Abstract
Thermoelastic buckling behavior of thick rectangular plate made of functionally graded materials is investigated in this article. The material properties of the plate are assumed to vary continuously through the thickness of the plate according to a power-law distribution. Three types of thermal loading as uniform temperature raise, nonlinear and linear temperature distribution through the thickness of plate are considered. The coupled governing stability equations are derived based on the Reddy’s higher-order shear deformation plate theory using the energy method. The resulted stability equations are decoupled and solved analytically for the functionally graded rectangular plates with two opposite edges simply supported subjected to different types of thermal loading. A comparison of the present results with those available in the literature is carried out to establish the accuracy of the presented analytical method. The influences of power of functionally graded material, plate thickness, aspect ratio, thermal loading conditions and boundary conditions on the critical buckling temperature of aluminum/alumina functionally graded rectangular plates are investigated and discussed in detail. The critical buckling temperatures of thick functionally graded rectangular plates with various boundary conditions are reported for the first time and can be served as benchmark results for researchers to validate their numerical and analytical methods in the future.
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Abbreviations
- a, b:
-
Length and width of plate, respectively
- h :
-
Plate thickness
- x, y, z:
-
Rectangular Cartesian coordinates
- P(z), P c , P m :
-
Material properties of the functionally graded material (FGM), ceramic and metal
- E(z), E c , E m :
-
Young’s modulus of the FGM, ceramic and metal
- K(z), K c , K m :
-
Coefficient of thermal conductivity of the FGM, ceramic and metal
- α (z), α c , α m :
-
Coefficient of thermal expansion of the FGM, ceramic and metal
- n :
-
Power of FGM
- ν :
-
Poisson’s ratio
- U1, U2, U3:
-
Components of displacement field
- u, v, w:
-
Displacements of mid-plane of the plate in the x, y and z directions, respectively
- ψ x , ψ y :
-
Rotation functions
- ε xx , ε yy :
-
Normal strains
- γ xy , γ xz , γ yz :
-
Shear strains
- σ xx , σ yy :
-
Normal stresses
- σ xy , σ xz , σ yz :
-
Shear stresses
- Q11, Q22, Q12:
-
Elements of the reduced stiffness matrix
- N i , M i , P i , Q j , R j :
-
Stress resultants
- NT, MT, PT:
-
Thermal stress resultants
- T(x, y, z):
-
Temperature distribution
- T c , T m :
-
Temperatures of full-ceramic and full-metallic surfaces of the plate
- A ij , B ij , C ij , D ij , F ij , H ij :
-
Plate stiffness coefficients
- \({u^{0}, v^{0}, w^{0}, {\psi _x^0}, {\psi _y^0}}\) :
-
Displacement components related to equilibrium state
- \({u^{1}, v^{1}, w^{1}, {\psi _x^1}, {\psi _y^1}}\) :
-
Incremental displacement components
- \({N_i^0, M_i^0, P_i^0, Q_j^0, R_j^0 }\) :
-
Stress resultants related to equilibrium state
- \({N_i^1, M_i^1, P_i^1, Q_j^1, R_j^1}\) :
-
Incremental stress resultants
- \({B_1, B_2,\hat{{B}}, C_1, C_2, \hat{{C}}, \overline{{C}}, H_1, \hat{{H}}, A_2, \hat{{A}}, \hat{{F}}}\) :
-
Constant material coefficients
- \({\overline{{D}}}\) :
-
Equivalent flexural rigidity of the FG plate
- \({\varphi _4 }\) :
-
Boundary layer function
- m :
-
Number of half-waves in the x direction
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Bodaghi, M., Saidi, A.R. Thermoelastic buckling behavior of thick functionally graded rectangular plates. Arch Appl Mech 81, 1555–1572 (2011). https://doi.org/10.1007/s00419-010-0501-0
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DOI: https://doi.org/10.1007/s00419-010-0501-0