International Journal of Applied Mechanics

The Robertson–Stiff fluid (RS) is a yield-pseudo-plastic model which has been used to describe the rheological properties of drilling fluids, cement slurries and bentonite suspensions. Experimentally, several rheological data showed that this model provides more consistently accurate descriptions of the rheology of such fluids than other viscoplastic models. This result motivates us to study theoretically the peristaltic transport for this shear-thinning model and for other viscoplastic models in the presence of heat and mass transfer in a cylindrical tube. For long wavelength and low Reynolds number approximations, an analytical solution is obtained. The results showed that the velocity and the temperature decrease with increasing the yield parameter and the power index while they increase with the increase in the occlusion parameter. We also observed an opposite behavior of the concentration versus these physical parameters. Moreover, all these parameters enhance the mechanical efficiency of pumping. In addition, the comparison shows that the velocity, temperature and the absolute value of concentration are greater for the proposed model than those of Herschel–Bulkley, Bingham and Casson models, respectively.

In this paper, nonlinear dynamic buckling of laminated composite cylindrical panels subjected to in-plane impulsive compressive load is studied along with the failure analysis. Balanced and symmetric angle-ply laminated composite curved panels are considered. Convergence study is performed, and results are validated with the results from the existing literature, and then the dynamic buckling loads are calculated. The failure index of laminated composite curved panel is also calculated to check the precedence of first ply failure load over nonlinear dynamic buckling load. The effect of aspect ratio, loading function, and radius of curvature is studied. The analysis is carried out using finite element method. It is observed that the first ply failure for balanced and symmetric angle-ply laminated composite curved panels occurs after the panel has buckled due to dynamic impulse loads.

Mode mixity plays an essential role in the criteria of mixed mode fracture. In this paper, a novel approach for precisely controlling mode mixity under dynamic loading is proposed. Numerical simulation of all fracture mode (AFM) specimen and modified compact tension shear (MCTS) specimen loaded by split Hopkinson tension bar (SHTB) apparatus is carried out. With a constraint on MCTS specimen on the direction perpendicular to the incident bar, the dynamic stress intensity factor (DSIF) ratio of mode I to mode II remains constant during the loading process. When the constraint is absent, the DSIF ratio varies due to the vibration of clamps and specimen. The DSIF of MCTS specimen under different loading angles is also studied, and the ratio $K_{\mathrm{\text{I}}}/K_{\mathrm{\text{I}}\mathrm{\text{I}}}$ approximately equals the tangent of loading angle, which is also proven in experiments. Moreover, numerical results indicate that the influence of the shape of clamps is significantly reduced by applying a constraint on the specimen. It is concluded that AFM specimen is not suitable for dynamic fracture tests owing to over complicated clamps.

In this paper, the uncertain mechanical parameters are modeled as spatial random fields (RFs). A new tetrahedral discretization methodology of three-dimensional (3D) RF is proposed based on the local average (LA) theory. An analytical formula and a numerical formula of the covariance for any two tetrahedral RF elements are developed. Its main advantage, compared to similar studies employing hexahedral discretization method, is that tetrahedral LA method can perfectly combine with tetrahedral finite element (FE) method. Also, the corresponding relation between RF mesh and FE mesh is clearer and the computer codes are simpler. The accuracy of proposed LA method in this study was verified by comparing with other discretization techniques of RF. Finally, an illustrative example is presented to demonstrate the analysis process. The validity and the advantage of the proposed LA method are proven. Taking the spatial variations of uncertain mechanical parameters into account, the stochastic effects of scale of fluctuation on the RF are estimated. The proposed method can be widely applied to 3D stochastic FE analysis, and the sample results will improve our understanding of the stochastic influence of scale of fluctuation on the RF.

The aeroelastic flutter analysis of thick porous plates surrounded with piezoelectric layers in supersonic flow is studied. In order to aeroelastic analysis of the thick porous-cellular plate, Reddy’s third-order shear deformation plate theory and first-order piston theory are used. Furthermore, the plate is composed of two face piezoelectric layers and three functionally graded porous distributions core. Applying the extended Hamilton’s principle and Maxwell’s equation, the governing equations of motion are obtained. The partial differential governing equations are transformed into a set of ordinary differential equations by applying Galerkin’s approach. The effects of porosity coefficient, porosity distributions, piezoelectric layers, geometric dimensions, electrical and mechanical boundary conditions on the flutter aerodynamic pressure and natural frequencies of porous-cellular plates are investigated.

This paper presents a comparative study of two typical inverse algorithms, i.e., direct and iterative inversion methods, to reconstruct the shear modulus distribution of linearly elastic solids. Both approaches are based on the finite element framework and compared utilizing both the simulated and experimental data. The reconstruction results demonstrate that both approaches are capable of identifying the nonhomogeneous shear modulus distribution of solids well. It can also be found that the direct inversion method is much faster than the iterative inversion method, whereas the iterative inversion method is capable of yielding better shear modulus ratio between the stiff inclusion and the soft background even with very high noise levels. Afterwards, a thorough comparison on the advantages and disadvantages of these two approaches has been performed. This comparative study provides useful information on the selection of the proper inverse scheme in estimating nonhomogeneous elastic property distribution of soft solids nondestructively.

Due to the interesting properties such as light weight and high deformation ability, dielectric elastomer (DE) resonators can be good alternatives for conventional silicon resonant beams used in micro-electro-mechanical systems (MEMS). This paper proposes a modeling in which a pre-stretched clamped-clamped DE-based microbeam oscillating above the ground substrate is subjected to an external electrostatic pressure. Using a DE-based beam affects the total rigidity of the system, which may lead to an anticipated saddle-node or pitchfork bifurcation. Hence, the present study tries to analyze the effects of DE properties on changing the stability regime of DE-based microbeams under electrostatic actuation. The stability of the system has been investigated using an eigen-value form of the problem. The effects of DE properties including pre-stress, relative permittivity and voltage value across the electrodes on pull-in or divergence instability as well as the frequency response of the system have been investigated. Moreover, the critical values of the DE voltage as a booster of instability occurrence have been obtained in either the presence or absence of the direct current (DC) voltage. It has been found that the pre-stress and appropriate DE permittivity can provide a needed magnitude of the DE actuating voltage to alter the resonance frequency and stability positions of the structure.

The buckling and free vibration of a Euler–Bernoulli beam composed of two-directional functionally graded materials (FGMs) in thermal environment are analyzed. The material properties and temperature distributions are considered to be continuously varied along both axial and thickness directions. Such two-directional FGMs provide the basis of a promising strategy to tune the dynamic behavior of a structure in a controlled fashion, achieving tunable response as desired. The dynamic equation of the beam and relevant boundary conditions are derived based on Hamilton’s principle. The generalized differential quadrature method is used for determining the exact buckling configuration and the natural frequencies of the beam with different boundary conditions. Numerical results are presented to examine the effects of material gradations on the critical buckling temperature. It is concluded that both temperature change and material properties have significant influences on the natural frequency, which suggests that it is possible to tailor or tune the dynamic behaviors of a beam by using man-made FGMs in a complex environment.

Given its essential nonlinearity, nonlinear energy sink (NES) has been extensively studied as a promising vibration energy harvesting device. Internal resonance, which is due to strong energy exchange between modes, also provides a valuable idea for vibration energy harvesting. Combining these two advantages, we put forward a 3:1 internal resonance system, which consists of an NES and a coupled linear oscillator, as an enhanced method for vibration energy harvesting. The multiscale method is applied to derive the relationship between amplitude and frequency response. Simulations are carried out to evaluate the performance of the proposed method. Results show that the internal resonance system can remarkably improve the vibration energy harvesting performance. The numerical solutions verify the accuracy of the analytical solutions. The results demonstrate that the internal resonance system with NES for energy harvesting has better output power and bandwidth compared with noninternal resonance system. Overall, the comprehensive design improves the performance of NES for vibration energy harvesting.

A double finite sine integral transform method is employed to analyze the buckling problem of rectangular thin plate with rotationally-restrained boundary condition. The method provides more reasonable and theoretical procedure than conventional inverse/semi-inverse methods through eliminating the need to preselect the deflection function. Unlike the methods based on Fourier series, the finite integral transform directly solves the governing equation, which automatically involves the boundary conditions. In the solution procedure, after performing integral transformation the title problem is converted to solve a fully regular infinite system of linear algebraic equations with the unknowns determined by satisfying associated boundary conditions. Then, through some mathematical manipulation the analytical buckling solution is elegantly achieved in a straightforward procedure. Various edge flexibilities are investigated through selecting the rotational fixity factor, including simply supported and clamped edges as limiting situations. Finally, comprehensive analytical results obtained in this paper illuminate the validity of the proposed method by comparing with the existing literature as well as the finite element method using (ABAQUS) software.

This is the first research on the vibration and buckling analysis of a graphene nanoplatelet composite (GPLRC) microdisk in the framework of a numerical based generalized differential quadrature method (GDQM). The stresses and strains are obtained using the higher-order shear deformable theory (HOSDT). Rule of the mixture is employed to obtain varying mass density, thermal expansion, and Poisson’s ratio, while the module of elasticity is computed by modified Halpin–Tsai model. Governing equations and boundary conditions of the GPLRC microdisk are obtained by implementing Extended Hamilton’s principle. The results show that outer to inner ratios of the radius ($R_{\mathrm{\text{o}}}/R_{\mathrm{\text{i}}})$, ratios of length scale and nonlocal to thickness $(l/h$ and $\mu \mathrm{\text{/}}h)$, and GPL weight fraction $(g_{\mathrm{\text{GPL}}})$ have a significant influence on the frequency and buckling characteristics of the GPLRC microdisk. Another necessary consequence is that by increasing the value of the $R_{\mathrm{\text{o}}}/R_{\mathrm{\text{i}}}$, the distribution of the displacement field extends from radial to tangent direction, especially in the lower mode numbers, this phenomenon appears much more remarkable. A useful suggestion of this research is that, for designing the GPLRC microdisk at the low value of the $R_{\mathrm{\text{o}}}/R_{\mathrm{\text{i}}}$, more attention should be paid to the $g_{\mathrm{\text{GPL}}}$ and $R_{\mathrm{\text{o}}}/R_{\mathrm{\text{i}}}$, simultaneously.

In this paper, a coupling of improved element-free Galerkin (IEFG) method and semi-analytical finite strip (FS) method is presented for free vibration analysis of thin plates. This method is very easy to implement and has advantages of both IEFG and FS methods, so that IEFG method is used in sub-domain with complex geometry, and FS method is used for the remaining domains. The use of the FS method considerably reduces the analysis time, and the essential boundary conditions are easily enforced in FS sub-domain. In the IEFG method, the shape function does not have the Kronecker delta function property. Therefore, Lagrange multipliers method is used to satisfy the boundary conditions. Finally, five examples are presented to show the effectiveness of this work.

In this paper, the improved interpolating complex variable moving least squares (IICVMLS) method is applied, in which the complete basis function is introduced and combined with the singular weight function to achieve the orthometric basis function. Then, the interpolating shape function is achieved to construct the interpolating trial function. Incorporating the IICVMLS method and the Galerkin integral weak form, an improved interpolating complex variable element free Galerkin (IICVEFG) method is proposed to solve the 2D potential problem. Because the essential boundary conditions can be straightaway imposed in the above method, the expressions of final dispersed matrices are more concise in contrast to the non-interpolating complex variable meshless methods. Through analyzing four specific potential problems, the IICVEFG method is validated with greater computing precision and efficiency.

In this paper, the improved complex variable element-free Galerkin (ICVEFG) method is proposed for solving the bending problem of thin plate on elastic foundations. In the ICVEFG method, the approximation function regarding the deflection of thin plate is formed with the improved complex moving least-squares (ICVMLS) approximation, the discrete equation is obtained from Galerkin weak form of bending problem of thin plate on different elastic foundations, and essential boundary conditions are considered based on penalty method. As the ICVMLS approximation is based on the complex variable theory, it can obtain the shape function quickly with high precision. Three sample problems are used to discuss the advantages of the ICVEFG method, and the numerical results show that the ICVEFG method presented in this paper has a fast convergence speed and great computational accuracy.