DETERMINATION OF STRESSES IN A CYLINDRICAL SHELL TAKING INTO ACCOUNT HOLES

Abstract

Perforated elements are widely used in collectors of nuclear power plants, chemical devices, construction equipment. Perforation allows to reduce the material consumption of an expensive product, to facilitate the design and is performed for design reasons. At the same time, there is a concentration of stresses near the holes, which significantly reduces the durability of the perforated parts of the products, as well as determines the relevance of the study of the stress-strain state in the perforated parts. The paper presents an analytical description of the problem of the theory of elasticity for a perforated thick-walled cylinder in thermomechanical formulation. The problem of cylindrical bodies of rotation was considered in the axisymmetric three-dimensional formulation in displacements with the definition of stress and strain tensors. It is shown that numerical methods, in particular the finite element method, must be used to solve problems on the stress-strain state of perforated cylinders. For thick-walled perforated cylinders, it is advisable to use finite three-dimensional elements. Problems for homogeneous thick-walled and perforated cylinders were solved using three-dimensional and shell finite elements. Both four-node shell and three-dimensional eight-node prismatic finite elements were used in the numerical solution of this problem. The loading of the cylinder with holes was internal pressure. From the comparison of the results it follows that in the absence of holes it is enough to use two-dimensional shell finite elements, but in the presence of holes in perforated thick-walled shells there is a concentration of stress, so in this case it is advisable to consider the problem in three-dimensional form. It is shown in the paper that the solution of the problem taking into account the consolidated stiffness for the shell model gives an underestimated value of stresses, because it does not take into account the stress concentration on the inner surface of the shell. The coefficient of stress concentration obtained in the work due to the presence of holes was equal to two.