ABSTRACT
This chapter devotes to consideration of some of the foundations of the theory of elastic stability. It examines the meaning of stability, especially in the context of variational methods, and discusses methods of obtaining stability bounds for various problems. The chapter utilizes the simple Euler column problem to indicate a variety of approaches. It also utilizes variational methods to set forth approximate techniques for solving stability problems involving columns and plates. The chapter considers the elastic stability of columns, through which extends the conclusions reached above and presents again, by example, other notions pertinent to the understanding of elastic stability. The theories are fundamentally different, as the first is based on the incompressible (inextensible) behavior of the column centerline, while the latter is based on the coupling between the out-of-plane bending deflection and the (nonlinear) strains in the middle surface of the structure.
