Mechanics of Solids最新文献

This article highlights the study of thermoelastic interaction in a homogeneous, orthotropic, rotating medium due to the influence of an instantaneous heat source. This study employs the three-phase-lag model. A differential equation in vector-matrix form has been formulated with the help of combined Laplace–Fourier transformation and the solution is obtained by using the eigenvalue approach. The Gaussian quadrature formula and the Bellman method are employed to numerically estimate the displacement components, temperature, and thermal stress components. Finally, the numerical outcomes are depicted graphically and compared with those of the Lord–Shulman and Green–Naghdi type III models.

For a satellite with a ball damper, the effect of internal dissipation on rotational motion in the central gravitational field is studied. The equations of rotational motion of a dynamically symmetric satellite with a ball damper in an elliptical orbit are obtained. For the case of a circular orbit, using the averaging method, spatial resonant rotations of a dynamically symmetrical satellite with a ball damper were studied.

This investigation aims to develop a thermoelasticity model to analyze the propagation of thermoelastic waves in a composite hollow circular cylinder with an LEMV/CFRP interface layer. The model integrates a modified non-local couple stress theory to address challenges related to higher-order time derivatives. The derivation yields three partial differential equations governing the modified non-local couple stress of the cylinder in axisymmetric mode. By applying linear elasticity theory, these equations are solved to derive frequency equations for the cylinder’s external surface under traction-free conditions while ensuring boundary continuity. The study investigates how variations in wave number and thickness affect the frequency, temperature, and displacements within the field. To evaluate the impact of different thermoelasticity theories and non-local coupled stress parameters, the research employs tables and graphs for comparison and estimation. These visual aids provide valuable insights into the behavior of the composite cylinder across various scenarios.

The article presents an analytical solution for the problem of a circular pipe turning inside out in a rigid gasket. Formulas for the magnitude of the radial stress, which is responsible for the adhesion between the pipe and the gasket, have been obtained. The solution is obtained for an arbitrary incompressible hyperelastic material with a hyperelastic potential that depends only on the first invariant of the left Cauchy–Green deformation tensor (various generalizations of the neo-Hookean solid) or on the second invariant of the logarithmic Hencky strain tensor (various generalizations of the incompressible Hencky material). The solution considers the occurrence of plastic flow in areas adjacent to the lateral surfaces of the pipe. Both ideally plastic and isotropically hardening materials of a general type are considered. For the latter, a solution scheme is given; in the particular case of a linearly hardening material, a closed-form solution is obtained. For the perfect plasticity model, a closed-form solution was obtained for the neo-Hookean solid, for an incompressible Hencky material, and for the Gent material.

Based on experimental data on the destruction of the adhesive layer that interfaces two plates in a given area, and the well-known analytical solution corresponding to the design scheme, variants of the destruction criterion are considered, taking into account hydrostatic pressure and invariant components of elastic energy. One- and two-parameter criteria are studied, in which the products of the deformation energy of volume and shape and the layer thickness form the critical flow of elastic energy density. It is shown that the loosening of a thin adhesion layer with a two-parameter criterion quasi-linear with respect to the deformation energy of the volume most accurately describes the critical state.

Artificial intelligence has been widely used in engineering. In this paper, we propose to combine the backpropagation neural network (BPNN) with the refined plate model based on Carrera Unified Formula (CUF) to advance the development of damage detection. The prediction model is built by utilizing the error back propagation function of the neural network. In addition, MATLAB uses Taylor’s interpolation algorithm and lower degrees of freedom yet achieves the same accuracy as ANSYS, and the improved plate model accurately reproduces the mechanical properties of the metal plate. A database is then built based on the mechanical model to detect the location of damaged elements and node displacements. The nodal displacements were used as inputs while the locations of damaged elements were used as training outputs for the neural network. The effectiveness of the proposed method was verified through various damage scenarios. The results show that the method can accurately predict individual damage locations based on node displacements alone. The neural network combined with the plate model achieved a detection accuracy of 91% with a regression coefficient of 0.95.

The thin composite von Kármán plates in postbuckling are considered. Using the first Piola stress tensor and the displacement gradient tensor, the complementary energy variational theorem is proven. The Kirchhoff assumptions are adopted. The plate lay-up is symmetric and pointwise. According to the theorem, at the actual stress state of the plate the complementary energy (as a functional of the internal forces and of the moments) reaches its stationary value. The stationary feature of the actual state is valid as compared to other feasible states satisfying the static equilibrium and the static boundary conditions. The theorem is a consent of the static variational principle. The principle leads to the linear relations between forces/moments, created by the corresponding first Piola stress tensor components, and the 2D-strains/curvatures. An illustrative plate example is given.

The distributions of the principal stresses, the radial velocity, and the relative density are determined in an infinite dilatant medium in which a spherical cavity expands from a zero radius. The medium obeys the Drucker–Prager yield criterion. The plastic potential is also of Drucker–Prager type but differs from the yield criterion. Moreover, it involves the relative density and results in the incompressibility equation at a certain relative density value. A detailed analysis of the solution is provided for a specific dependence of the plastic potential on the relative density. It is shown that the qualitative behavior of the solution near the cavity’s surface depends on a constitutive parameter involved in this dependence. A numerical example illustrates the general solution.

The purpose of this research is to examine the effects of magnetic field and thermal diffusion on a photo-thermoelastic semiconducting medium under the theory of hyperbolic two-temperature. During the formulation of the problem using the hyperbolic two-temperature theory, the relation between plasma and thermoelastic waves was explored. The medium is assumed to be a semiconducting medium with isotropic and homogeneous characteristics. The Laplace transform technique is used to construct analytic formulations for physical quantities such as stresses, displacement components, temperature field, and mass concentration. To show the results, numerical computations are done using the MATHEMATICA program for the selected material (Si). To demonstrate the significance and effectiveness of the obtained results, the full solutions of the major physical variables in the space-time domain are found using a numerical method based on the inverse of the Laplace transform. A comparison is carried out with and without a magnetic field, at different theories (CTE, LS, GL) and with another research that agree with the previous paper when the new parameters neglected.

Some effects of the stress-strain state, such as vibration creep, creep acceleration and ratcheting, observed and studied in the experimental mechanics of a deformable solid, are proposed to be modeled on the basis of constitutive relations implemented in tensor nonlinear viscoelastic models of the Maxwell type. The apparatus of isotropic tensor functions is used, depending on two symmetric tensor arguments. Examples are given of a complex stress state in a tubular sample, when there is a significant disproportionate increase in time of the axial component of deformation under the combined action of constant axial and oscillatory shear loads compared to the case of action of only axial load. The concepts of generalized and combined ratcheting under complex stress conditions are introduced.