Информационная система "Конференции"

Abstracts

Numerical solution of differential and integral equations

In this work we formulate the technical solutions which make for the ahead of the carbon destruction and cracs based on the thermoelastic model of the aluminum cell. The preheating the aluminum cell connect with with growth of the temperature deformations and stress of the carbon block. It is well known that the destroy of the carbon block under preheating connect with the stuffing seams and cathode blocks. It is detail considered and published in the many works. The deformation source and the reason of cracks of crack appearance under the heating of the cathode blocks is collector steel bar which is hardly assembling in the carbon blocks when the cast iron is inputing to the carbon block. The main reason of the destroy of the carbon block at the preheating aluminum cell is following. The linear temperature coefficients of the steel bar is greater in five time then the linear temperature coefficients of the carbon block. The deformations of the steel bar are an example $1,5%$ under heating to the temperature $700 - 750^o C.$ The begining length of the steel bar increase to the $30 mm$ and width to $2,7 - 4 mm.$The concentration deformation is formed at the neighbour of the steel bar and it's intensity is greater by two order the strength limit of the carbon block. Often the crack is formed at the carbon block corner and go from the inputing cross steel bar corner in the direction to the surface under the angle $45^o.$ The arising through crack assist to the diminution period service aluminum cell and diminish the quality metals. Obvious that this result depend by the temperature character distribution by the height aluminum cell. For the elaborate the technical solutions which make for ahead to exception of the cathode cracks it is necessary to consider the destroy condition under the heating and evaluate the influence the temperature field and constructive cathode factors. We write the production problem in the following form begin{equation} frac{partial sigma_x}{partial x} + frac{partial tau_{xy}}{partial y} = 0, quad frac{partial tau_{xy}}{partial x} + frac{partial sigma_y}{partial y} = 0. end{equation} and the relation between strains and stresses is defined the following equation $$ frac{partial u_x}{partial x} = frac{ 1 - nu^2}{ E} sigma_x - frac{nu , (1+ nu)}{E } sigma_y + ( 1+ nu ) alpha , T, $$ $$ frac{partial u_y}{partial y} = frac{ 1 + nu^2}{ E} sigma_y - frac{nu , (1+ nu)}{E } sigma_x + ( 1+ nu ) alpha , T, $$ $$ frac{partial u_x}{partial y} + frac{partial u_y}{partial x} = frac{2 , (1+ nu)}{E } tau_{xy} . $$

Note. Abstracts are published in author's edition

Mail to Webmaster

|Home Page| |English Part|

Go to Home