Vol 53, No 4 (2018)

The article deals with an arbitrary elastic 3D-system (body) that performs a controlled finite rotation with respect to some fixed axis and small nonstationary oscillations. The system oscillations occur due to external load (power control) or inertial load of the rotational transportation of the carrying body (kinematic control). The linear equations of oscillations are used in normal coordinates, in which motion is represented by eigenmodes of vibrations for system that is free in the rotation angle (including system rotation as a solid body in the case of power control) and for system fixed in rotation angle in the case of kinematic control. It is assumed that the (power or inertial)load acting on the system is proportional to some controlling finite time function from a certain class. The purpose of this article is to solve the problem of system rotation for a certain time from one rest position to another at a given finite angle using the given control function and to eliminate the elastic oscillations on the several lowest eigenmodes at the stopping time.

The relations between the time of the system rotation under the action of a given control function and the eigenmodes frequencies for oscillations being eliminated are obtained on the basis of the exact solutions of the equations in normal coordinates. These relations satisfy the zero initial and final conditions. They are “tuned” by minimizing the positive definite quadratic form written for them by varying the system parameters to fulfill these relations simultaneously for several eigenfrequencies. As an example, the calculations for a model of a symmetrical spacecraft with two identical elastic solar cell panels consisting of four planar non-deformable sections connected by elastic hinges are carried out for comparison and analysis of the results accuracy. The finite rolling motion of the system with the damping at the stopping time of rotation for several (from one to three) lowest eigenmodes of antisymmetric vibrations is considered. The comparisons of the initial equations of motion for the system in generalized coordinates using several simple control functions and the found parameters of the “tuned” system with numerical solutions are accomplished.

The problem of quantitative estimation of the power schemes of structures is considered. The integral characteristic of structures, the “power factor,” which simultaneously reflects the magnitude and extension of the action of internal forces arising from an external load, is discussed. Geometrically similar transformations of constructions are considered. As a measure of the effectiveness of power schemes, a dimensionless criterion is proposed, which is calculated as the ratio of the power factor to the characteristic size and load. Examples of the definition of this criterion for aircraft wings, pressure vessels and structures operating in bending and torsion are given. The application of a dimensionless criterion is demonstrated by comparing the variants of power schemes, building weight formulae for estimating the absolute and relative mass of structures and solving problems of multidisciplinary optimization.

Ablock based finite element approach is proposed for layer-by-layer analysis of the stress strain state (SSS) of three-layer shells with an irregular structure. The shell aggregate can be modeled by the required number of finite elements over its thickness, which allows to take into account the change in the geometric and physico-mechanical properties of the material and the SSS parameters in all three coordinates to which the shell is related. According to the developed algorithm for constructing the finite elements (FE) of the aggregate, the inner and outer surfaces of the shell are accepted as datum surfaces and in the aggregate elements joined to the bearing layers, the same number of nodes is accepted as in the elements of the bearing layers. The same generalized displacements and approximations as for the elements of the bearing layers are taken as the nodal unknowns and the approximating functions of the aggregate, which allows to avoid errors caused by the breakdown of the generalized displacements on the interfaces between the layers. The algorithm for constructing a block-based finite element model for the layer-by-layer SSS analysis is considered using the example of irregular three-layer conical shells with moment-carrying layers and three-dimensional aggregate.

As an example, the problem of the stressed state of a three-layer conical shell with a cut-out and a hatch closed with a lid was solved.

The review paper is devoted to the problem of designing mesh composite structures that are widely used in Russian rocket and space technology. Mesh structures developed in our country and made of composites by the method of automatic continuous winding significantly exceed the traditional stringer and three-layer structures, both metal and composite, in terms of their weight efficiency. The features of the structural-technological concept of aerospace mesh structures, their design methods and basic applications are considered. The results obtained in this area by the scientific school of academician V.V. Vasiliev are discussed.

The fundamental spatial problems of the theory of elasticity such as the problem of constructing Green tensor and the Boussinesq problem of the action of a concentrated force on a half-space are considered. According to the classical theory of elasticity, these problems are singular. It is shown that ananalytical solution of such problems can be constructed by the Papkovich—Neuber representation without invoking symmetry conditions. This makes it possible to present the solution of the problems under consideration in a single form and allows us to write an explicit solution of half-space loaded by a concentrated vector-force having non-zero projections onto the normal to the plane bounding the half-space and onto the plane itself.

This paper deals with the generalized regular solutions of the considered fundamental problems of the elasticity. The solutions are limited at a singular point and damp at infinity.

For a certain class of elastic lattice shells experiencing finite deformations, a continual model using the equations of the so-called six-parameter shell theory has been proposed. Within this model, the kinematics of the shell is described using six kinematically independent scalar degrees of freedom — the field of displacements and turns, as in the case of the Cosserat continuum, which gives reason to call the model under consideration as the theory of micropolar shells. Nonlinear equations of state for the surface energy density of the shell deformation are derived. The obtained relations of the continuum model are a special case of the general defining relations of elastic micropolar shells for finite deformations.