ABSTRACT
In this chapter, the authors present some of the foundations of the theory of elastic stability. They examine the meaning of stability, especially in the context of variational methods, and discuss methods of obtaining stability bounds for various problems. The authors use the simple Euler column problem to indicate a variety of approaches and variational methods to set forth approximate techniques for solving stability problems involving columns and plates. They say that a configuration in a state of equilibrium is stable if, after some slight disturbance causing a small change in the configuration there follows a return to the original configuration. The authors use variational considerations to present powerful approximating techniques giving us discretized approximate solutions to important classes of boundary-value problems. Modern design of complex structures makes much use of the finite element procedure, as do other areas of study of fluid mechanics, heat transfer, and electromagnetic theory, where difficult problems must be solved.
