254
7 Mathematical Models of Functionally Graded Beams in Temperature Field
Table 7.14 Thermal load types, boundary conditions and associated temperature distributions
[reprinted with permission from the International Journal of Non-Linear Mechanics publishers]
Type no.
Boundary condition
Temperature distribution
Type 1
T (x, z) = T z = −1/2
0 < x < 1
T (x, z) = 0 z = 1/2
0 < x < 1
T (x, z) = 0 x = 1
−1/2 <
z < 1/2
T (x, z) = 0 x = 0
−1/2 <
z < 1/2
Type 2
T (x, z) = T z = −1/2
0 < x < 1
∂ T
∂z = const z = 1/2
0 < x < 1
T (x, z) = 0 x = 1
−1/2 <
z < 1/2
T (x, z) = 0 x = 0
−1/2 <
z < 1/2
Type 3
T (x, z) = T z = −1/2
0 < x < 0.5
∂ T
∂z = const z = −1/2
0.5 < x < 1
T (x, z) = 0 x = 1
−1/2 <
z < 1/2
T (x, z) = 0 x = 0
−1/2 <
z < 1/2
Type 4
T (x, z) = T z = −1/2
0 < x < 1
T (x, z) = 0 z = 1/2
0 < x < 1
T (x, z) = 0 x = 1
−1/2 <
z < 1/2
T (x, z) = T x = 0
−1/2 <
z < 1/2
Type 5
T (x, z) = 0 z = −1/2
0 < x < 1
T (x, z) = 0 z = 1/2
0 < x < 1
T (x, z) = 0 x = 1
−1/2 <
z < 1/2
T (x, z) = T x = 0
−1/2 <
z < 1/2