The model of the total state function for structural materials

摘要

This paper applies the theoretical method of the structural total state function to obtain control partial differential equations, path equations, and constitutive relations of the total state function of structural materials, as well as three analytical solutions for special states, namely the plane-form solution, cylindrical-form solution, and spherical-form solution. According to the research, the total state function of elastic-perfectly plastic materials is completely consistent in form with the strength theory of classic elastic-plastic theory; moreover, the path equation is consistent with the flow rule, and the constitutive relation conforms completely to the form in classic elastic-plastic theory as well. So far, these equations have been able to obtain conclusions and results that completely agree with classic elastic-plastic theory by means of applying the theories of the structural total state function to elastic-perfectly plastic materials. More importantly, the concepts, theories and methods of the total state function unify the strength theory, flow rule, and constitutive relation in classic elastic-plastic theory under a theoretical framework, endowing them with a unified theoretical basis.