Mechanics of Solids最新文献

One of the ways to describe the reaction of an anisotropic elastic body to external force and thermal influences is to construct functional dependencies of the measure of finite deformations on the stress tensor and temperature. To find such dependencies, the inverse thermomechanical problem is formulated. The solution of the thermomechanical problem is based on the use as hypotheses of generalizations of A.A. Ilyushin particular isotropy postulate, formulated for finite deformations of anisotropic bodies. Nonlinear dependencies of the strain tensor on the stress tensor and temperature are obtained using the Gibbs thermodynamic potential.

The paper considers the problem of classifying a system of the partial differential equations of three-dimensional problem of the theory of perfect plasticity (for the stressed states corresponding to an edge of the Tresca prism), as well as determining the substitution of independent variables in order to reduce these equations to the analytically simplest Cauchy normal form. The initial system of equations is presented in the isostatic coordinate net and is essentially nonlinear. The criterion of maximum simplicity is formulated for the Cauchy normal form. The coordinate system is found to reduce the initial system to the simplest possible Cauchy normal form. The obtained condition when the system of equations takes the simplest possible normal form, shown in the paper, is stronger than the t‑hyperbolicity condition according to Petrovskii if we take t as the canonical isostatic coordinate which level surfaces form the spatial layers, that are normal to the field of the principal directions corresponding to the greatest (the lowest) principal stress.

In this work, we investigate the effect of characteristic length and lattice parameter, associated with microinertia, on internal state variables (displacement, polarization, and electric potential) and constitutive relations (stress, higher-order stress, electric field, and electric field gradient) within a dielectric crystal subjected to gradient of an electric field on its upper surface. To derive the field equations and boundary conditions, we employ the simplified strain gradient theory of elasticity, combined with the variational principle of the electric enthalpy functional and external forces. The resulting boundary conditions are divided into mechanical boundary conditions (including stress vector, higher-order stress vector, and displacement) and electrical boundary conditions (such as electric potential, surface/volume charges, and electric field). The field equations and boundary conditions are then expressed in non-dimensional form. A wave solution approach is used to solve the mathematical model for a half-space occupied by dielectric crystals with cubic symmetry, and the physical quantities are subsequently plotted and analyzed.

This study investigates the thermoelastic response of a thin, slim strip subjected to a moving heat source using the Moore-Gibson-Thompson (MGT) theory of thermoelasticity. The novelty of this work lies in the application of the MGT theory to analyze the influence of heat source velocity on the mechanical and thermal behavior of the strip, providing a more comprehensive understanding of wave propagation in thermoelastic materials. The primary objective is to examine the effects of different thermoelastic theories on displacement, stress distribution, and temperature variations induced by the moving heat source. To achieve this, the coupled thermoelastic governing equations are formulated and solved analytically using the Laplace transformation technique. The numerical inversion of the Laplace transform is then applied to obtain time-domain solutions, and the results are presented graphically. The findings demonstrate that the velocity of the moving heat source has a significant impact on the distribution of the main physical fields, influencing thermoelastic wave propagation. The study provides deeper insight into the behavior of thermoelastic materials subjected to dynamic thermal loads, which is crucial for applications in high-speed manufacturing, aerospace engineering, and thermal stress analysis in thin-walled structures.

Lattice structures are employed in the aerospace, automotive, and medical industries due to their high energy absorption, high porosity, and high strength-to-density ratios. Besides the traditional manufacturing approach, here we employed additive manufacturing, Fused deposition modeling (FDM) approach. In this paper, effect of struts on compressive deformation behavior of Body-centered cubic (BCC), Helix body-centered cubic (HBCC), Half vertical strut body-centered cubic (HVSBCC) and Full vertical strut body center cubic (FVSBCC) structures are examined both numerically and experimentally. The results show that the half verticle strut body center cubic has superior properties. The compressive strength of the Half vertical strut body-centered cubic (9.5 MPa) is ~436.72% higher than simple body-centered cubic (1.77 MPa), ~139.89% higher than the helix body-centered cubic ( 3.96 MPa), and ~25% higher than full vertical strut body-centered cubic (7.6 MPa). Also, The energy absorption of half vertical strut body-centered (3.49 MJ/m³) is ~14817.39% higher than the simple body-centered cubic (0.23 MJ/m³), ~711.62% higher than the helix simple cubic (0.43MJ/m³) and ~36.8% higher than the full vertical strut body-centered cubic. Further, the strut variation among structures controls the Poisson ratio and ultimately the strain-induced deformation response. Hence, optimizing local strut alignments in the lattice structures guides to betterment of mechanical properties for varied applications.

This paper introduces a novel higher-order shear and normal deformation theory (HOSNDT) for bending analysis of thick beams, addressing the limitations of existing beam theories and providing significantly improved accuracy in predicting stress and strain distributions. Unlike conventional approaches, the proposed HOSNDT model employs a sophisticated fifth-order polynomial function, meticulously developed and validated through MATLAB simulations. The theory is applied to simply supported beams constructed from materials with constant elasticity modulus and functionally graded materials, showcasing its versatility and robustness. Key parameters, including transverse displacement, transverse shear stress, and axial normal stress, are analyzed comprehensively, with boundary constraints free of traction ensuring the model’s broader applicability across diverse structural configurations. The inadequacies of conventional beam theories in describing the stress-strain distribution in thick beams are highlighted. The proposed four-variable model addresses these challenges effectively by incorporating both normal and transverse shear deformations, resulting in more precise and reliable predictions of beam behavior under varied loading conditions. Comprehensive experiments validate the model’s improved stability and accuracy, demonstrating its potential as a powerful tool for structural engineering applications. These findings establish a solid foundation for future research on diverse beam configurations and advanced material combinations, offering promising directions for innovation in structural engineering analysis, optimization, and design.

The present work investigates the forced vibrations of a functionally graded (FG) nano-beam by considering the harmonic moving force with constant acceleration and initial velocity. There is no exact solution to the vibrations of nano-beam with accelerated harmonic moving force, so the main purpose of this paper is to provide a method to obtain an accurate solution for nanoscale structures under accelerated harmonic moving force. For this purpose, the equations governing nano-beam vibrations of an FG porous with the Hamilton principle are extracted by considering Euler Bernoulli’s beam theory and using the nonlocal strain gradient theory. By applying the Galerkin method, partial equations are converted to differential equations. The Laplace transform method is used to solve the differential equations. An exact solution of the temporal response for FG nano-beam under harmonic motility with constant acceleration and initial velocity in the presence of temperature is obtained. The results section investigates the effect of various parameters such as excitation frequency, power law index, temperature, porosity, and changes in moving force acceleration on the maximum dynamic displacement of nano-beam. The simultaneous effect of nonlocal parameters and dimensionless longitudinal scale on maximum dynamic displacement has also been studied. For the accuracy of the results, the natural frequency of the nano-beam is compared with previous research work. The innovation of the presented article is in providing an accurate solution using the Laplace method to analyze the forced vibrations of a porous nano-beam with an accelerated harmonic dynamic force, which has not been done so far.

This paper presents an exact analytical solution of one-dimensional consolidation for unsaturated soils under the local surcharge load using the mode superposition method. Based on the solution to Boussinesq’s problem, the distribution of total normal stress is considered in the consolidation equations. Then, the excess pore-air and pore-water pressures are expressed in a series of products of eigenfunctions concerning depth and normal coordinates concerning time, respectively. After matrix algebraic manipulation, the normal coordinates can be determined by the initial conditions and the loading function, and the final solutions for the unsaturated consolidation are obtained. This solution can avoid inconvenient Laplace transform and inverse Laplace transform and can be degenerated to the existing formulation. Through calculating two classic examples, the validations of the proposed analytical solution are verified against other analytical solutions and the developed finite difference solution. According to the proposed solutions, the consolidation behaviors involving three loading patterns and two loading histories are graphically demonstrated and discussed.

In recent years, with the explosion of the industrial revolution 4.0, terms such as artificial intelligence (AI) have become familiar and increasingly widely applied in the engineering field. This study focuses on the study and evaluation of AI models to predict the axial strength of concrete-filled steel tube columns (CFST). In particular, this study introduces and highlights a new AI model, Kolmogorov-Arnold Networks (KAN), and compares its performance with the previously existing AI model, support vector regression (SVR), along with Eurocode 4. A large dataset consisting of two types of CFST columns (hollow circular and hollow square CFST columns) with different concrete strengths was created using ABAQUS software. The AI models were evaluated based on important statistical indices such as MAPE, MAE, RMSE, and correlation coefficient R. The analysis results showed that the KAN model was the most effective AI model when compared with other models. The R indices were always greater than 0.9 and the MAPE, MAE, RMSE indices were the lowest among the compared models. At the same time, the predicted data from the KAN model showed the highest similarity with the actual data in predicting the axial strength of four types of CFST columns. Therefore, the KAN model can be considered as a powerful and accurate tool in predicting the compressive strength of CFST columns.

To investigate the elastic responses of materials with memory for a rotating media subjected to magnetic effects, an innovative mathematical model in micropolar generalized thermoelasticity is being developed. The novelty of the current study lies in integrating memory effects with microstructural features, which allows for the investigation of advanced materials that possesses both micro and macro level time-dependent nature. To determine the analytical solution of the required problem, the normal mode technique along with the Helmholtz potential’s, is being used. The normal mode technique transforms the system of partial differential equations into a system of ordinary differential equations, resulting in an analytical solution of the problem. Graphical analysis has been provided, depicting variations in the temperature distribution, force stress, couple stress, and displacement components.