Vol 238, No 2 (2019)

The problem of stability of shells compliant to shear and compression is studied by the finite-element method. On the basis of relations of the geometrically nonlinear theory of thin shells compliant to shear and compression (six-mode version), we write the key equations for the determination of their initial postcritical state and formulate the corresponding variational problem. A numerical scheme of the finite-element method is constructed for the solution of the problems of stability of these shells. The order of the rate of convergence of the scheme proposed for the numerical solution of the problems of stability is investigated.

We formulate a complete system of relations of the local gradient electromagnetothermomechanics of electrically conductive nonferromagnetic polarizable solid media. The nonlocal character of the constitutive relations of the proposed mathematical model is explained by the presence of electric quadrupole moments in the polarization current. As a result of taking into account these moments, the space of parameters of the thermodynamic state of the body is expanded by including a pair of additional conjugate parameters, namely, the quadrupole moment and the gradient of the vector of electric-field intensity. It is shown that the developed model takes into account the electromechanical interaction for materials with high level of symmetry (isotropic materials) and describes the flexoelectric and thermopolarization effects. We also present the key system of equations for a physically and geometrically linear medium.

We consider conjugate boundary-value problems of heat exchange for the cases where a viscous incompressible liquid moves through channels with noncanonical cross section flowing around a bundle of rods. The influence of the type of packing on the velocity and temperature distributions is investigated. For the solution, we use the R-functions method in combination with the Ritz variational method. We consider the cases of cyclic, staggered, and rectangular packing of fuel elements.

We study the problem of optimization of motion of a two-link manipulator, which performs transport operations under the action of controls (moments of forces in the hinges). The initial and the final position of the gripping device of the manipulator and the time of the operation are regarded as known. The quality of motion of the manipulator is estimated by a quadratic functional. Possible configurations of the manipulator at the beginning and at the end of the operation are taken into account. We propose an algorithm for the construction of suboptimal solutions of the problem based on the parametrization of the angular coordinates of the manipulator by the sum of a cubic polynomial and a finite trigonometric series and on the use of the methods of inverse problems of dynamics and numerical procedures of nonlinear programming. The influence of configurations of the manipulator and the parameters of the trigonometric series on the characteristics of the suboptimal process is analyzed.