Archive of Applied Mechanics最新文献

Conformal mapping functions have significant applications in mechanics and other fields, and their computation methods have drawn considerable attention. We propose an iterative algorithm to compute the conformal mapping from the unit disk to physical domains with regular boundaries, defined by having only prime ends of the first kind. The mapping function is expanded into a Laurent series and use its truncated partial sum as an approximation. The Schwarz–Christoffel mapping formula provides the initial estimates for the series coefficients, which are then iteratively optimized. This algorithm efficiently handles complex domain shapes, such as winding orifices and slits, with high computational speed. Moreover, it offers valuable insights for designing algorithms to solve other types of conformal mapping problems and has practical significance in applications involving conformal mappings.

This study introduces a generalized photothermal model to analyze the coupled thermo-hydromechanical behavior of a poroelastic, nonlocal semiconductor medium subjected to laser excitation. The medium is modeled as a saturated, dynamic, poroelastic half-space under time-harmonic loads, including thermal and mechanical forces and plasma electron distribution induced by laser pulses. A novel framework that integrates photo-thermoelasticity with hydrodynamic and poroelastic effects, capturing the nonlocal interactions at the nanoscale. At first, we subjected this medium to time-harmonic loads comprising thermal and normal loads and a distribution of plasma electrons applied with heating laser pulses. Afterward, we compared the photo-thermoelastic dynamic models to the coupled thermo-hydromechanical ones. The resulting nondimensional coupled equations were solved using two-dimensional normal mode analysis. The resulting nondimensional coupled equations were solved using two-dimensional normal mode analysis. The study examined the effects of nondimensional displacement, mechanical stress, excess pore water pressure, carrier concentration (density), and temperature distribution on the poroelastic half-space medium. Graphical representations were produced to highlight these effects based on specific parameters.

In this paper, we describe an approach for the structural analysis of isotropic composite structures by combining the reduced order model of limit analysis with artificial neural networks (ANN). At first, the ANN is introduced in order to represent the effective strength surface of isotropic composites implicitly in the macro principal stress space. The input neurons are the macro principal stress components, while ANN output neuron is the limit load factor. In order to estimate the limit load factor, the reduced order model of limit analysis for the representative volume element is used. Then, the structural analysis can be easily implemented in the computational framework of the FEM. Macro stress is evaluated by using the elastic analysis of the homogenized composite structure, and the safety is estimated via the effective strength surface represented by ANN. As a result, structural analysis of composites can be reduced into that of common homogeneous materials. Numerical examples show that the proposed method is an efficient approach of the structural analysis of composites structures.

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.