Mechanics of Solids最新文献

In this study, a new analytical model based on an nth-order shear deformation theory formulation is used to analyse the post buckling of porous FGM plates resting on an elastic Winkler–Pasternak type foundation. The model presented contains a smaller number of variables than other higher-order theories in the literature. In addition, with this model, the effective properties of the structure are calculated as a function of the even and odd distributions of the porosity, and these distributions follow the power and sigmoid laws. The behaviour of the elastic foundation is governed by the constant Winkler parameter, which represents the reaction of the elastic springs, and the Pasternak parameter in the form of a shear layer of the foundation. The non-linear equilibrium equations are based on Von Karman’s theorem, the principle of virtual work and the equilibrium criterion. To solve these equations, approximate solutions and boundary conditions are considered. The accuracy of the nth-order HSDT model used takes into account the uniform, linear and non-linear variation of temperature across the thickness. We obtained several results for the evolution of the critical temperature: as a function of the amplitude/height ratio, as a function of the porosity and as a function of the foundations. The relative error between our results and those in the literature is generally less than 5%.

One of the main problems when conducting laboratory tests of rock specimens aimed at determining their mechanical and strength properties is to transfer the test results of relatively small specimens to sufficiently large areas of a rock massif, often with a complex structure. This is due to the fact that generalized numerical indicators characterizing the degree of influence of structural heterogeneities of various sizes on the deformation and destruction of rocks and massifs are not yet available. In addition to heterogeneity, other factors also affect the processes under study, such as the stress state of the massif, the presence of geological disturbances, macrofractures, etc. These issues are studied in this paper based on a comparison of the results of experiments performed on the Triaxial Independent Loading Test System of the Institute of Problems in Vechanics of the Russian Academy of Sciences using the “hollow cylinder” scheme on specimens with a central hole of 10 and 20 mm in diameter and physical modeling of deformation processes in the vicinity of wells with a decrease in pressure at their bottomhole for reservoir rocks of the Prirazlomnoye oil field.

Expressions for T-stresses are obtained based on the exact analytical solution of the two-dimensional problem of a strip of orthotropic material with the principal axes of the elasticity tensor directed parallel and perpendicular to its boundaries and a central semi-infinite crack. A balanced system of loads in the form of four independent active loading modes is assumed to be applied sufficiently far from the crack tip. It is shown that for two (antisymmetric) loading modes the T-stresses are equal to zero, and for the other two (symmetric) modes they are determined by one or two parameters composed of the elasticity tensor components. The T-stress dependencies for symmetric loading modes are obtained in the form of double integrals from combinations of elementary functions depending on one of the dimensionless parameters, the second of the dimensionless parameters is included in the expression for the T-stresses of only one of the modes in the form of a multiplicative coefficient.

The article analyzes an approach that goes back to Maxwell to the representation of a potential, in particular, the potential of the Newtonian field of gravity as a sum of potentials of multipoles of different orders. Critical cases of the algorithm for finding the parameters of a multipole, namely, its axes and moment, are indicated. The cases take place when the body has certain symmetries in the mass distribution. Recommendations for overcoming the identified difficulties are formulated. For a body with a triaxial ellipsoid of inertia, explicit expressions for the axes and moment of a second-order multipole that are expressed via second-order inertia integrals are given. It is shown that the axes of the multipole are orthogonal to the circular cross-sections of the ellipsoid of inertia of the body. Critical cases of calculating a third-order multipole are considered using the example of a model body with constant density, that has the shape of an equihedral tetrahedron. A method for calculating the axes and moment of a third-order multipole for such a body is given.

Based on Euler beam theory and Hamilton’s principle, the free vibration control equation for the variable cross-section beam was established. Galerkin discretization and eigenvalue methods were used to solve the natural frequencies of beams under simply supported-simply supported (SS) and simply-clamped supported (SC) boundary conditions. The vibration characteristics of beams with annular, rectangular frame and rectangular cross-section at different cross-sectional parameters (taper, thickness, and aspect ratio) are explored. The calculation example shows that the natural frequency of the beam is closely related to changes in taper. Especially for rectangular cross-section, the change in taper in the height direction of the beam has a large effect on the frequency, while the change in taper in the width direction has a smaller effect. Increasing the outer thickness of the annular cross-section beam has a different effect on the beam’s natural frequency than the inner thickness, while increasing the thickness of the rectangular frame cross-section beams will result in a decrease in the natural frequency of the beams. Increasing the aspect ratio of a rectangular variable cross-section section beam increases the natural frequency of the beam. Under the same cross-sectional area, the rectangular frame cross-section beam frequencies are higher than other cross-section beams.

Joint clearances and uncertain parameters of a parallel mechanism will cause the error between the actual dynamic response and the desired dynamic response, leading to a dynamic reliability problem. Currently, the reliability analysis of mechanisms mainly focuses on mechanism with clearances or with uncertain parameters, very few involve considering both clearances and uncertainty parameters simultaneously. The main purpose of this article is to propose a dynamic reliability analysis method of a parallel mechanism with revolute clearance and uncertainty parameters. The dynamic reliability analysis of a parallel mechanism with lubrication revolute clearance joints and uncertain parameters is studied in this paper. The 3-RRPaR spatial parallel mechanism is taken as an example, lubrication revolute clearance joints model is established, and the dynamic model of mechanism with lubrication revolute clearance joints is derived. The dynamic reliability model of mechanism with lubrication revolute clearance joints and uncertain parameters is developed. The effects of various random uncertain parameters on the dynamic reliability of mechanism with lubrication revolute clearance joints are analyzed. This can not only provide a new method for dynamic response reliability analysis of mechanism with lubrication clearances and uncertain parameters, but also lay the foundation for dynamic response and reliability optimization design.

For conservative mechanical systems, the method of normal coordinates is known, which uses the theorem on the reduction of two quadratic forms to the sum of squares. In this case, the system of differential equations is split into a system of independent oscillators. A linear dissipative mechanical system with a finite number of freedom degrees is defined by three quadratic forms: the kinetic energy of the system and potential energy of the system, and the dissipative Rayleigh function. We study the linear problem of forced oscillations of a double pendulum when the friction coefficients are proportional to the masses. Then all three quadratic forms are reduced to the sum of squares by a single transformation. In normal coordinates the system splits into two independent systems of second order. An analytical solution is constructed in the most general form for arbitrary rod lengths and point masses. A complete analysis of the oscillations in the non-resonant case and in the case of resonances is given. Formulas for the error of the analytical formulas if the proportionality of the friction coefficients and masses is violated are also obtained.

This study examines the mixed-mode fracture criterion for Alumina/Zirconia functionally graded materials (FGMs), based on the concept of the equivalent stress intensity factors K_eq. For this purpose, a computational algorithm is developed and incorporated into a finite element software, using a combination of five methods (FE method, Crack box technique CBT, Displacement extrapolation technique DET, Crack propagation criteria and Tanaka’s approach), in order to then determine the critical loading necessary to control the risk of crack propagation, as well as the determination of the different parameters (Stress intensity factors SIFs, bifurcation angle and T-stress). The mechanical properties of the Alumina/Zirconia FGM are supposed to change gradually through the cracked plate width, according to an exponential law (E-FGM). The continuous variation in material properties for Alumina/Zirconia FGMs is addressed by defining these properties at the centroid of each finite element. The proposed fracture criterion was identified according to the geometry of the specimen, the loading conditions and the mechanical properties of the FGM material. The frontier of crack propagation given by the proposed criterion is well defined and excellent results are obtained under pure mode-I and mixed-mode loadings.

Anomalous guided waves appearing at a non-semisimple degeneracy of the fundamental matrix are observed and analyzed in the framework of the Cauchy sextic formalism. The non-semisimple degeneracy condition is explicitly constructed for the most general case of Lamb waves propagating in a traction-free layer with arbitrary elastic anisotropy. A new type of dispersion equation and the corresponding dispersion solution are obtained. The connection with surface waves of the non-Rayleigh type is discussed.

This study presents coupled flexural-torsional buckling analysis of the thin-walled columns with nonsymmetric open cross-sections in dimensionless and exact man- ner. Transfer matrix method coupled with iterative eigenvalue solution procedure is used to calculate nondimensional buckling loads of the thin-walled columns. For all end conditions considered, closed-form solutions are also presented for the comparison. The related tables show that, to some extent, all results are in good agreement. However, the closed-form solutions available in literature do not completely capture the buckling loads obtained using the transfer matrix method for fixed-fixed, fixed-pinned, and fixed-free end conditions. Therefore, there is a need to find new expressions for buckling parameter to calculate analytically buckling loads. This is carried out by using the Euler’s theory of columns for doubly symmetric cross sections. Through using these expressions, a good matching between the results obtained from the transfer matrix method and closed-form solutions is provided. On the other hand, as a case study, nondimensional solution procedure is applied to the optimization of critical buckling load of the columns. Nondimensionalization is a useful procedure for optimization such that it has led to a naturally scaled optimization model. Three column configurations with different numbers of segments in the longitudinal direction were considered and the maximum dimensionless critical buckling load without constraint violations is attained for the five-segmented column and it is 7.2, which represents 48.0415% gain.