Vol 54, No 3 (2019)

The problem of inelastic bending deformation of plates is formulated using the idea of the method of time steps in rectangular Cartesian and cylindrical coordinate frames based on two versions of the Tymoshenko theory and taking into account plates weakened resistance to transverse shears during plane-cross reinforcement and. The mechanical behavior of the materials of the components of the composition is described by the nonlinear-hereditary Rabotnov’s creep theory. The bending behavior under creep conditions of ring plates made of D16T aluminum alloy and axisymmetrically reinforced along boron and spiral-circular trajectories by boron fibers is studied. It is shown that under short-term loading the classical theory is quite acceptable for calculating the mechanical behavior of such composite structures. Under prolonged loading in the creep process, transverse shear deformations actively and rapidly develop in the binder material of the plate. Therefore, taking into account the weakened resistance to transverse shear after calculating the creep of thin-walled reinforced structural elements is needed. The compliance of the reinforced plates under long-term loading predicted by the classical theory and the first version of the Tymoshenko’s theory is significantly less than that determined by the second version of the Tymoshenko’s theory. Therefore it is recommended to use the second version of the Tymoshenko’s theory for adequate calculations of the creep of the reinforced plates.

An idea of using computer mechanics for inertial navigation systems is given and examples are presented. The equations, algorithms, and properties of the pendulum-type strapdown inertial navigation system are analyzed. As a result, it has been stated that such a system is analogous to analytical systems. A similar comparison for both semi-analytical and strapdown inertial navigation systems, in which the Schuler’s pendulum models are described in a horizontal coordinate system, is carried out. An analogy of their properties is established. By comparing the analytical system, platform axes of which are directed along the axes of the inertial coordinate system (orientation of the Schuler’s pendulum is also described in the inertial coordinate system), and the strapdown inertial navigation system with the same orientation of the platform’s computer model (the comparison is also made for the operation algorithms of such systems), an analogy of such systems has been established. The degree of use of computer mechanics in all types of strapdown inertial navigation systems is much greater than in platform ones. According to the degree of utilization for principles of computer mechanics, types of inertial navigation systems can be arranged in the following order: strapdown pendulum, other strapdown systems, semi-analytical, analytical, and geometric platform inertial navigation systems. Their accuracy depends on the degree of sophistication of the element base, that is, on sensitive elements and on-board computers. We claim that the smaller the volume and mass of the mechanical part of the system the better its weight-and-dimensional characteristics and cost.

The article deals with the experimental and theoretical study of deformation processes in a reinforced concrete structure, which is a part of a hybrid precast/cast-in-place building on a scale of 1:2. The propagation of elastic waves caused by shock impact on various structure parts is analyzed. The results of numerical simulation of elastic wave propagation through structural elements are presented. Based on the data of mathematical modeling, experimental algorithms for structure investigation have been developed. The parameters of the shock impact and the characteristics of the equipment measuring the deformation response have been selected. The data of a physical experiment on shock-wave exposure on a structure in the elastic deformation mode are presented.

The article deals with the modeling the stiffness properties of flange rotor joints, which significantly determine their overall dynamics. Investigation is conducted on the example of flange joint of the compressor shaft and turbine disk in the GTE gas generator. It is noted that the moment stiffness of the flange joint is a nonlinear function of bending moment, the magnitude of which is associated with the rotor deflection due to action of unbalanced forces. It is shown that the value of moment stiffness substantially depends on bolt tightening force, axial force, tensile connection, and contact deformations of the flange surfaces. An analysis of the influence of moment stiffness values obtained for different models of flange connection on the general dynamics of the rotor has showed the necessity to take into account the whole set of factors acting at a place of joint.

The stress-strain state (SSS) of three-layer shells with cutouts has not been sufficiently studied, which is one of the reasons limiting their use in modern designs. Based on the block finite element approach, a refined model of the layer-by-layer analysis of the SSS of irregular three-layer shells is developed. The considered approach allows us to fairly accurately model the heterogeneity of the package of layers and the aggregate layer, the conditions for fixing the layers and the application of loads to them, to apply various models to study the bearing layers and the aggregate. Using approximations of the finite elements (FE) of the bearing layers, approximating functions of the displacements of the three-dimensional FE of the aggregate are constructed and based on them, a model is developed for the accurate calculation of the SSS, allowing to take into account the change in the characteristics of the material and the stress state, including the radial coordinate in the aggregate layer. The study of the stress-strain state in the layers of three-layer shells with cuts, including through-holes, was carried out in a refined formulation. A significant reduction and smoothing of the stresses of the edge effect in the layers of three-layer shells with non-through cutouts compared with through cut due to the redistribution of the load was revealed, since a significant part of it is taken over by layers with undisturbed continuity.

The problem of energy-optimal turn maneuver of a solid having arbitrary dynamic configuration is considered within the framework of the quaternion formulation with arbitrary boundary conditions and without restrictions imposed on the control function. This turn maneuver is performed in fixed time. In the class of generalized conical motions, the optimal turn maneuver problem has been modified. As a result, it is possible to obtain its analytical solution. The analytical solution of the modified problem can be considered as an approximate (quasi-optimal) solution of the traditional optimal turn maneuver problem. An algorithm for the quasi-optimal turn maneuver of a solid is given. Given numerical examples illustrate that the solution of the modified problem is a close approximation for the solution of the traditional problem on the optimal turn maneuver of a solid. In addition, the examples show that the kinematic characteristics of the optimal motion in the traditional problem (attitude quaternion and angular velocity vector) depend weakly on the dynamic configuration of a solid and are mainly determined by the boundary conditions of the problem (anyway, for ϕ≥ π/2 where ϕ is the Euler angle). The weak dependence of the kinematic characteristics of the optimal motion of a solid on its dynamic configuration guarantees the closeness of the solutions of the modified and traditional problems of optimal turn maneuver of a body with an arbitrary dynamic configuration.