Basic relations for physically and geometrically nonlinear problems of deformation of prismatic bodies

Abstract

A number of responsible structures elements, which are prismatic bodies, are undergoing a significant shaping in the process of manufacturing and operation, which often take place at high temperatures, which leads to changes in the physical and mechanical characteristics of the material and the development of various types of deformations. The solution authenticity of such problems of the deformable body mechanics depends essentially on the adequacy of the physical relations used to the considered processes of the material deformation, in particular taking into account the presence of large deformations.

The initial relations of thermo elastic-plastic deformation of prismatic bodies are given in the paper. A Cartesian coordinate system used as a basis for the study of prismatic bodies. The relation for determining the deformation components through displacement values in the local coordinate system are formulated. The components of the complete thermo elastic-plastic and creep deformation tensor are taken as amount of appropriate deformation components. The plastic deformation described with associated law of plastic yield, a creep deformation – in accordance with the theory of strengthening The basic concepts, indifference of deformation tensors, with the condition of energy conjunction in description of the shaping process are laid out on the basis of classical work.