Abstract:
On the basis of Kirchhoffs assumption and geometrically nonlinear theo~y for
axially extensible bars, this thesis presents an exact mathematical model for the
thermal post-buckling of an elastic bar with different immovable end conditions and
subjected to a transversely non-uniformly temperature rising. In order to describe
accurately the post-buckling of the heated bar with axial extension, an axial
stretching, !!(x) has been introduced, and the arc length, s(x), of the deformed central
axis is taken as one of the basic unknown functions in the mathematical model.
This is a two point boundary value problem of first order ordinary differential
equations with high nonlinearity. Using the multi-segment integration method in
conjunction ~ith the concept of analytical continuation, the nonlinear boundary value
problems are numerically solved. The range of safe buckling temperature is
determined, and some comparisons between the nonlinear and linear buckling
behaviors of the bars are discussed. Some quantitative results of thermal postbuckled
configurations and secondary equilibrium paths of the problem with some
specific parameters, for example, buckling temperature and the slenderness ratio are
obtai?ed for immovably pinned-pinned, pinned-fixed and fixed-fixed ends.
The numerical results show that both the critical buckling temperature and the postbuckled
temperature of the bar are sensitively influenced by the slenderness ratio,
which is distinctively different from that of the post-buckling of the inextensible rod
subjected to mechanical compressive loads. In addition, it is found that the
magnitude of the axially constrained force reaches a maximum value at the onset of
the buckling state and then decreases as the temperature increases in the post-.
buckling regime. Moreover, the influences of the transverse temperature change on
the thermal post-buckling deformations are examined.
