NUMERICAL MODELING OF THE STRESS FIELD IN THE CYLINDER WITH HONORS

In this paper, the thermoelastic formulation of the problem of a stress-strain state in a thick-walled cylinder is considered. It is noted that in the case when the bodies of rotation have a complicated geometric shape or heterogeneous physical and mechanical characteristics on the axis of rotation and radius, the use of analytical methods for solving the problem of determining the stress-strain state is ineffective. For example, to solve the problem of a stress-deformed state in a thick-walled cylinder with many openings, using analytical approaches for this, one has to face the problem of summation of infinite series and the calculation of singular integrals; therefore, it is necessary to rely on numerical methods. It is specified that if the method of finite elements is used as a numerical method, then there is also a question of choosing the type of finite elements. In this paper, the problem of the stress state in a perforated thick-walled cylinder with the use of both shell finite elements with four nodes and three-dimensional prismatic finite elements with eight nodes is solved by the method of finite elements in a thermoelastic formulation. The choice of this type of finite elements allows to determine with high accuracy the stress-strain state and take into account the existing local increase of stresses in a cylindrical thick-walled tube with many openings. The obtained field of stresses in a pipe is analyzed and the level of local increase of stresses near the openings of a cylindrical pipe is investigated. It is noted that the magnitude of the obtained coefficient of local stress increase reaches 2. In the work it is shown that the solution of this problem, taking into account the reduced rigidity when using the shell model of the cylinder, gives understated stresses, while the increase of stresses on the inner surface of the shell is not taken into account.