Archive of Applied Mechanics最新文献

The damage and aging of short fiber-reinforced rubber composites (SFRCs) have a significant impact on the performance and stability of associated products. However, the presence of internal short fibers and the large deformation characteristics of rubber materials make it difficult to characterize the damage behavior. Therefore, it is imperative to investigate the material’s damage behavior, as well as the influence of aging on mechanical properties, and develop a precise constitutive model. This study extends configurational mechanics to hyperelastic materials and introduces the concept of equivalent configurational stress as a physically meaningful variable representing damage, thereby establishing a constitutive model that couples aging and damage. Uniaxial tensile tests were performed on samples in various aging states to analyze the damage behavior of SFRCs and validate the accuracy of the proposed constitutive model. Furthermore, this research highlights the prospective application of configuration mechanics in characterizing damage in composite materials.

A PD-FEM coupling scheme with the potential to solve large-scale or multi-scale models is proposed which utilizes the advantages of PD in solving discontinuities and the computational efficiency of the finite element method. The scheme can perform the global unstructured discretization of the model, ensure that the crack initiation and propagation are not affected by the grid, and the boundary conditions can be flexibly arranged. The non-overlapping domain coupling method is used to couple the finite element domain and the circumferential dynamic domain to reduce the influence of the ghost force on the model solution. In order to verify the ghost force, the proposed PD-FEM model is used to simulate the displacement field distribution of the two-dimensional plate under uniaxial tension and the cantilever beam under concentrated force. The calculation results are compared with the theoretical calculation results and finite element calculation results. In addition, the scheme takes advantage of the high computational efficiency of the finite element method, and uses the OpenMP parallel computing framework of Fortran language to realize the efficient solution of the three-dimensional model. The validity and computational efficiency of the PD-FEM model are verified by the tensile test of the prefabricated cracked square plate, the double-notched specimen, the three-dimensional l-shaped plate and the composite mode fracture test of the three-dimensional three (four) point bending beam.

For a thick sandwich plate, transverse stretching vibration and in-plane vibration might occur before bending vibration in practical applications, which may threaten the dynamic safety of composite structures. Therefore, this work attempts to improve the in-plane and transverse stretching stiffness of sandwich structures by using carbon nanotubes (CNTs) to reinforce face sheets. To this end, it is necessary to understand well the influence of CNTs distributions on the three-dimensional (3D) vibration of functionally graded sandwich plates. Therefore, an extended global–local higher-order model will be proposed to accurately predict 3D vibration behaviors of sandwich structures reinforced by the CNTs, as the existing equivalent single-layer models will encounter difficulties in accurately analyzing such issues. Based on the proposed model, analytical solutions and finite element formulation have been presented to study the dynamic behaviors of sandwich plates with reinforcement of the CNTs, which have been verified by 3D elasticity solutions and three-dimensional finite element results. Moreover, the influence of the CNTs distributions and volume fractions on the vibration behaviors of sandwich plates has been investigated. Finally, by selecting appropriate profiles of the CNTs through the thickness, the in-plane and transverse stretching stiffness of sandwich structures can be significantly improved.

The main objective of this study is to uniformly solve the buckling problem of fully clamped (CCCC) orthotropic/isotropic rectangular plates with different thicknesses. The analysis uses the symplectic superposition method. This method describes the buckling problem of orthotropic rectangular moderately thick plates (RMTPs) in the Hamiltonian system for treatment in the symplectic space. First, the governing equations of RMTPs are represented by Hamiltonian canonical equations. Then, the original buckling problem of a CCCC rectangular moderately thick plate (RMTP) is divided into two sub-buckling problems. The variable separation method in the Hamiltonian system is used to calculate the general solutions of these two sub-buckling problems. The symplectic superposition solution of the original buckling problem is obtained by superimposing the general solutions of the two sub-buckling problems. Finally, the analysis results of the buckling load and modal shape of orthotropic rectangular plates under various thicknesses and aspect ratios are presented in numerical examples.

Nowadays, the extensive applications of the ultrafast heating technologies (e.g., laser burst, induction heating, etc.) in the fabricating and manufacturing of the porous elastic solids (e.g., cellular material, mesoporous material, macroporous material, etc.) have aroused great interests on investigating the constitutive modeling and transient dynamic responses analysis of the porous-thermo-elastic coupling. Although the fractional temperature rate-dependent porous-thermo-elasticity theories have been historically proposed, the theoretical formulations still adopt the classical fractional derivatives with singular kernels, and the inherent strain relaxation effect and the associated memory dependency are not considered yet in the ultrafast heating condition. To compensate for such deficiency, the present work aims to establish a fractional-order rate-dependent porous-thermo-elasticity model based on the new fractional derivatives with the non-singular kernels (i.e., Caputo–Fabrizio, Atangana–Baleanu, and tempered Caputo fractional derivatives). With the aids of the extended thermodynamic principles, the new constitutive and governing equations are obtained. The proposed theoretical model is applied to investigate the 1D transient dynamic response analysis of magnesium-based porous half-space with voids by applying the Laplace transformation approach. The influences of the new fractional derivatives on the wave propagations and structural transient dynamic responses are evaluated and discussed.

In this paper, we present a series solution for free in-plane vibration of composite plates with arbitrary shape by using the domain segmentation integral method and derive the tangential and normal vibration displacement equations for the plate boundaries. The solution presented is widely applicable to the analysis of free in-plane vibration of plates; it can accurately and effectively solve the in-plane free vibration problem of arbitrarily shaped non-homogeneous orthotropic plates of variable thickness, complex geometry and variable material properties with respect to in-plane coordinate parameters. To verify the effectiveness, accuracy and applicability of the proposed solution, we perform a computational analysis of different orthogonalization intervals, weight functions, penalty stiffness and the truncation number of orthogonal polynomials. Additionally, the effects of the parameters of thickness and nonhomogeneity on the in-plane vibration characteristics of plate are studied. As a result, we present a new series of natural frequencies and mode shapes for arbitrarily shaped non-homogeneous orthotropic plates of variable thickness.

Permanent magnetic bearings (PMBs) hold great potential for various applications such as artificial heart pumps, space equipment, and flywheels. This is due to their notable advantages, including the absence of mechanical contact, no friction, and no control system requirements. However, in many practical scenarios involving PMBs, the bearing installation base is often subject to external excitation, which can interfere with its stability. Currently, the impact of base excitation on the PMB-rotor system and methods for enhancing the stability of the PMB-rotor system under base excitation remain subjects of investigation. Hence, this study focuses on conducting stability analysis of the PMB-rotor system under the influence of base excitation. Firstly, the theoretical model of PMB based on the Halbach array is established, and then the system dynamics model of PMB-rotor under base excitation is established by using the second Lagrange equation. Finally, according to the established dynamic model, the effects of base excitation parameters, structural parameters, and external damping on the stability of the PMB-rotor system under base excitation are analysed through the root locus method. The research results presented in this study provide a theoretical reference for further engineering applications of PMBs.

This paper presents a modified tempered fractional thermal conductivity model aimed at enhancing the analysis of thermal behavior in magnetic thermoelastic solids, particularly in response to time-dependent laser pulse heating. Current literature lacks comprehensive approaches that effectively account for the complex interactions of thermal, mechanical, and magnetic fields within such materials. This gap is critical, as understanding these interactions is essential for optimizing the performance and reliability of advanced materials in engineering applications. Our study addresses this need by introducing a fractional model that employs modified tempered Caputo fractional derivatives in conjunction with a single-parameter Mittag–Leffler function. This innovative adjustment incorporates a parameter specifically designed to capture memory effects, resulting in a more accurate representation of the intricate thermal dynamics at play. We solved the governing equations directly using the Laplace transform method, providing exact formulas for displacement, temperature, and thermal stresses in copper. The graphical representations included in the study illustrate the material's deformation and the development of thermal stresses under thermal loading conditions. The findings demonstrate that the introduction of the memory effect parameter significantly enhances the thermoelastic model's ability to characterize the behavior of materials and structures subjected to thermal loads, thereby contributing valuable insights to the field of magnetic thermoelasticity.

In this study, the scattering of water waves by an undulating bottom in a two-layer fluid with current, surface tension, and interfacial tension is investigated. The perturbation technique followed by the Fourier transform technique are applied to solve the coupled boundary value problem. A Bragg resonance arises between the surface waves and the bottom ripples, which is associated with the reflection of incident wave energy. Hence, the Bragg coefficients namely, Bragg reflection and transmission coefficients, and associated velocity potentials are analysed which are obtained in integral forms. In order to clearly understand the efficacy of the present study, a certain type of undulating bottom, known as sinusoidal bottom undulation, has been examined. It has been shown that when the combined effects of surface tension, interfacial tension, and current are taken into account, the wave reflection is minimal. Moreover, a shift in the Bragg resonant frequency is seen with a change in current speed. In addition, interfacial tension influences both surface and interfacial waves, whereas surface tension primarily impacts surface waves. The results obtained here are expected to be qualitatively helpful in tackling problems of flexural gravity waves in two-layer fluid in the presence of current.

This study presents a finite element model formulated to analyze accurately the bending behavior of functionally graded (FG) plates, employing an improved first-order shear deformation theory (FSDT). In contrast to the conventional Mindlin–Reissner theory, our enhanced FSDT incorporates a parabolic shear strain distribution, providing a more realistic depiction of shear strain throughout the plate’s thickness. Material properties of the FG plates are modeled to undergo continuous variation through the thickness, utilizing power law, exponential, and sigmoid distributions. The investigation focuses on assessing the impact of material composition and geometric parameters under both sinusoidal and uniformly distributed loads, considering various boundary conditions. Comparative analyses with previously published literature underscore the precision and simplicity of our model. The obtained results demonstrate strong agreement with solutions derived from other high-order theories, affirming the accuracy of our proposed model. This research contributes valuable insights into the bending behavior of FG plates and reinforces the reliability of the developed finite element model.