Part IV. - Further Discussions in the Theory of Elasticity

Abstract

This chapter presents an extended consideration of the material that has been discussed in the previous chapters and of some important problems in the theory of elasticity. The main observable entities of the phenomenon of elasticity in a structure are the elastic force, the resistance of the body to the change, and the change itself that is the deformation. The characteristic of resistance to deformation was described as ER. The variable part of the resistance depends mainly on the geometry of a structure. The value of geometrical stiffness has a dimensional level corresponding to the values of deformation. Geometrical stiffness can be presented in the same scale as deformation. This correction of the equation of deformation gives reliable results both for the deformation and for the rate of change of deformation. Rate of change of deformation describes the elastic behavior of a structure, and more specifically, describes its elastic stability. The limit of elasticity corresponds to the limiting geometrical stiffness, resulting in accurate prediction of the individual limiting stress depending on the geometrical stiffness. Furthermore, the analysis of a graph presenting the function versus an independent variable plays an important and independent role in the selection of the variables and in the construction and verification of analytical description of the phenomenon.