Modeling of external force action on a shell mold for pouring steel

The paper formulates and solves the problem of determining the force effect of the support filler on the resistance of the shell form during the crystallization of liquid metal (steel) in it. As the leading physical quantity that affects the crack resistance of shell form, the tensile normal stress that occurs in the outer layers of the mold in the first temporary moments when pouring liquid metal into it is accepted.
The force factor affecting the stress-strain state of is the friction between the shell form and the support filler, which appears during the elastic expansion of the outer layer in the shell form as a result of temperature exposure from the crystallizing liquid metal. A mathematical programming problem (min max function) is formulated to determine the coefficient of friction between the shell form and support filler in order to obtain the lowest value of the normal tensile stress in the support filler over the considered area in the presence of a system of constraints.
An axisymmetric body of rotation having four regions is considered: liquid metal, solid metal, shell shape, support filler, which is considered to be a solid body that creates friction at the contact point with the outer layer of. To solve the problem, the equations of the linear theory of elasticity, the equation of thermal conductivity and a proven numerical method are used, according to which the area under study is divided by a system of orthogonal surfaces into elements. For each element, a formulated system of equations is written in a difference form. An algorithm for solving the problem is developed and the results of the solution are presented, stress diagrams in the support filler are constructed according to the found value of the coefficient of friction. The analysis of the obtained results is given.