M. Khaing and A. V. Tkacheva
Calculation of the Thermal Stresses in an Elastoplastic Plate Heated by Local Heat Source
153 - 158
2018
12
8
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/10009422
https://publications.waset.org/vol/140
World Academy of Science, Engineering and Technology
The work is devoted to solving the problem of temperature stresses, caused by the heating point of the round plate. The plate is made of elastoplastic material, so the PrandtlReis model is used. A piecewiselinear condition of the IshlinskyIvlev flow is taken as the loading surface, in which the yield stress depends on the temperature. Piecewiselinear conditions (Treska or IshlinskyIvlev), in contrast to the Mises condition, make it possible to obtain solutions of the equilibrium equation in an analytical form. In the problem under consideration, using the conditions of Tresca, it is impossible to obtain a solution. This is due to the fact that the equation of equilibrium ceases to be satisfied when the two Tresca conditions are fulfilled at once. Using the conditions of plastic flow IshlinskyIvlev allows one to solve the problem. At the same time, there are also no solutions on the edge of the IshlinskyIvlev hexagon in the planestressed state. Therefore, the authors of the article propose to jump from the edge to the edge of the mine edge, which gives an opportunity to obtain an analytical solution. At the same time, there is also no solution on the edge of the IshlinskyIvlev hexagon in a plane stressed state; therefore, in this paper, the authors of the article propose to jump from the side to the side of the mine edge, which gives an opportunity to receive an analytical solution. The paper compares solutions of the problem of plate thermal deformation. One of the solutions was obtained under the condition that the elastic moduli (Young&39;s modulus, Poisson&39;s ratio) which depend on temperature. The yield point is assumed to be parabolically temperature dependent. The main results of the comparisons are that the region of irreversible deformation is larger in the calculations obtained for solving the problem with constant elastic moduli. There is no repeated plastic flow in the solution of the problem with elastic moduli depending on temperature. The absolute value of the irreversible deformations is higher for the solution of the problem in which the elastic moduli are constant; there are also insignificant differences in the distribution of the residual stresses.
Open Science Index 140, 2018