Archive of Applied Mechanics最新文献

This study investigates the stationary interacting of multiple cracks within both the interface and the embedded layer of a homogeneous half-plane coated with a functionally graded material (FGM) under elastodynamic in-plane loading. Leveraging the distributed dislocation technique, this research provides a novel framework for exploring the intricate fracture mechanics of this specific material configuration. To accurately quantify dynamic stress intensity factors (DSIFs) within this complex medium, the study employs the method of integral transformations. This approach involves strategically positioning Volterra-type climb and glide edge dislocations at the critical interface between the half-plane and the FG coating. To characterize the traction vector along the surfaces of multiple cracks, we construct systems of Cauchy singular integral equations using dislocation solutions. By numerically solving these equations, we precisely determine the dislocation density along the crack surfaces. This critical information then enables exceptionally accurate computation of DSIFs at the crack tips. This study's numerical findings reveal how material gradient characteristics, Poisson's ratio, excitation frequency, coating thickness, crack length and crack interactions collectively govern the DSIFs of graded coatings. These results clarify the complex mechanics of these materials under elastodynamic loading.

Accurately assessing the fatigue performance of components is the key to ensuring structural integrity and reliability, but there is a lack of fatigue life prediction methods that effectively couple the stress gradient effect, the non-proportional additional strengthening effect, and the size effect. Accordingly, a fatigue life prediction model for notched specimens under multiaxial loading is established by analyzing the influence of tension–torsion proportional load and tension–torsion non-proportional load on the fatigue strength of notched specimens. Firstly, based on the energy critical plane method, the location of the critical plane is determined with the help of the coordinate transformation principle. Secondly, the material constant is used to quantify the level of cyclic strengthening, and a non-proportional additional strengthening function is proposed by considering the influence of phase difference. Thirdly, the influence of the non-uniform stress field at the notch root on the fatigue life is considered, and the distribution of equivalent stress on the specific paths is extracted and normalized to give an equivalent stress gradient factor. Then, a fatigue strength reduction factor is constructed by considering the influence of different notch geometrical parameters. Finally, a fatigue life assessment method for notched specimens is proposed based on the Manson–Coffin equation. With the help of the test data of three materials, En8, Al7050-T7451, and GH4169, the method is validated and compared with the calculation results of the Manson–Coffin equation, SWT model, and FS model. The results show that the prediction accuracy of the method in this study is high, which is located in the two-fold error dispersion band, and the prediction results are better than that of the other three models.

Buckling of axially loaded beams is discussed in the context of Λ-fractional analysis and mechanics. An axially compressed cantilever beam is considered in the Λ-fractional space, and the critical load is defined. The variational buckling problem of the simply supported beam is considered in the Λ-fractional space. It is pointed out that the Euler–Lagrange equation corresponding to the minimization of the total energy function with the Weierstrass–Erdmann conditions is only acceptable. The Λ-fractional buckling elastic curve of a simply supported beam is presented. That elastic curve is transferred into the initial space. The post-critical buckling deformations are defined in the context of globally stable equilibrium deformations.

In recent years, the examination of blood flow in diseased arteries has been an essential field of research. Atherosclerosis is one of the most common arterial diseases, usually known as stenosis. The current work investigates the combination impact of electric and magnetic fields of the unsteady, two-dimensional and laminar pulsatile non-Newtonian flow of blood in an axisymmetrically inclined tapered porous stenotic artery containing gold nanoparticles with different shapes subject to body acceleration and slip effect at the wall. Heat source and thermal radiation are also considered. The phenomenon of the imposed electric field is described by the Poisson–Boltzmann equation. To immobilize the effect of the vessel wall, a transformation of the radial coordinates is used. The adoption of gold nanoparticles as nanomaterials for drug delivery is mainly due to their stability, inert nature, absence of cytotoxicity, high disparity and biocompatibility. An explicit scheme of finite differences is employed for solving the nonlinear partial differential equations that govern the current problem, as well as the prescribed boundary conditions. The applied magnetic and electric fields have significant effects on the flow field and heat transfer.

This study deals with the size-dependent nonlinear vibration and dynamic responses of microplates reinforced by the porous Graphene Platelets (GPL) nanofillers under the thermal environment. The heat conduction is taken into account by the graphene platelets dispersion and porosity distribution, and the nonlinear temperature rise is assumed to be varied in thickness. To pursue the research purpose, the modified couple stress and nonlocal theories with the geometrically nonlinear analysis based on the higher-order shear strains are integrated to describe the mechanical characteristics of microplates. Three GPL distributions in conjunction with three porosity patterns dispersed along the thickness cause the nonlinear temperature profiles to vary with the relative density and porosity. The nonclassical motion equilibrium equations are established with the aid of the virtual work’s principle, the Halpin–Tsai micromechanical modeling, and the new nonlinear temperature profiles solved by heat conduction. Moreover, the improved iterative method produced into the Bézier extraction approach scrutinizes the microplate's size-dependent thermal frequency-deflection responses. Consequently, the desired mechanical properties and the structural characteristics of the GPL intact and hearted cutout microplates have been efficiently enhanced by incorporating the porosity coefficient, GPL dispersion, negative GPL thermal expansion, and length scale parameter, particularly under nonlinear temperature conditions.

A new analytical solution based on the Ritz method is presented in this paper for analyzing the free vibration and buckling behavior of porous bi-directional functionally graded (2D-FG) beams under various boundary conditions. The solution is based on first-order shear deformation theory (FSDT). The selection of solution functions used in Ritz methods distinguishes the methods from each other and determines the accuracy of the analytical solution. To accurately capture the system's behavior and achieve the desired results, these functions have been carefully selected as a combination of polynomial and trigonometric expressions tailored as mixed series functions for each boundary condition. The study considers three types of porosity, namely PFG-1, PFG-2, and PFG-3. The equations of motion are derived using Lagrange's principle, taking into account the power-law variation of the beam material components throughout the volume. The non-dimensional fundamental frequencies and critical buckling loads are calculated for different boundary conditions, gradation exponents in the x and z directions (p_x, p_z), slenderness (L/h), porosity coefficient (e), and porosity types. Initially, the accuracy of the mixed series functions is investigated for non-porous bi-directional functionally graded beams, and the numerical results are compared with existing literature to validate the proposed solution. Subsequently, the paper focuses on analyzing the influence of porosity on the free vibration and buckling behavior of bi-directional functionally graded beams using the developed solution method.

In engineering, soft rock is often damaged by dynamic loads such as dynamic compaction, vibrating compaction and blasting, resulting in varying degrees of damage. To understand the compressive response, fracture characteristics and energy dissipation characteristics of red bed soft rock under different dynamics, we carried out a series of dynamic impact tests by the separated Hopkins pressure bar system. The experimental results show that the dynamic peak stress, critical strain and toughness of red bed soft rock increase with the increase in strain rate with the increase in strain rate, which ranges from 37 to 102 s⁻¹. Specifically, the dynamic compressive strength of red bed soft rock at 98 s⁻¹ is 4.63 times that of the quasi-static average. As the strain rate increases, the fracture characteristics: integrity, slightly split and pulverized, and the size of fragments decrease and the number of fragments increases. When the strain rate exceeds the critical value 72 s⁻¹, the fracture characteristics are pulverized. The energy dissipation density increases with the strain rate and increases faster when the strain rate exceeds the critical value. The energy utilization first increases and then decreases, when the strain rate is 88 s⁻¹, the maximum utilization rate is 38%.

Determining the stress state in a circular ring has been a classical topic in the stress analysis literature. Based on the principle of superposition, the results may be obtained by adding known solutions to an associated ring problem, where the boundary stresses on the inner and outer walls of the ring are represented in Fourier series. In this work, the coefficients of the Fourier series are generated through an algorithm based on the fast Fourier transform (FFT). In the case of concentrated loading, the required additional fundamental solutions are derived in closed-form. The presented numerical method allows for accurate and efficient computations of the stress distributions in a circular ring in static equilibrium under arbitrary in-plane loading; and generally, the FFT-based algorithm provides a convenient and versatile tool for handing some two-dimensional problems involving circular boundaries.

The series tuned inerter dampers (STID) with distributed inerters are proposed in this paper to suppress seismic response for ground motion excited structures with broadband characteristics. In order to reveal the mechanism of the STID for vibration mitigation, the dimensionless displacement objective function of a single degree of freedom structure equipped with an STID under random Gaussian white noise base excitations is thereupon derived. Based on the principle of the reasonable distribution of inertance, the analytical optimal design parameters of STID are obtained under constraint for total inerter-mass ratio. The vibration mitigation performance of the STID is evaluated and further compared with the tuned inerter damper (TID), tuned mass damper (TMD) and typical series dampers using same mass ratio or inerter-mass ratio when structure is subjected to harmonic and random excitation. Results demonstrate that the performance of structural vibration control and broadband characteristics of STID outperform both the TMD and TID. On the condition of same inerter-mass ratio, the deformation enhancement of damping element can be further increased compared with TID because of dual-tuning effect of series inerters. The higher vibration control performance of STID is realized by using very small nominal damping ratio compared with the TMD and TID. Meanwhile, there exist two grounded inerters in STID compared to other series dampers, and both two subsystems are not affected by base random acceleration excitation which also brings STID a wider VSB and better seismic response mitigation effect. Substantially, due to STID is a type of dual-grounded inerter-based device, for force and base acceleration excited main system, the optimal expressions are identical. Hence, STID can adapt to more complex practical engineering and random and diverse excitations. Hence, the STID can be deemed to be a broadband, high effectiveness and high-performance inerter system. Meanwhile, considering low damping, lightweight and flexible install of STID, it is easier for implementation in practical engineering.

Usually, detailed impact simulation models within flexible multibody systems have to be set up manually rather than being generated automatically. This is because the process requires prior knowledge of the time and location of the impact, as well as the element resolution within the contact area. If the penalty method is used to determine the occurring contact forces, the corresponding penalty factor also needs to be determined manually. This work, however, presents an adaptive algorithm to simulate impacts within flexible multibody systems fully automatically using reduced isogeometric analysis models, the floating frame of reference formulation, and quasistatic contact models for an efficient but still accurate simulation. The adaptive algorithm detects impacts in the system, determines the contact locations on the bodies, refines the contact area, and determines the penalty factor, and therefore automatically simulates impacts. The work shows how to automatically simulate impacts in flexible multibody systems without user action or prior knowledge of impact location and size. The first application example simulates significant elastodynamic effects within a long flexible rod. The goal is to validate the algorithm by preserving the wave propagation and energy of the system. The second application example simulates the impacts of two flexible double pendulums. This setup is a suitable benchmark for the complete adaptive impact analysis procedure as the flexible double pendulums undergo large rigid body motions.