The static stability problems of an elastic continuum subjected to follower-type loading

Abstract This study involves the fundamental aspects of stability of elastic systems and its solutions, and presents a new formulation of the static stability criterion. The purpose of the study is to show that by using the constructed self-adjoint boundary problem of a deflected elastic continuum subjected to follower-type loads, a static method of solution may be utilized. To demonstrate this approach we start with the illustrative examples where we can find either a physical analogy for determination of self-adjoint equations, or a mathematical determination of these self-adjoint equations using the Green's integral (for the static solution). Determination of the coefficients for constructing self-adjoint equations can then be accomplished solving the original equations.