Vol 53, No 1 (2018)

Within the framework of the theory of large elastoplastic deformations generalized to the case of viscous and thermophysical properties of materials, we give a solution of a sequence of coupled problems on the onset and development of a flow in a material layer filling the gap between two rigid coaxial cylindrical surfaces under increasing pressure drop and on the subsequent flow deceleration under decreasing pressure gradient. Here the thermophysical and deformation processes are coupled, and the yield stress depends on temperature. Heat production due to the layer material friction against the rough cylindrical boundary surfaces is taken for an additional heat source.

We use the solution of a one-dimensional problem of the theory of thermal stresses in an elastoplastic tube heated on its interior surface and maintained at a constant temperature on the exterior surface as an example to make a comparison of both the results and solution methods depending on the choice of each of three conventional yield criteria: piecewise linear criteria of maximum shear and maximum reduced stresses and a smooth criterion of maximum octahedral stresses. It is established that while the transition of stresses from the face of the Tresca prism to its edge (change in the flow regime) in the first of the piecewise linear yield criteria takes place at the plastic flow onset, in the second one, this transition occurs on the elastoplastic boundary. The yield stress is assumed to be temperature dependent.

The results of an experimental study of quasistatic and dynamic penetration of solids into sand concrete are presented.Cylindrical bodies with conical tips and a ball were used. The resistance forces are compared for the taper angles of 180◦, 90◦, 60◦, 30◦, 9.5◦ and a ball. The flow character in the quasistatic immersion regime and in dynamic immersion due to inertia is determined.

The article deals with constant-speed sliding of a smooth indenter along the boundary of a viscoelastic layer coupled with a rigid half-space. The problem is investigated in a quasistatic statement by constructing a solution for the case of a load sliding, distributed inside of a rectangular element, which allows using the boundary element method and an iterative procedure. The effect of sliding velocity and layer thickness on the contact pressure distribution and the deformation component of the frictional force is studied.

On the example of a one-dimensional nonstationary problem of oblique impact on the boundary of a nonlinear elastic isotropic half-space, the question of the manifestation of nonlinear deformation effects via basic evolution equations is studied. Much attention is given to the behavior of the solution behind the leading edge of a quasi-transverse shock wave. For particular cases of boundary conditions, it is shown that the onset region of the evolution equation of a quasi-transverse wave is preceded by a series of preliminary transitions to the intermediate internal problems of the small parameter method determined by the type of preliminary bulk deformation. This deformation consistently affects the distortion of the characteristic coordinates and the leading edge of the quasitransverse process. As a consequence, the transition to the evolution equation of quasi-transverse waves occurs with simultaneous change of all independent variables of the boundary value problem.

New ways of numerical simulation of nonstraight laying of reinforcing fibers in panels of variable rigidity and variants of setting optimization problems for them are proposed. The problem of parametric optimization of the dimensions and stacking of carbon fiber reinforced plastic layers in the design of the bracket for the installation of a star tracker was solved.

For piecewise linear models of multimodulus elastic media, exact analytical solutions of one-dimensional dynamic deformation problemswith plane or sphericalwave surfaces are presented. Compression-extension regimes with the appearance of a centered Riemann wave and extensioncompression with formation of a shock wave are considered. As the main solution method for the compression phase, we use the method of inverse determination of the boundary condition from known information on the nature ofmotion of the shock wave. Essential qualitative differences of the solutions obtained from the corresponding classical results for linearly elastic media are especially important in the study of the dynamics of porous and cohesive granular media.