A very simple example of thermoelastic stability — thermal buckling of a rectangular plate — has been treated in Section 4.10. The solution of the problem was based there on the approximate solution of the governing differential equation. An entirely different approach will now be presented in this chapter. It is known as Lyapunov’s direct (or second) method. The advantage of this method is that it is not necessary to explicitly solve the differential equation which, particularly in nonlinear problems, may be a difficult task. The method also provides a deeper insight into the philosophy of the problem. On the other hand, the construction of the Lyapunov functional may be quite complicated.
KeywordsHelmholtz Free Energy Column Stability Governing Differential Equation Thermal Buckling Thermoelastic System
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