卷 231, 编号 5 (2018)

For a countable quasilinear system of differential equations whose coefficients have the form of absolutely and uniformly convergent Fourier series with slowly varying coefficients and frequency, we obtain conditions for the existence of a partial solution of a similar structure. As a result, we establish conditions for the possibility of complete decomposition of a countable linear homogeneous differential system with coefficients of the same structure.

By using the N th order approximation of temperature function and its first derivative by Legendre polynomials, we construct the solution of problem of heat conduction for a thin-walled shallow isotropic shell and deduce the system of resolving equations for the N th approximation. For the first and third approximations, we solve this problem for the case of concentrated heat sources. In the third approximation, we also construct the plots of the dependences of temperature on the distance to the heat source and on the curvature of the shell under the conditions of symmetric or asymmetric stationary heat exchange.

We consider the axisymmetric problem of creep and creep damage of a hollow cylinder and develop a numerical-analytic method for the solution of this nonlinear initial-boundary-value problem. We also present an example of evaluation of creep and the time to fracture for a cylinder loaded by internal pressure. The results accumulated by using a three-dimensional model are compared with the data obtained on the bases of the refined model of the theory of shells.

We consider a problem of contact of an elastic strip with a semiinfinite punch with rounded edge indented into one face of the strip, while the other face of the strip is fixed. Friction forces in the contact zone are neglected. By the Wiener–Hopf method, we obtain the exact analytic solution of the problem. The distributions of contact stresses, the stresses inside the strip and along its fixed face, and the normal displacements of points of a part of the load-free face of the strip are determined. We construct the isochores and determine the position of the point at which the maximum values of the principal shear stresses are attained.

We consider the problem of determination of the parameters of a measurement grid, which guarantees the exactness and stability of the solution of the inverse problem. The choice of the points of measurements is performed under the assumption of existence of the most informative data. We present the results illustrating the influence of the number of measurement points on the data of reconstruction of the parameters of the load function acting upon the cylindrical shell in a strip located along the length of the shell.