Mechanics of Solids最新文献

The elastic properties of single crystals of nickel-base superalloy VGM7 have been investigated by speckle interferometry. Plate-shaped specimens of different crystallographic orientations were loaded under pure shear conditions and speckle interference patterns from the deformed specimens were imaged. Numerical processing of these interference patterns allowed us to determine the values of Young’s modulus in directions [001] and [011], ({{E}_{{001}}}) = 138 GPa and ({{E}_{{011}}}) = 241 GPa, the basic value of Poisson’s ratio, ({{nu }_{0}}) = 0.39, in the coordinate system 〈001〉, as well as its minimum and maximum values, ({{nu }_{{{text{min}}}}}) = −0.10 and ({{nu }_{{{text{max}}}}}) = 0.69, under longitudinal loading along [101] when the specimen transversely deforms along [10(bar {1})] and [010], respectively. Using the measured values ({{E}_{{001}}}), ({{E}_{{011}}}), ({{nu }_{0}}), ({{nu }_{{{text{min}}}}}), and ({{nu }_{{{text{max}}}}}) the single-crystal elastic stiffnesses, ({{C}_{{11}}}) = 264 GPa, ({{C}_{{12}}}) = 166 GPa, and ({{C}_{{44}}}) = 133 GPa, and the elastic compliances, ({{S}_{{11}}}) = 7.35 TPa^–1, ({{S}_{{12}}}) = –2.84 TPa^–1, and ({{S}_{{44}}}) = 7.52 TPa^–1, were calculated. The applied method allows one to unambiguously determine the sign of Poisson’s ratio and, therefore, it should be recommended for studying the elastic properties of auxetic materials, for which determination of the sign of Poisson’s ratio is of great importance.

The article is an analytical review and is devoted to the problem of constructing non-classical theories of beams, plates and shells, the demand for which is associated with the emergence of new structural materials with properties that do not fully correspond to the hypotheses adopted in constructing classical theories. The presentation is based on the analysis of the problem of reducing the order of elasticity theory equations for thin-walled structural elements and the mathematical and physical methods used for this purpose. The main attention is paid to the correctness and energy consistency of these methods. The presentation is illustrated by examples of specific theories.

This work presents a method for numerically determining the thermal damages of cylindrical living tissue due to laser irradiation utilizing a hyperbolic bioheat model. To assess thermal injuries to the tissues, the Arrhenius relation must be used to assess the amount of denatured protein. Because the governing formulations are complicated, the finite element approach is used to solve this kind of problem. Moreover, the correctness of the numerical solution is confirmed by contrasting the numerical outcome of the finite element technique with recent experimental data. Explanatory graphics of the numerical results exhibit the increment in displacement, temperature, thermal damages and the stresses in responses to changes in the duration of laser exposure, the intensity of laser and blood perfusion rate. Additionally, the numerical outcome and the available experimental data are compared, showing that the present mathematical model is a useful tool for evaluating bio-heat transport in cylindrical human tissue.

The failure and damage of brittle rock is attributed to crack development, there is crack propagation inside the brittle rock even the applied stress is lower than the rock strength. Establishing the theoretical relationship between the external loading and the local stress that around the crack is not only helpful for understanding the mechanisms underlying the creep behavior of brittle rock, but also offers the possibility of theoretically estimating the creep-life of brittle rock. In this paper, the cracks in the cylindrical rock specimen are assumed to be uniformly distributed and penny-shaped with their major axes parallel to the axial direction of the cylindrical rock specimen, the creep-life of brittle rock refers specifically to the total time consumed in the subcritical crack growth stage. The expressions and direction of the local stresses around the crack tips are derived based on dividing the local stress into two parts. The phenomenon of brittle rock exhibiting tensile failure under the uniaxial compression is preliminarily explained. The crack propagation rate that directly related to the local tensile stress is derived. The requirements for subcritical crack growth are theoretically analyzed. A new expression of creep-life of brittle rock with a clear physical meaning and the key parameter “(Psi )” is established. Considering that the theoretical studies on estimating the creep-life of brittle rock are rare, and the experiments related to the creep-life are very time-consuming. Therefore, this study may provide an effective approach for theoretically estimating the creep-life of brittle rock under the given uniaxial compressive stress state.

In this paper, the Green-Lindsay theory is used to study two-dimensional interactions in fibre-reinforced orthotropic magneto-thermoelastic media with temperature dependence and gravity. Formulations are subjected to mechanical stress. An exact solution to the problem is achieved by applying normal mode techniques. In addition, comparisons were made to analyze the effects of temperature-dependent properties, gravity, magnetic field, time and gain parameters. Displacement, stress and temperature components are numerically calculated for appropriate materials and presented graphically. Graphical results show that reinforcement, gravity, magnetic field, temperature-dependent properties and time have a significant influence on the distribution of all physical quantities. Some interesting special cases emerge from this report.

In the present article, a method for solving a boundary value problem for an elliptical boundary layer occurring in thin-walled shells of revolution under normal-type impacts on the front surfaces is constructed. The elliptical boundary layer is constructed in the vicinity of a conditional front of Rayleigh surface waves and is described by elliptic equations with boundary conditions specified by hyperbolic equations. In the general case of shells of revolution, the methods for solving equations for an elliptical boundary layer developed for shells of revolution of zero Gaussian curvature cannot be used. The previously considered scheme for using the integral Laplace and Fourier transforms ceases to work since the resolving equations become equations with variable coefficients. The method for solving the equations of an elliptical boundary layer proposed in this paper is based on the use of an asymptotic representation of the images of the Laplace solution (in time) in exponential form. The paper presents a numerical calculation of the normal stress based on the obtained analytical solutions for the case of a spherical shell.

Uncertainty is omnipresent in manufacturing and engineering community. This paper develops an efficient robust optimization framework for a two-bar structural model under uncertain loading, which includes magnitude and direction uncertainty following Gaussian distribution. This framework aims to simultaneously minimize the expectancy and standard deviation of structural compliance with volume constraints. A reasonable and efficient estimation of the statistical moment of structural compliance is recognized the critical to the probability-based RTO problem. To address the computational challenges associated with high dimensionality in traditional surrogate models, a decoupling technique based on non-intrusive polynomial chaos expansion is developed. Such a numerical evaluation tool is generic for different types of structures. In addition, an analytical expression based on a two-bar structure is derived as a standard reference. The cross-sectional area and angle with horizontal direction of each bar are taken as design variables and optimization is achieved using the optimality criteria. Numerical examples demonstrate that the accuracy and efficiency of the reported algorithm are significantly improved compared to conventional methods such as polynomial chaos expansion and Monte Carlo simulation. The optimized designs prove a better robust performance than their counterparts.

The solution of a non-one-dimensional boundary value problem of the theory of plane temperature stresses is used to calculate the level and distribution of temperature stresses at each time point during the process of performing the technological operation of assembling a composite disk by hot fitting, when the enclosed assembly part is different from a circular plate. Residual stresses in the assembly elements and the resulting interference fit in it after its cooling to room temperature are calculated. Current and residual stresses are calculated depending on the preliminary heating of the enclosing ring, the thermomechanical properties of the mating parts and their initial geometry. The yield strengths of the elastic-viscoplastic elements of the assembly are assumed to be essentially dependent on the local temperature. Attention is drawn to the need to exclude singularity when setting boundary conditions on the mating surfaces of the assembly parts.

A microstructural model of a coil composite piezoelectric fiber disk (FibrCD) actuator has been developed. The actuator is formed by winding a large number of turns of a thin electroded piezoelectric fiber in the form of a shielded single-core cable with a radially polarized piezoelectric interelectrode layer, followed by impregnation and continualization of the turns with a polymer binder. An exact analytical solution has been obtained for the electric and deformation fields of the axisymmetric coupled boundary value problem of electroelasticity on the elementary composite cell “piezoelectric cable/binder shell.” Further, the exact solution for electroelastic fields inside a composite cell loaded with electric voltage on the cable electrodes is used to find exact analytical solutions for the tensors of effective coefficients of piezoelectric stresses and linear piezoelectric expansion (deformations) of the fiber composite as a homogeneous disk FibrCD actuator with cylindrical anisotropy within the framework of the known polydisperse model of the composite structure. The calculation and numerical analysis of the FibrCD actuator characteristics are performed for various values of its macroscopic and structural parameters, in particular, the disk (ring) thickness, the difference between the outer and inner radii of the ring, the relative sizes of the radius of the conductive core and the thickness of the binder layer between adjacent cable turns. The efficiency of the FibrCD actuator is confirmed in comparison with the characteristics of traditional actuators.

A solution is obtained for the coupled boundary value problem of non-isothermal deformation of a material forming a finite-length plug in a non-deformable round pipe. Under conditions of rigid adhesion to the pipe surface, the material is deformed under the action of a variable pressure drop specified on the end surfaces of the plug. Irreversible deformation is associated with both creep and viscoplastic flow of the material and causes its heating. Additionally, the dependences of the yield strength, viscosity coefficient, and creep parameters of the material on temperature are taken into account. Using the large deformation model, the processes of creep and viscoplastic flow with increasing and constant pressure drop, flow braking and unloading of the medium with decreasing pressure, as well as cooling of the material after complete removal of the mechanical load are studied.