (in press).
Liew K. M., Yang J. and Kitipornchai S., "Postbuckling of Piezoelectric FGM Plates Subject to Thermoelectro- mechanical Loading", Int. J. of Solids and Struct. 2003, 40, pp.3869-3892.
Shen H-S., "Postbuckling of FGM Plates with Piezoelectric Actuators Under Thermo-Electro-Mechanical Loadings", Int. J. of Solids and Struct., 2005, 42, pp.6101-6121.
Prathap G., Naganarayana B.P. and Somashekar B. R., "A Field Consistency Analysis of the Isoparametric Eight-noded Plate Bending Elements", Computers and Structures, 1988, 29, pp.857-874.
Ganapathi M., Varadan TK. and Sarma B.S., "Nonlinear Flexural Vibrations of Laminated Orthotropic plates", Computers and Structures, 1991, 39, pp.685- 688.
Cheng Z-Q. and Batra R. C., "Three Dimensional Thermoelastic Deformations of a Functionally Graded Elliptic Plate. Composites Part B", Engineering, 2000, 31, pp.97-106.
Mori T. and Tanaka K., "Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions". Acta Metallurgica, 1973, 21, pp.571-574.
Zienkiewicz O. C. and Taylor R. L., "The Finite Element Method", McGraw-Hill, Singapore, 1989.
Hinton E. and Huang H. C., "A Family of Quadrilateral Mindlin Plate Elements with Substitute Shear Strain Fields", Computers and Structures, 1986, 23, pp. 409-431.
Singha M. K., Ramachandra L. S. and Bandyopadhyay J. N., "Thermal Postbuckling Analysis of Laminated Composite Plates", Composite Structures, 2001, 54, pp.453-458.
Wang S., "Buckling Analysis of Skew Fibre-reinforced Composite Laminates Based on First-order shear Deformation Theory", Composite Structures, 1997, 37, pp.5-19.
Sundaresan P., Singh G. and Rao G. V., "Buckling and Post-buckling Analysis of Moderately Thick Laminated Rectangular Plates", Computers and Structures, 1996, 61, pp.79-86.