MECHANICAL BEHAVIOR OF FUNCTIONALLY GRADED MATERIAL PLATES UNDER TRANSVERSE LOAD-PART I: ANALYSIS

Abstract An elastic, rectangular, and simply supported, functionally graded material (FGM) plate of medium thickness subjected to transverse loading has been investigated. The Poisson’s ratios of the FGM plates are assumed to be constant, but their Young’s moduli vary continuously throughout the thickness direction according to the volume fraction of constituents defined by power-law, sigmoid, or exponential function. Based on the classical plate theory and Fourier series expansion, the series solutions of power-law FGM (simply called P-FGM), sigmoid FGM (S-FGM), and exponential FGM (E-FGM) plates are obtained. The analytical solutions of P-, S- and E-FGM plates are proved by the numerical results of finite element method. The closed-form solutions illustrated by Fourier series expression are given in Part I of this paper. The closed-form and finite element solutions are compared and discussed in Part II of this paper. Results reveal that the formulations of the solutions of FGM plates and homogeneous plates are similar, except the bending stiffness of plates. The bending stiffness of a homogeneous plate is Eh 3 /12(1 −  ν 2 ), while the expressions of the bending stiffness of FGM plates are more complicated combination of material properties.

[1]  Patrick Kwon,et al.  Automating the Design Process and Powder Processing of Functionally Gradient Materials , 1997, Composites and Functionally Graded Materials.

[2]  Y-D. Lee,et al.  Residual/thermal stresses in FGM and laminated thermal barrier coatings , 1994 .

[3]  M. Petyt,et al.  Thermal stresses III: 1989, edited by R. B. Hetnarski, Amsterdam, New York: Elsevier Science Publishers. Price (hardback): Dfl. 375·00 (Amsterdam), US$183·00 (New York): pp.574 + x.ISBN 0-444-70447-7 , 1991 .

[4]  Shaker A. Meguid,et al.  Nonlinear analysis of functionally graded plates and shallow shells , 2001 .

[5]  Robert J. Asaro,et al.  Crack deflection in functionally graded materials , 1997 .

[6]  Yen-Ling Chung,et al.  Cracking in coating–substrate composites with multi-layered and FGM coatings , 2003 .

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

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

[9]  S. Suresh,et al.  Fundamentals of functionally graded materials , 1998 .

[10]  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.

[11]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[12]  Richard L. Williamson,et al.  Finite element analysis of thermal residual stresses at graded ceramic‐metal interfaces. Part II. Interface optimization for residual stress reduction , 1993 .

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

[14]  Gang Bao,et al.  Crack bridging in functionally graded coatings , 1998 .

[15]  D. A. Howells,et al.  Energy and finite element methods in structural mechanics, By I. H. Shames, C. L. Dym, Hemisphere Publishing Corp., New York, 1986, No. of pages: 757. Price:$44.95 , 1988 .

[16]  R. Batra,et al.  STRESS INTENSITY RELAXATION AT THE TIP OF AN EDGE CRACK IN A FUNCTIONALLY GRADED MATERIAL SUBJECTED TO A THERMAL SHOCK , 1996 .

[17]  J. N. Reddy,et al.  Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates , 1998 .

[18]  F. Erdogan,et al.  CRACK PROBLEMS IN FGM LAYERS UNDER THERMAL STRESSES , 1996 .

[19]  Masayuki Niino,et al.  Recent development status of functionally gradient materials. , 1990 .

[20]  K. Liew,et al.  Active control of FGM plates with integrated piezoelectric sensors and actuators , 2001 .

[21]  Jacob Aboudi,et al.  Buckling analysis of functionally graded plates subjected to uniaxial loading , 1997 .

[22]  D. Munz,et al.  Stress Analysis In A Two Materials Joint With A Functionally Graded Material , 1997 .

[23]  S. Suresh,et al.  Determination of processing-induced stresses and properties of layered and graded coatings: Experimental method and results for plasma-sprayed NiAl2O3 , 1997 .

[24]  Naotake Noda,et al.  Crack-Tip Singular Fields in Nonhomogeneous Materials , 1994 .