258
7 Mathematical Models of Functionally Graded Beams in Temperature Field
Fig. 7.20 Beam deflection versus external load for different k x and fixed temperature T [reprinted
with permission from the International Journal of Non-linear Mechanics publishers]
beam deflection. Observe that the type of the temperature load and its intensity have
an influence on the initial beam deflection for q = 0, which yields an increase in the
beam deflection while losing stability.
7.6.4.4 Influence of the Beam Curvature
In Fig. 7.21, dependencies T (w) for the boundary conditions (7.89) and for different types of temperature fields (Table 7.14) are reported. The used notations “−”
and “+” refer to the dependencies construction for the heat transfer equation with
and without curvature parameter k x , respectively. It has been found that occurrence
of the beam curvature in the heat transfer equations implies a change in the beam
deflection for the same values of the temperature load.
The most remarkable influence of the beam curvature is given by the type 5
temperature field (Table 7.14), where also an essential difference comparing to the
case k x = 36 has been detected. In the case of temperature fields of types 1, 2 and
7 Mathematical Models of Functionally Graded Beams in Temperature Field
Fig. 7.20 Beam deflection versus external load for different k x and fixed temperature T [reprinted
with permission from the International Journal of Non-linear Mechanics publishers]
beam deflection. Observe that the type of the temperature load and its intensity have
an influence on the initial beam deflection for q = 0, which yields an increase in the
beam deflection while losing stability.
7.6.4.4 Influence of the Beam Curvature
In Fig. 7.21, dependencies T (w) for the boundary conditions (7.89) and for different types of temperature fields (Table 7.14) are reported. The used notations “−”
and “+” refer to the dependencies construction for the heat transfer equation with
and without curvature parameter k x , respectively. It has been found that occurrence
of the beam curvature in the heat transfer equations implies a change in the beam
deflection for the same values of the temperature load.
The most remarkable influence of the beam curvature is given by the type 5
temperature field (Table 7.14), where also an essential difference comparing to the
case k x = 36 has been detected. In the case of temperature fields of types 1, 2 and