"Вестник МГСУ"

The authors have employed analytical methods to identify the nature of dependence of the elastic modulus distribution over the thickness of a cylinder, loaded by internal pressure p , if the equivalent stress is the same in all points, according to Mohr’s theory of strength. The problem in which dependence of an elastic modulus is to be identified along the radius, and the stress value is available, is called the inverse prob- lem. The idea of the method is that if a certain area of a body has the value of its elastic modulus lower than the one in the homogeneous material, stresses in this area are also reduced. The problem is solved for the case of plane strain and plane stress in the elastic formulation. It is proven that assurance of artificial heterogeneity reduces the maximal equivalent stress. Therefore, we have taken two variants of shells: one having inner radius a = 1 m and outer radius b = 2 m, the other one having inner radius a = 1 m and outer radius b = 0.52 m. The value of the maximal equivalent stress calculated using Mohr’s theory reduces almost two-fold in the first case and 1.5-fold in the second case. Moreover, the use of non-uniform thick-walled cylinders can significantly reduce their thickness with the value of the internal pressure being the same. In our case, the shell thickness reduces from 1 m to 0.52 m, which is almost 2 times. We also proven that the first, second and third strength theories in the case of an axisymmetric problem are the special cases of Mohr’s strength theory. This result coincides with well-known analytical and numerical solutions.

Among the classical works devoted to Solid Mechanics a significant place is occupied by the studies taking into account the physical and geometric nonlinearity. Also there is enough of works, which concern linear problems taking into account the inhomogeneity of the material. At the same time there are very few publications, which take into account both effects (non-linearity and inhomogeneity). This is due to the lack of experimental data on the influence of various factors on the parameters defining the non-linear behavior of the materials. Thus it is of great importance to study the influence of inhomogeneity when solving the problems of structures made of physically nonlinear materials. This article provides a solution to one of the problems of the nonlinear theory of elasticity taking into account the inhomogeneity. The problem is solved in an axisymmetric formulation, i.e. all the parameters of the nonlinear relationship between the intensities of stresses and strains are functions of the radius. The article considers an example - the stress distribution in the inhomogeneous soil massif with a cylindrical cavity.

This paper presents t experimental and numerical studies of cracking in the thick-walled filament-wound cylindrical shells made of fiber reinforced plastic during the manufacturing process (specifically, in the process of curing and cooling). The experiments have shown that, when the cylinder is cooled by optimum cooling regime, at the end of the cooling process the obtained cylinder is monolithic and without ring cracking. In this regard, the residual thermal stresses in thick-walled cylinder in the cooling process is calculated using finite element method with account for transient heat conduction and the temperature dependence of the mechanical properties of the material and the viscoelastic behavior of the polymer. The calculations are conducted for cooling in standard and optimum regimes. The results showed that the maximum radial stress in the most dangerous initial area is several times less when the cylinder is cooled down in the optimum regime than when it is cooled in the standard regime.