Vol 51, No 3 (2016)

We construct a mathematical model describing thermomechanical interaction between composite structure elements (isotropic particles of the matrix and anisotropic short fibers) and the macroscopically isotropic elastic medium with desired thermoelastic characteristics. At the first stage of this model, the self-consistency method is used to obtain relations determining the elasticity moduli of the composite, and at the second stage, the model permits determining its linear thermal expansion coefficient. The dual variational statement of the linear thermoelasticity problem in an inhomogeneous solid permits obtaining two-sided estimates for the bulk elasticity modulus, shear modulus, and linear thermal expansion coefficient of the composite under study. The calculated dependencies presented in the paper permit predicting the thermoelastic characteristics of a composite reinforced by anisotropic short fibers (including those in the form of nanostructure elements).

It was earlier shown that a rod can buckle under the action of a sudden longitudinal load smaller than the Euler critical load. The buckling mechanism is related to excitation of periodic longitudinal waves generated in the rod by the sudden loading, which in turn lead to transverse parametric resonances. In the linear approximation, the transverse vibration amplitude increases unboundedly, and in the geometrically nonlinear approach, beats with energy exchange from longitudinal to transverse vibrations and back can arise. In this case, the transverse vibration amplitude can be significant. In the present paper, we study how this amplitude responds to the following two factors: the smoothness of application of the longitudinal force and the internal friction forces in the rod material.

The conditions of force interaction and friction on the contact between bodies are related to the intermediate layer structure in the contact region, i.e., to the appearance of fracture products or intensive deformation in this region. The subsequent interaction between the bodies occurs through elements of the intermediate layer structure. In the present paper, we determine conditions and the basic mechanism controlling the formation of the interface structure when the interaction between the bodies is implemented through structure elements of the intermediate layer (balls) which are capable of rolling.

We experimentally modeled two modes of motion, namely, the approach of elements to each other and their turn and rolling on the contact interface.We constructed an analytic model corresponding to the mechanism of transformed (viscous) friction under compression shear conditions. We also considered the modes of ball mutual rotation and rolling in direct contact and the effects of free volume variations (dilatancy) near the balls due to these motions.

Various nonlinear effects manifesting themselves in the deformation of filled elastomers are analyzed, and the advantages and restrictions in the use of several constitutive relations proposed to describe the nonlinear viscoelastic behavior of the materials under study are discussed. We also note that further development of models of nonlinear deformation of filled elastomers under finite strains, which would permit describing their deformation properties more completely, is highly desirable.

The axisymmetric problem on the stress-strain state of a long thick-walled circular cylinder made of shape memory alloy experiencing the direct thermoelastic martensite phase transition under the action of constant internal and external pressures and a constant axial force is solved. The problem of limit loads in such a process is also considered.

The theoretical foundations, methods, and algorithms developed to analyze the stability and postbuckling behavior of thin elastic axisymmetric shells are discussed. The algorithm for numerically studying the processes of nonlinear deformation of thin-walled axisymmetric shells by the solution parametric continuation method is generalized to solving the practical problem of design of mechanical actuators of discrete action. The synthesis algorithm is based on the method of changing the subspace of control parameters, which is supplemented with the procedure of smooth transition in changing the subspaces. The efficiency of the proposed algorithm is illustrated by an example of synthesis of a thermobimetallic actuator of discrete action. The procedure of determining an isolated solution, whose existencewas predicted byV. I. Feodosiev, is considered in the framework of studying the process of nonlinear deformation of a corrugated membrane loaded by an external pressure.

We consider the axisymmetric vibrations of a composite structure shaped as a system of thin shells of revolution connected by rings and filled with an ideal incompressible liquid. The structure is divided into independent shell blocks and frame rings. According to the Riesz method, the displacements of each free block treated as a momentless shell are represented as a series in prescribed functions supplemented with local functions of the shell boundary bending.

According to the method of variations in displacements, the axisymmetric vibrations of a liquid in an elastic shell of revolution are described by plane displacement and deplanation of the liquid cross-sections. The plane displacement of the liquid is integrally expressed in terms of the shell normal displacements, and the deplanation is represented as a series in prescribed functions of the axial coordinate. The potential and kinetic energies of the system are first written in terms of generalized coordinates of independent free shell and frame blocks filled with the liquid and with free surfaces at the ends. Then the kinematic conditions of conjugation of the shell edges with the frame and the liquid surfaces are used to eliminate a part of generalized coordinates. Moreover, the generalized coordinates representing the deplanation of the liquid cross-sections in the cavities are also eliminated as cyclic coordinates. As a result, the potential and kinetic energies of the systemare written in terms of the basic generalized coordinates of the composite structure as a whole.

As an example, the natural axisymmetric vibrations are calculated for a tank filled with a liquid, which consists of a cylindrical shell, spherical bottom shell, and the frame connecting these shells. The Riesz method convergence is estimated by the number of prescribed functions, as well as the influence of the deplanation of the liquid cross-sections and the shape of the transverse cross-section of the frame.