A Mathematical Model of the Strain and Stress Kinetics during Welding of Thin-Walled Products

¹ Kutaisi Technological Academy, 4600 Kutaisi, Georgia
² Akaki Tsereteli State University, Engineering-Technical faculty, 4600 Kutaisi, Georgia

Abstract

The paper dwells on the mathematical model of the strain and stress of the elements of the thin-walled systems. A version of the sophisticated theory of shells with the use of several base surfaces has been developed at the Kutaisi Technical University [3,8]. The theory is based on a kinematic hypothesis thereby facilitating the construction of a three-dimensional field of deformation of shell by deformation of two or more surfaces. The use of several base surfaces allows not only for accounting the transverse shears and crimping, but also, with account for the shell thickness, for modeling the mechanical and thermal phenomena on the front surfaces of the layers. In doing so, the geometrical and mechanistic interpretation of generalized displacements and generalized internal forces is clear enough, and the basic equations are simple. The model is based on a geometrically linear version of the theory of shells with the use of several base surfaces and the theory of non-isothermal plastic flow [4]. The developed mathematical model of the strain and stress kinetics allows for evaluating the temperature and strain-stress states of thin-walled products during welding.