Inelastic Buckling-From a Designer's Viewpoint

Abstract

I HAS B E E N nearly 70 years since the first analysis was made of a stability problem in which the compressive stress was greater than the proportional limit of the material. The classical papers of Engesser, Considere, von Karman, and Southwell, 1 f published between 1889 and 1912, extended the column theory of Euler into the inelastic or plastic range. By rationalizing the short column theory, these authors also strengthened the Euler presentation which was in some disrepute due to a lack of agreement with experiments in the short column range. Although some papers continued to be published in this field after 1912, it was not until approximately 1940 t ha t a new major a t tack was made on the problem. This was largely due to the increased efforts of the aircraft designer to achieve lighter and more efficient structures for the air frame. Still more recently a new parameter has been added to the problem, t ha t of elevated temperature and the creep associated with high temperatures in structural materials. These temperatures arise from the aerodynamic heating tha t , in turn, is caused by the ever-increasing flight velocities of aircraft and missiles. The problem of plasticity and plastic buckling is many-faceted, and the l i terature on it is extensive. Prager has indicated tha t the field can be roughly divided into three major parts—namely, (1) the physical theory of plasticity, which is based on the general concepts of the structure of mat te r ; (2) the mathematical theory of plasticity, which is concerned with a critical discussion of the fundamental stress-strain laws in the plastic range; and (3) the solution of concrete problems of stress and strain in the plastic range. I t is the third of the above fields of interest t ha t will be discussed here. The questions t ha t will be posed, and to which partial answers have been found, are the following: from an engineering design standpoint, what stability problems concerning stresses above the proportional limit have been solved to such an extent t ha t design equations are available to the stress analyst; what are the orders of accuracy of these equations; and what areas need further experimental and /o r theoretical investigation? The hypothetical engineer asking these questions is not, in general, concerned with