Fundamental Equation of Thermal Stress of Material which does not obey Hooke's Law and its Application

Abstract

The problem of thermal stress has been discussed on the elastic body under Hooke's law and many essays have been developed. The author discusses the problem on pseudo elastic bodies such as cast iron, and develops the fundamental equation of thermal stress in the Cartesian, spherical and cylindrical coordinates under the assumptions of (1) the relation of stress and strain given by Cox and Lang's hyperbola previously introduced by Dr. Kakuzen, (2) strains due to stresses being able to be superposed, and (3) the Poisson's ratio being constant. The author calculates the three dimensional stress problem on a thick cylinder with temperature difference between the inner and outer surfaces and with uniform hydraulic pressure on these surfaces.