Mechanics of Solids最新文献

The dynamic anti-plane response of a circular inclusion embedded in a strip domain under line source excitation is investigated using the complex variable method and Green’s function approach. First, the total wave field with undetermined coefficients is constructed by employing the method of infinite mirror images. Then, a system of equations is formulated based on the continuity conditions at the boundary of the circular inclusion, allowing for the determination of the unknown coefficients and the derivation of the complete wave field within the strip domain. Finally, numerical examples are presented to analyze the dynamic stress concentration around the circular inclusion. The results demonstrate that low-frequency excitation significantly amplifies the dynamic stress concentration in the vicinity of the inclusion. Moreover, this amplification effect becomes more pronounced with increasing contrast in wave numbers between the inclusion and the matrix.

The primary objective of this study is to analyze the effect of inhomogeneity in an orthotropic elastic material within a magneto-elastic cylinder containing (i) an isotropic core and (ii) a rigid core. An analytical approach is developed to investigate the behavior of a non-homogeneous orthotropic material in the presence of a magnetic field. Stresses and displacement have been expressed in closed forms. The study focuses on the dynamical response of an orthotropic cylinder. Analytical expressions are derived for displacement components and stress components in both cases. Numerical calculations are performed to evaluate the radial variation of displacement and stress throughout the cylinder. By solving the dynamic problem, stress wave propagation and displacement are analyzed through graphical representations. The results reveal a significant influence of the magnetic field on both displacement and stress components. The Mathematica software is utilized to visualize and interpret these effects graphically.

This article presents the propagation of waves in a functionally graded micropolar thermoelastic plate in the presence of diffusion and memory-dependent derivatives (MDD). The material properties are assumed to be functionally graded and non-homogeneity vary exponentially along the -direction. The basic equations are converted into dimensionless form and Helmholtz decomposition technique is employed to simplify these equations. The analytical expressions for potential functions, temperature, mass concentration and micro-rotation are obtained by using normal mode analysis. Normal mode analysis method is momentous as it relinquishes complex coupled dynamics into easier explicable and analyzable components disclosing wherein system inherently react, convulse or rebound to stimulants. The propagation equations for insulated impermeable and iso-thermal iso-concentrated boundaries are obtained. The magnitudes of force stresses, couple stresses, mass concentration and temperature for the symmetric and asymmetric systems are calculated using the suitable boundary conditions. The analytically obtained results are numerically analyzed for aluminium-epoxy material under Lord-Shulman (LS) and Green-Lindsay (GL) models for different kernel functions and non-homogeneity parameters. This study is useful for researchers working in thermodynamic engineering, material science and micropolar thermoelastic diffusion model under different physical parameters.

The study of thermal behavior in hollow cylindrical structures under ramp-type heating is critical for applications in aerospace, mechanical, and thermodynamic engineering. However, existing research has largely overlooked the influence of memory-dependent derivatives (MDD) combined with time delay parameters on temperature and stress distributions in such systems. This work addresses this gap by introducing a novel mathematical model for a semi-infinite hollow cylinder subjected to ramp-type heating at its lower surface, incorporating MDD to capture memory effects in heat conduction. The novelty lies in the integration of time delay parameters within the MDD framework, offering a more realistic representation of thermal and stress responses. Using Laplace, Hankel, and Fourier transform methods, analytical solutions are derived in the Laplace domain, with numerical inversion applied to obtained results. The model assumes convective boundary conditions on the cylinder’s curved surfaces and employs copper material properties for numerical analysis. Key contributions include the derivation of closed-form expressions for temperature, displacement, and stress distributions, and the demonstration of significant time delay effects on these variables. Results reveal that increasing time delay parameters reduces temperature and angular stress while altering displacement and radial stress profiles, with maximum stresses observed at specific radial and axial positions. These findings enhance the understanding of memory-dependent thermo-elasticity, providing valuable insights for designing robust cylindrical structures in high-temperature environments, such as spacecraft and industrial machinery.

This paper focuses on the penetration process of a 93W alloy long-rod into a RHA 603 steel target. Using a combined experimental and numerical simulation approach, the influence of the target' Johnson-Cook constitutive model parameters (yield strength A, hardening modulus B, hardening exponent n, strain rate sensitivity coefficient C, thermal softening exponent m) on penetration depth was systematically investigated. A two-dimensional axisymmetric finite element model was established based on LS-DYNA, and simulation results were verified against experimental penetration depths with an average error less than 1.5%. The influence of each parameter on the dimensionless penetration depth (P/L) was analyzed within a range of  0.5 to 2.5 times their baseline values. To verify the reliability of the results, five velocities within the range of 1200–2000 m/s were selected for repeated calculations. The results show that: 1. An increase in A, B, and C significantly reduces penetration depth, with A having the most pronounced effect (at an impact velocity of 1600 m/s, as A/A₀ increased from 0.5 to 2.5, the dimensionless penetration depth decreased by 49.52%; increases in B and C resulted in depth reductions of 17.27 and 16.09%, respectively); 2. An increase in n slightly enhances penetration depth (at 1600 m/s, when n/n₀ increased to 2.5, the penetration depth increased by only 6.56%); 3. A increase of m affects the penetration depth in a certain range (at 1600 m/s, as m/m₀ increased from 0.5 to 1.5, penetration depth decreased by 8.59%, with its influence saturating beyond 1.5). Furthermore, energy analysis indicates that plastic energy dissipation during target crater formation follows the same trend as the change in penetration depth and is the primary energy dissipation mechanism. This research reveals the intrinsic mechanisms through which key constitutive parameters influence penetration depth by regulating target strength, hardening behavior, and thermal softening effects, providing a theoretical basis for optimizing penetration prediction models and rod projectile design.

In this study, the vibration behavior of a nanobeam is analyzed within the framework of a modified couple stress (MCS) thermoelastic model under the hyperbolic two-temperature (HTT) theory. The governing equations are formulated using the Euler-Bernoulli beam theory and non-dimensional parameters for simplification. The Laplace transform, combined with an eigenvalue approach, is employed to solve the equations. Most of the problems studied so far in MCS thermoelastic media involve the use of potential functions; however, the eigenvalue approach has the advantage of determining the solution of the governing equations in matrix form. The nanobeam, assumed to be simply supported along its length (aligned with the x₁-axis), is subjected to an exponentially decaying thermal source. The chosen boundary conditions are reflective of practical nanostructures experiencing localized laser heating or rapid transient effects. Key physical field quantities, including displacement, lateral deflection, temperature distribution, conductive temperature, and axial stress, are derived in the transformed domain. A general algorithm is developed for the numerical inversion of the Laplace transform, and results are computed and presented graphically. The study highlights the influence of single-temperature (1T), two-temperature (2T), HTT models, and characteristic time parameters on the system’s response. Some particular cases of interest are also reduced.

The space behind the fabric panel, known as the air gap, has been shown to improve ballistic performance, but the underlying mechanisms remain unclear. This study aims to clarify the ballistic mechanisms of soft fabric panels that incorporate air gaps. We developed finite element (FE) models for non-perforated ballistic impact on 24 layers Twaron^® fabrics using a clay backing to simulate deformation. The FE models were validated against experimental data and analytical results. In the FE modelling, the air gap varied from 0 to 8 mm. The results were analysed and computer vision was used to quantify the stress distribution for enhancing the analyses. The findings reveal that as the air gap increases, the clay experiences lower stress and deformation. The ballistic mechanisms lie in: providing cushioning space; diminishing initial contact areas; reducing stress and deformation in the clay. As the air gap increases, the cushioning effect becomes more pronounced. This study lays a theoretical foundation for designing soft body armour with considerably enhanced ballistic performance by simply adjusting the air gap.

In the present work, we have studied the thermodynamical interactions in a two-dimensional thermoelastic medium with initial stress and magnetic field. The purpose of the current study is to establish a novel mathematical model in the micropolar theory of generalized thermoelasticity under the framework of photothermal theory. For the solution of the required problem, by employing the Lame’s potential and normal mode technique, we derived analytical expressions for field quantities such as thermal stresses, displacement components, temperature field, carrier density and couple stress. For graphical representation of different physical quantities such as displacement components, stress and couple stress components and carrier density as well as the temperature distribution, Matlab software has been used. The theoretical and numerical computations are found to be in close form. The comparison of our results for the accuracy of physical quantities with previous research work is carried out graphically that indicates to the strong impact of the external parameters in photothermaol phenomenon

We derive the time fractional heat conduction equation (FHCE) for a functionally graded elliptical annulus plate using non-Fourier heat conduction principles that account for memory effects rather than instantaneous responses, influenced by a moving laser heat source. Thermal conductivity, heat capacity, and density are presumed to vary axially and depend on temperature. The upper and lower plates are at zero, while Biot criteria and the Kirpichev reference number for convection energy transfer boundaries regulate the geometrically curved areas. Kirchhoff’s variable transformation linearises the FHCE governing the given conditions. The heat equation is resolved through the application of the Laplace transform, modified Mathieu transform, and Taylor series, followed by their inversions. The inverse of Kirchhoff’s Laplace domain transformation establishes the temperature distribution. Numerical analyses of titanium carbide and nickel properties yielded graphs depicting temperature, motion, and stress variations during laser pulse duration and velocity.

This paper presents a new membrane finite element with in-plane rotational degrees of freedom and an additional internal node formulated using the assumed strain formulation. Designed for static and free vibration analyses, the proposed element is a quadrilateral with five nodes, which contains two translational and one in-plane rotational degrees of freedom at each corner node and only two in-plane translations for the central node. To improve computational efficiency, the static condensation concept is applied to remove the degrees of freedom of the central node, reducing system complexity without affecting accuracy or stability. A series of extensive static tests, including well-known reference problems such as cantilever beams with different shapes, and thick cylinders subjected to internal pressure, demonstrated the element’s superior performance on both regular and distorted meshes. In addition, the present element showed good agreement in free vibration studies of a cantilever wall, a cantilever beam, a variable-section cantilever beam, and a wall with openings. Results indicate that the proposed element achieves an accuracy comparable to higher-order elements, making it an effective and reliable choice for modeling thin-walled structures with significant in-plane behavior.