Mechanics of Solids最新文献

Based on the wave theory of unsaturated porous medium, this paper establishes a free-field model of unsaturated soil with a thickness of H overlying a horizontal, uniform, semi-infinite bedrock layer under P-wave incidence. Drawing upon the Helmholtz principle, the wave field within an unsaturated soil site is examined, and the analytical solutions for the dispersion characteristics of bulk waves and the attenuation coefficient are derived. Through numerical simulations, the dispersion phenomenon induced by plane P-wave incidence is analyzed, and the effects of frequency, angle of incidence, saturation level, porosity, and soil layer thickness on the amplitude attenuation coefficient in an unsaturated soil free-field under P-wave excitation are discussed. The findings show that within a specific frequency range, P₁-wave and S-wave in an unsaturated soil free-field exhibit no dispersion characteristics, whereas P₂-wave and P₃-wave demonstrate distinct dispersion behavior. The amplitude attenuation coefficient generally rises with increasing frequency and initially increases before decreasing as the incident angle grows. Simultaneously, the change of amplitude attenuation coefficient with saturation, porosity and soil thickness shows different trends in different incident angle ranges. However, at most incident angles, the amplitude attenuation coefficient is greater than 1, indicating that seismic waves usually produce vibration amplification effect, and vibration attenuation effect occurs only when the incident angle is close to vertical.

Fiber-reinforced cemented soil (F-RCS) is an artificial multiscale geo-material, the strength of which is determined by the physical and mechanical properties of various substances of the F-RCS. To study the effect of fiber content and fiber length on the shear strength of the F-RCS, the substance phases of the F-RCS are divided into reinforcement fiber and cemented soil matrix to establish a meso cell structure of the F-RCS, which can reflect the internal substance properties of the F‑RCS. Moreover, according to microscopic kinetic characteristics of reinforcement fiber and cemented soil matrix and the mesoscopic strain gradient theory, a multiscale Mohr-Coulomb strength criterion (MCSC) of the F-RCS is deduced, and its yield locus is drawn on the π plane. Furthermore, consolidated and undrained triaxial compression tests are conducted on the F-RCS samples with various fibre content and fibre length to obtain the model parameters, and verify the proposed multiscale MCSC of the F-RCS. Results show that the multiscale MCSC the F-RCS is capabel of effectively predicting the shear strength of the F-RCS. The shape of the yield locus of the MCSC of the F-RCS is hexagonal and expands with increasing fiber content and fiber length. The shear stress of the F-RCS predicted by the multiscale MCSC of the F-RCS showcases good agreement with the test results.

This article presents a novel optimization algorithm, JAYA-HCO (High-Cost Optimization), which combines the strengths of JAYA and SCA algorithms. By incorporating the update mechanism of SCA for global search and JAYA’s rapid search capability, JAYA-HCO improves the utilization of the population in JAYA algorithm and makes it more suitable for high-cost computing. Furthermore, JAYA-HCO uses sine functions to introduce mutations at appropriate times to expand the search space. Initially, a set of benchmark functions, including single and multi-modal functions, were used to compare JAYA-HCO with other algorithms in terms of mean value and computation speed. Then, a numerical example of optimizing the fiber orientation angle of laminated composite plates under unidirectional axial compression was conducted to demonstrate the effectiveness and reliability of the proposed algorithm. The objective was to maximize the critical buckling load of the laminated composite plate by adjusting the fiber orientation angle of each layer. The results show that JAYA-HCO algorithm can provide accurate and efficient optimization results, which are validated by comparison with other algorithms and finite element calculations.

To improve the service life of the slewing bearing, the location of the roller subjected to the maximum load is identified using both finite element analysis (FEA) and experimental methods. The plastic deformation behavior of solid and hollow rollers under identical operational conditions is subsequently compared. The accuracy of the simulation results is verified through experimental testing, thereby ensuring the reliability of the analysis. Additionally, simulation data under different degrees of hollowing are systematically analyzed through curve fitting. The results suggest that the optimal hollowness for minimizing plastic deformation is 18% for the main thrust force and 36% for the reverse thrust force, with a notable reduction in plastic deformation under these conditions. These findings indicate that optimizing the hollowing design can effectively reduce plastic deformation.

This paper establishes a four-degree-of-freedom half-vehicle model with nonlinear springs and dampers to study the nonlinear vibration of a car moving on a rough road. According to D’Alembert’s principle, the nonlinear dynamical differential equations of the vehicle system under sinusoidal road excitation are obtained. A system of first-order differential equations is obtained using nondimensionalization and some techniques for order reduction of nonlinear systems with time. Then it is used to investigate the effects of damping and frequency ratios on the body displacement, pitch angle, and displacements of front and rear wheels. The numerical calculation of the equations demonstrates that the damping and frequency ratios control the nonlinear vibration behavior of the vehicle system. The proposed model can also predict the possible motion state of the vehicle system under sinusoidal road excitation at different velocities. The vehicle system will transform periodic motion into chaotic motion. The conclusions provide some available evidence for the design and improvement of the vehicle suspension system.

Generalized Cesaro formulas are found, allowing to determine the displacement field with an accuracy of up to quadratic polynomials through integro-differential operators from the strain tensor-deviator in 3D elasticity theory and 4D elasticity theory. It is shown that quadratures for the pseudovector (pseudotensor in 4D elasticity) of local rotations and deformation of volume change are determined by the strain deviator field with an accuracy of up to linear polynomials in coordinates. Conditions for the existence of the listed quadratures are presented in the form of five (nine for 4D) third-differential order compatibility equations with respect to the strain tensor-deviator components.

This paper develops a mathematical model for modified heat conduction by applying exponential operators and Eringen’s non-locality stress theory within an infinite-length cylindrical cavity subjected to various time-dependent sectional heat supplies. The study employs both the Caputo-Fabrizio and Rabotnov fractional differential operators, which, despite both utilizing exponential functions, differ significantly in their definitions. The Caputo-Fabrizio operator is widely used in fractional calculus due to its nonsingular kernel and broad applicability. In contrast, the Rabotnov operator is particularly effective for modeling complex physical processes and real-life phenomena. The study material is homogeneous and isotropic with uniform surface pressure across boundaries; the model derives exact solutions to the modified heat conduction equations using the integral transformation technique. Solutions in the Laplace transform domain are inverted back to the time domain via the Gaver-Stehfest algorithm. This research highlights the importance of temperature distribution in predicting the behavior of non-local thermoelastic displacement and stress functions with fractional exponential operators. The model, grounded in Eringen’s non-local continuum theory, provides numerical solutions illustrated graphically. The special case analyzed involves various sectional heat supplies affecting the inner curved surface, emphasizing the non-Fourier thermal behavior and the influence of non-local parameters on transient thermoelastic responses. These findings are crucial for accurate predictions in the design and processing of micro- and nanostructures.

Thermodynamic entropy and four different functions used to describe it within mechanical models are considered. It is shown that all four variants have properties that differ significantly from the properties of entropy introduced in thermodynamics based on experimental data. It is established that, in order to comply with the approaches used in thermodynamics, the widely used mechanical model of a rarefied gas should consider almost exclusively processes that assume the presence of external forces acting on the system. It is noted that such a requirement allows a new approach to the use of mechanical models for studying irreversible physical phenomena.

At present, nano-plates with flexoelectric effect have become a research hotspot because they are not affected by material symmetry, so the range of material choices is significantly expanded compared with traditional piezoelectric materials. In this study, considering the flexoelectric effect and utilizing the nonlocal strain gradient theory (NSGT), a novel model is introduced for analyzing transversely isotropic rectangular nano-plates under a distributed load. This new model takes into account nonlocal effect, size effect, and flexoelectricity. By applying the Hamilton principle, the governing equations are derived for two different circuits. In order to verify the validity of the new model, we compare it with the results of the finite element method (FEM) and give its first eight mode shapes. At the same time, the theoretical model is numerically solved, and based on the numerical results, the mechanical properties of the flexoelectric nano-plate are analyzed and discussed. The theoretical and simulation results of this paper provide a reliable theoretical support for the design of devices based on flexoelectric nano-plates.

An innovational method for solving the Euler–Bernoulli problem of an overall buckling of the uniform column supported by rotational springs of stiffnesses γ₁, γ₂, N ∙ m free from traditional simplifications (invariable flexural rigidity and length) is given. It is based on a natural and comprehensive constraint on the restored axis length. A system of algebraic equations relating the critical stress σ_cr to the nonlinear compression diagram ε(σ) of the material, the slenderness of the column λ and the values γ₁, γ₂ has been obtained, solved and verified in important special cases. It is shown that columns of the same material with the same so-called the reduced spring stiffnesses have identical dependencies σ_cr(λ). It is shown that columns with λ ≤ λ_min(γ₁, γ₂) cannot be buckled by any axial load F for various types of ε(σ) (Ramberg-Osgood, rational fraction, polynomial, etc.).