A numerical–analytical approach to the problem of determining the stress–strain state of bimaterial structures with interphase ribbon-like deformable inhomogeneities under combined force and ...dislocation loading has been proposed. The possibility of delamination along a part of the interface between the inclusion and the matrix, where sliding with dry friction occurs, is envisaged. A structurally modular method of jump functions is constructed to solve the problems arising when nonlinear geometrical or physical properties of a thin inclusion are taken into account. A complete system of equations is constructed to determine the unknowns of the problem. The condition for the appearance of slip zones at the inclusion–matrix interface is formulated. A convergent iterative algorithm for analytical and numerical determination of the friction-slip zones is developed. The influence of loading parameters and the friction coefficient on the development of these zones is investigated.
The effect of a functional gradient in the cross-section material (FGM) of a thin ribbon-like interfacial deformable inclusion on the stress-strain state of a piecewise homogeneous linear-elastic ...matrix under longitudinal shear conditions is considered. Based on the equations of elasticity theory, a mathematical model of such an FGM inclusion is constructed. An analytic-numerical analysis of the stress fields for some typical cases of the continuous functional gradient dependence of the mechanical properties of the inclusion material is performed. It is proposed to apply the constructed solutions to select the functional gradient properties of the inclusion material to optimize the stress-strain state in its vicinity under the given stresses. The derived equations are suitable with minor modifications for the description of micro-, meso- and nanoscale inclusions. Moreover, the conclusions and calculation results are easily transferable to similar problems of thermal conductivity and thermoelasticity with possible frictional heat dissipation.
Within the framework of the concept of deformable solid mechanics, an analytical-numerical method to the problem of determining the mechanical fields in the composite structures with interphase ...ribbon-like deformable multilayered inhomogeneities under combined force and dislocation loading has been proposed. Based on the general relations of linear elasticity theory, a mathematical model of thin multilayered inclusion of finite width is constructed. The possibility of nonperfect contact along a part of the interface between the inclusion and the matrix, and between the layers of inclusion where surface energy or sliding with dry friction occurs, is envisaged. Based on the application of the theory of functions of a complex variable and the jump function method, the stress-strain field in the vicinity of the inclusion during its interaction with the concentrated forces and screw dislocations was calculated. The values of generalized stress intensity factors for the asymptotics of stress-strain fields in the vicinity of the ends of thin inhomogeneities are calculated, using which the stress concentration and local strength of the structure can be calculated. Several effects have been identified which can be used in designing the structure of layers and operation modes of such composites. The proposed method has shown its effectiveness for solving a whole class of problems of deformation and fracture of bodies with thin deformable inclusions of finite length and can be used for mathematical modeling of the mechanical effects of thin FGM heterogeneities in composites.
The paper presents a fast and accurate numerical technique for evaluation of the 3D time-harmonic elastodynamic Green's function and its derivatives for anisotropic solids. Following Wang & Achenbach ...the Green's function is presented in the form of the sum of singular (static) and regular parts, which are both reduced to integrals over a unit sphere. Singular part and its derivatives are then reduced to the integrals over a unit circle, which can be efficiently (fast and accurately) evaluated using the trapezoid rule, which is exponentially convergent for integrals over the period of a periodic integrand. The regular time-harmonic parts are presented through the double integrals. The outer integral is also efficiently evaluated using the trapezoid rule. A special quadrature is developed for evaluation of the inner integral, which accounts for the highly-oscillating behavior of the integrand. Numerical examples are presented, which shows the advantage of the proposed technique over others.
The paper proposes a transparent and compact form of constitutive and equilibrium relations for the plane thermoelasticity of quasicrystal solids. The symmetry and positive definiteness of the ...obtained extended tensors of material constants are studied. An extension of the Stroh formalism is proposed for solving plane problems of thermoelasticity for quasicrystals. It is proved that the eigenvalues of the Stroh eigenvalue problem in the most general case of 3D quasicrystal materials do are purely complex. The relations between the matrices and vectors of phonon–phason elastic and thermoelastic coefficients of the proposed extended Stroh formalism are obtained. A fundamental solution to the plane problem of thermoelasticity of a quasicrystal medium is derived. The asymptotic behavior of physical and mechanical fields near the vertices of objects whose geometry can be modeled by a discontinuity line (cracks, thin inclusions) is studied, and the concepts of the corresponding generalized field (heat flux and phonon–phason stress) intensity factors are introduced. Examples of the influence of heat sources and sinks on an infinite quasicrystal medium containing a rectilinear heated crack are considered.
The research is devoted to the problem of determining the efficiency of the workpiece fixing mechanism operation. Improving characteristics of workpiece fixing is one of the required conditions to ...increase the cutting modes, which may help to enhance the machining productivity. The study investigates the main characteristics and general features of a new structure of clamping mechanisms with electromechanical actuators for fixation of rotation bodies. The main advantages of using electromechanical clamping actuators with self-braking gear are presented. Two simplified dynamical models for the description of different stages of the clamping process are developed. The calculation scheme was formulated to find out how the mass-geometric parameters of mechanism elements should influence the main characteristics of the clamping mechanisms of this type.
•We consider a thermoelastic medium with a rigid thread.•We derive new regularized boundary integral equations.•We propose analytic approach for their solution.
The paper presents a novel approach ...for analytic modeling and numerical analysis of spatial problems of thermoelasticity for isotropic solids containing thread-like nondeformable inhomogeneities. The inhomogeneity is removed from consideration as a geometric object, and its influence on the continuum is replaced by sought functions (of heat flux and mechanical forces) distributed along some line (the midline of inhomogeneity) inside the medium. The corresponding integral equations are derived and it is shown that the boundary conditions in this case results in the ill-posed boundary-value problem. A method for regularization of these integral equations is proposed, which allows obtaining an approximate (with arbitrary predetermined accuracy) solution of the problems of thermoelasticity for solids with thread-like inhomogeneities. An analytical approach to solving the obtained equations on the basis of Legendre polynomials is developed. Based on the performed numerical analysis the paper substantiates reliability, convergence and accuracy of the proposed method for the analysis of thermoelastic equilibrium of solids with nondeformable thread-like inhomogeneities.
•We consider a thermoelastic medium with a deformable thread.•We derive models of heat conductive deformable threads.•We obtain property contribution tensors of thread-like inhomogeneities.
The paper ...presents a novel approach for analysis of thermoelasticity problems for solids with deformable thread-like (wired, textile) inhomogeneities. It is proposed to model a thread-like inclusion with a spatial curve, with appropriate influence functions set on it. The mathematical models of heat conduction and thermoelasticity of thread-like inclusions are obtained, which account for thermal, elastic and thermoelastic properties of these inhomogeneities. Combined with the boundary integral equations for a medium with a thread-like inhomogeneity these models allow obtaining equations for determination of sought influence functions. Their solution technique is proposed based on the orthogonal polynomials approach. The methods for determination of thermoelastic property contribution tensors are considered, which allows determination of effective properties of fiber reinforced composite materials and has wide applications in modern material engineering. Corresponding numerical examples are presented and verified.
This work studies the problem of thermomagnetoelectroelastic anisotropic bimaterial with imperfect high-temperature conducting coherent interface, whose components contain thin inclusions. Using the ...extended Stroh formalism and complex variable calculus, the Somigliana-type integral formulae and the corresponding boundary integral equations for the anisotropic thermomagnetoelectroelastic bimaterial with high-temperature conducting coherent interface are obtained. These integral equations are introduced into the modified boundary element approach. The numerical analysis of new problems is held and results are presented for single and multiple inclusions.
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