Journal of Applied and Computational Mechanics
Volume:9 Issue: 4, Autumn 2023

This article presents a mathematical model for fluid and solute transport in an ultra-filtered glomerular capillary. Capillaries ‎are assumed to be converging-diverging tubes with permeable boundaries. According to Starling's hypothesis, ultrafiltration is ‎related to the variations in hydrostatic and osmotic pressures in the capillary and Bowman's space and takes place along the ‎length of the capillary. The governing equations of fluid flow for the case of axisymmetric motion of viscous incompressible ‎Newtonian fluid have been considered along with the solute transfer equation. The non-uniform geometry has been mapped ‎into a finite regular computational domain via a coordinate transformation. Correspondingly, the governing equations are ‎transformed to the computational space and solved to get the velocity and pressure values. The solute transfer equation is ‎also solved numerically using a finite difference scheme. The solutions provide the predictions of the axial distribution of ‎hydrostatic pressure and osmotic pressure, velocities, and concentration profiles at various points along the axis and solute ‎clearance quantities along the capillary. The current results are in good agreement with the earlier findings in limiting cases of ‎cylindrical tubes with a constant radius. It is found that there is a significant effect of osmotic pressure on the solute ‎concentration. Using a set of data, the influence of various physiological parameters on the velocity components and solute ‎concentration are presented and discussed through graphs to correlate with physiological situations. The generic structure of ‎the current model also provides an acceptable approach to exploring fluid exchange in organs apart from the glomerular ‎capillary.‎

This paper investigates the problem of free vibrations of a hemispherical shell resonator of a rate-integrating gyroscope. A new realization of the approximate Ritz method for determining the frequencies and forms of free vibrations of an elastic hemisphere is proposed. Based on comparison with the results of direct finite-element modeling, it is shown that the proposed approach provides significantly greater accuracy in solving the spectral problem as compared to the solution based on analytical Rayleigh expressions for the forms of pure bending of the hemispherical surface. The importance of considering the potential energy of stretching of the mid-shell surface for the exact determination of frequencies and resonators waveforms for typical geometric parameters is noted. The degree of influence of the introduced refinements into the resonator’s mathematical model on the values of frequency splitting associated with gyroscopic forces and mass imperfections is investigated.

The technique of numerical inversion of the Laplace transform is applied to solve the population balance equation (PBE). The model considers the dispersed phase systems in which nucleation and heterogeneous condensation are present. The studied phenomena model corresponds to a nonlinear integro-partial-differential equation. Test cases are solved considering two different collision mechanisms, the first-order removal mechanism and the effect of simultaneous coagulation and growth. Numerical results are compared with the analytical solution and with the literature. Based on these results, the technique applied in this work demonstrates to be a tool to solve problems in particulate systems, particularly for aerosol modeling where coagulation is the most important inter-particle mechanism affecting the size distribution.

General solution of the time-dependent strain energy release rate for delamination cracks in multilayered functionally graded load-bearing beam structures which exhibit non-linear creep is derived. The material is functionally graded along the length of layers. The Ramberg-Osgood stress-strain relation is used by assuming that the material in each layer behaves differently in tension and compression. The second term in the Ramberg-Osgood relation includes time dependence to treat the non-linear creep. The solution derived holds for multilayered functionally graded beams with arbitrary number of layers which have different width and material properties. The solution is applied for a delamination in a multilayered beam with a built-in end. An analysis is performed also by considering the balance of the energy in the multilayered beam configuration for the sake of verification. The effect of time is also studied. It is found that the strain energy release rate grows with the time. The results obtained here are useful for understanding the time-dependent delamination in multilayered functionally graded structural components subjected to non-linear creep.

In this article, the ways where thermal radiation, besides other sources of heat, influence the magnetohydrodynamic stream of a Jeffery nanofluid across a widening sheet is investigated. To recover the accuracy of the nanofluid model, the effects of viscous indulgence, chemical response, Brownian motion, and thermophoresis have all been incorporated. The mathematical model of this system is first determined in PDEs format and then turned into ODEs format by similarity process. The numerical simulation of the ensuing nonlinear ODEs with subsequent periphery conditions is established by employing the Runge-Kutta fourth-order integration scheme with the shooting technique. The role of various stream considerations on stream, temperature, nanoparticle concentration, skin friction coefficient, Nusselt and Sherwood quantities are conveyed and explored in graphs and tables. In a limiting sense, the legitimacy of computational outcomes is assessed by comparing them to previously published data. The stream distribution quickens as the Deborah quantity accumulates, whereas the temperature and concentration profiles reflect the downward pattern.

This paper presents a comparative study of different methods for obtaining the dispersion curves of ultrasonic guided waves in anisotropic media. First, we present the classical algorithms used to find zeros and propose some improvements. Next, the spectral method is explained for modeling the guided waves in anisotropic materials while presenting a technique that can distinguish the modes present in the structure. The dispersion curves are plotted using a Matlab program and the results are compared with those of the DISPERSE software. In addition, a comparison with the results obtained by Nayfeh’s works in the field of Nondestructive testing by ultrasonic guided waves is included. Then a discussion is developed to highlight the strengths of the spectral method. For proper non-destructive testing, we need reliable information about the modes that propagate in our waveguide. Both analytical and spectral approaches have limitations in obtaining the exact displacement and stress profiles in a plate media. To remedy this, normalization by the acoustic power is essential. Next, the displacement and stress fields obtained from the spectral method of the modes that can propagate in the plate are compared to those obtained analytically. A very good concordance is then noticed. Based on the results obtained, the spectral method presents a very good alternative for obtaining dispersion curves. It is a convergent method, stable, easy to implement with a very low calculation time.

The buckling behavior of functionally graded carbon nanotube (FG-CNT) reinforced polymer-based moderately-thick plates subjected to in-plane biaxial compressive loads in elastic and thermal environments in the framework of first-order shear deformation plate theory (FSDPT) is investigated. First, the temperature-dependent properties of CNTs and nanocomposites are defined and their constitutive relations are established, then the stability and strain compatibility equations in elastic media are derived in the framework of the FSDPT. Then, by applying the Galerkin method to the basic equations, a closed-form solution is obtained for the critical biaxial compressive loads. The specific numerical analyzes and interpretations are made for various plate sizes and CNT patterns on the Winkler elastic foundation and in thermal environments within FSDPT and classical plate theory (CPT).

This article consists of three methodological stages. In the first one, a 3D numerical model of hybrid fiber metal laminates (FML) is developed inside ANSYS Workbench Explicit Dynamics modulus and used to predict their strengths according to the ASTM D3039M-17 standard. In the second stage, hybrid FMLs are produced according to the 4/3 stacking order in the laboratory environment, in line with the numerical model. Pure epoxy resin is initially used then reinforced with, 0.2% clay, GNP and SiO2 nanoparticles: comparative tensile tests are carried out according to the above-mentioned standards. At the final stage, experimental data, computer and theoretical (analytical) models of nanocrack formation processes in 7075-T6 Al matrix nanoparticle-filled hybrid nanocomposite materials under the influence of high-speed and quasi-static deformation regimes are investigated. It is observed that there is a 5% difference between results from simulation and experiment.

Push-off samples are simulated using nonlinear finite element analysis (NLFEA) to evaluate the effects of increased temperatures on the interface shear strength. Firstly, a control shear-key model is created, calibrated, and confirmed against independently published experimental data. Twenty-four NLFEA models are then created with different variables, including temperature (23°C (Room Temperature), 250°C (Raised temperature), 500°C, and 750°C and the number of steel stirrups (none, 1, 2, 3, 4, and 5). The NLFEA results demonstrate that the decreased fracture opening and slide in the damaged shear keys compared to the intact control sample represent the amazing effect of the number of steel stirrups. In addition, it has been revealed that the longitudinal shear force and slide, mode of failure, rigidity, and toughness are all significantly impacted by the degree of heat damage. In particular, a simplified approach is proposed for calculating the shear strength of push-off samples subjected to higher temperatures.

In this paper, we investigate the effect of magnetic field on two-dimensional flow of a viscous, incompressible fluid through composite porous channel using non-primitive boundary element method (BEM). We consider a rectangular channel consisting of two packings that are filled with fully saturated porous medium. It is assumed that both the porous regions are homogenous and isotropic with different permeabilities. Brinkman equation governs the fluid flow through porous media. We analyze the effect of Hartman number, stress-jump coefficient, Darcy number, thickness parameter, electrical conductivity ratio, and viscosity ratio on fluid mechanics. We present the effect of stress-jump coefficients on the interfacial velocity of the fluid against the thickness parameter and observe that the interfacial velocity increases with increasing stress-jump coefficients. We notice that for a fixed value of thickness parameter, the magnitude of vorticity (at lower and upper walls) increases with increasing Darcy number. Moreover, we observe that the magnitude of vorticity at the lower wall decreases and increases at the upper wall with increasing thickness parameter. We compute the Brinkman layer thickness near the interface of the composite porous channel in terms of several flow parameters and observe that the Brinkman layer thickness is strongly depend on the Hartman number, Darcy number, viscosity ratios, and stress-jump coefficient, respectively.

The growing demand for energy resources highlights the need to optimize traditional energy transformation systems. Pelton-type turbines, which are extensively used in micro-generation systems, can be designed using different methodologies, however, no consensus has been reached on which methodology guarantees greater efficiency. This work aims to compare the fluid-dynamic behavior at the first-time instants of Pelton turbines for micro-generation dimensioned by three different methodologies, namely, OLADE, Nechleba, and Thake, evaluating their capacity to overcome the initial torque. The results show that OLADE methodology leads to the best fluid-dynamic performance, whereas Nechleba fails to overcome the prescribed torque. In the Thake methodology, the impact of water on the back face of buckets and the formation of reverse pressure gradients can counter the turbine rotation.

Antivibration isolators are made from both crystalizing rubbers and non-crystalizing rubbers. Their fatigue resistance is different. Although the recently developed effective tensile stress criterionhas been validated in crystalizing rubber under different R ratios (the ratio between the minimum stress value and the maximum stress value), its application to non-crystalizing rubbers has never been verified. In this study, this criterion was tested against a non-crystalizing rubber using two types of samples under R ≥ 0 conditions for 168 fatigue cases with different loading modes. Considering that a shape change may also cause fatigue damage, a new shear stress criterion was derived and subsequently tested. The unified S-N curves (2×102 - 3×106 cycles) obtained have achieved narrow bands with a scatter factor of 1.35 with a correlation coefficient R2 ≥  0.90 using these two criteria. This potential novel approach could be more effective than the current methods, which use fitting functions with adjustable parameters determined from an additional experiment. This offers greater choices and flexibility to engineers in their selection of the most appropriate suited criteria for their design in anti-vibration applications.

Renewable energy could solve the problems caused by fossil fuels. The Archimedes hydro screw turbine is a potential tool for generating power from river currents. In this paper, a turbine at a scale of 1:6 has been made. It is installed and tested at various flow rates. The system is optimized using a genetic algorithm to achieve maximum efficiency. Due to the limitations that existed for conducting experimental tests at the optimal flow rate, the turbine at optimal flow rate is studied by CFD. In the turbine numerical simulation, the hydrodynamic characteristics of the turbine, such as rotational speed, power, torque, efficiency, and power coefficient are compared in the optimal flow rate (2.6 (lit/s)) and a flow rate of 2.4 (lit/s) (the closest flow rate to the optimal one). The results show that these values are higher in the optimal flow rate. Furthermore, the behavior of the turbine in these two conditions is compared using velocity, vorticity, pressure, and phase contours, which indicates that the velocity and pressure values are higher, and the vorticity and immersion values are lower in the optimal flow rate. Finally, for economic analysis of operating the turbine at the prototype scale as a hydropower plant, the discounted payback period for the turbine is determined, which varies between 2.55 to 5.93 years depending on the discount rate. It is also shown that operating this turbine at the prototype scale as a hydropower plant in Iran leads to currency savings of 1561 $.

Lithium-ion battery technology in the modern automotive industry utilizes highly temperature-sensitive batteries. Here, air cooling strategies will be the most applicable for the chosen example based on strategies for temperature control. Simulations have been utilized to evaluate the different thermal management strategies. A battery model was developed using the solutions offered by Computational Fluid Dynamics (CFD) simulation technology. It utilizes the heat produced by the discharge of the battery cells. Due to the simulation's limited computational capacity, the energy transfer model was implemented with a simplified but sufficiently complex physical mesh. Ten actual measurements were conducted in the laboratory to investigate the heating of the cell during the charging and discharging of 18650-type batteries. The results were applied to validate the simulation model. The simulation outcomes and thermal camera readings were compared. The cell-level numerical model was then extended to examine the temperature variation at the system level. The primary design objective is to achieve the highest energy density possible, which necessitates that the cells be constructed as closely as possible; however, increasing the distance between the cells can provide superior cooling from a thermal management perspective. The effect of varying the distance between individual cells on the system's heating was analyzed. Greater distance resulted in a more efficient heat transfer. It was also discovered that, in some instances, a small distance between cells produces inferior results compared to when constructed adjacently. A critical distance range has been established based on these simulations, which facilitates the placement of the cells.

The planetary gear sets find application in the final stages of the helicopter transmission system. Unlike the single axis gear, the planetary gears have complex structural arrangement and unique operational characteristics which makes diagnosis of incipient fault much more challenging with planetary gears compared to the single axis gear. This study provides a background for effective planetary bearing fault analysis in an SA330 Super-Puma Helicopter Main gearbox by studying the characteristic of the planetary stage and investigating some prominent frequency components which are vital to fault feature extraction. Vibration data of healthy and faulty conditions at varying load regimes from a seeded fault experiment were captured. The analysis of the vibration transmission paths and the signal amplitude in the time and frequency domain provide the basis for the determination of the best signal quality. Eight transmission paths affecting the signal energy were established however, the shortest path to the radial direction of the faulty bearing assures better signal gain. The gear mesh frequencies and harmonics of the planetary stages are suppressed by the high amplitude frequencies of the forward, aft and bevel reduction gears. The impulsive carrier frequency at high speed has a strong correlation with gear-related frequencies. Though the fault frequencies can be traced in some instances, it is mostly dominated in the spectrum because of the gear-related frequencies and amplitude modulation of the planetary stages. This work enhances the planetary bearing fault extraction.

The paper develops the methods for computer simulation of the dynamics of absolutely rigid body systems with a tree structure. The equations of motion are presented in compact matrix form. The case of holonomic constraints is also considered. Since the independent parameters uniquely determine the positions and velocities of the bodies of the system in space, the generalized coordinates and variables with the dimension of impulses are chosen. A feature of the system of equations is that it is resolved with respect to the derivatives of the generalized momenta and does not contain constraint reactions. The derivation of the proposed form of the equations of motion from the Hamilton principle using the matrix-geometric approach is given. Recursive formulas for determining all kinematic and dynamic variables included in the equations are obtained. As an example of a mechanical system with six degrees of freedom, all stages of preparing primary information and compiling equations of motion in the proposed form are demonstrated. Three algorithms are presented that allow resolving the obtained extended system of equations with respect to the generalized velocities and momenta without direct formation of the Hamilton equations. The classification of the equations of motion of rigid body systems is carried out from their structure point of view. The place of the deduced equations in the general classification is also demonstrated. A comparative analysis of the computational complexity of the considered methods for various classes of mechanical systems is carried out. Some diagrams are constructed that allow choosing the most effective modeling method depending on the characteristics of the mechanical system: the number of bodies, the number of degrees of freedom and the structure of the system.

Taylor series method is a simple analytical method, which is accessible to all non-mathematician, has slow convergence. This paper develops a new Taylor series based numerical method to overcome the shortcoming of the Taylor series while maintaining its simplicity. Some examples are given, showing its reliability and efficiency. The proposed method is also proved to be extremely effective for initial value problems and boundary value problems. The method provides a universal approach to various highly non-linear problems, and it sheds a bright light on numerical theories for practical engineering applications.

An internal heat source is assumed to act on a cylindrical body with radiation-like boundary conditions to explore the memory-dependent thermoelastic response of a solid object. The top and bottom surfaces of the solid cylinder are subjected to additional heating conditions. To obtain the thermal behaviour of the considered medium, the integral transform method is used, while the inversion solution of the heat transfer equation, the thermoelastic displacement and stress functions are presented in the Laplace domain due to the complexity of the calculation. To understand the numerical calculations, the material properties of aluminium metal are taken into account, and all the obtained results are presented graphically.

Investigation of free vibration of porous power and sigmoid-law sandwich functionally graded (FG) plates with different boundary conditions is presented in this paper. The FG sandwich plate includes three layers. The face layers are fabricated of functionally graded material (FGM) and middle layer (core) is isotropic (ceramic). Imperfect sigmoid FG sandwich plates with even and linear-uneven porosities and nonporous core layer are studied. Developed approach has been realized in the framework of a refined theory of the first-order shear deformation theory (FSDT) using variational methods and the R-functions theory. The analytical expressions are obtained for calculating the elastic characteristics with the assumption that the values of Poisson's ratio are the same for constituent FGM materials. For rectangular plates, the obtained results are compared with known results and a good agreement is obtained. Vibration analysis of a complex-shaped porous sandwich plate made of FGM has been performed. The effect of various parameters on the dynamic behavior of the plate, such as the type and values of porosity coefficients, power index, lay-up scheme, types of FGM, has been studied.

This paper presents the results of the full-scale verification and validation of the mathematical model and numerical algorithm for the network computation of a single-phase flow in a highly branched pipeline chain. The essential difference of this work from others is that highly branched hydraulic networks with homogeneous and non-uniform permeability, containing more than 70 thousand branches, are considered. Such branched networks are important in many applications. Therefore, the development of algorithms for calculating flows in such networks is very important. The network model is based on hydraulic theory, and the numerical algorithm relies on the network analogue of the well-known control volume method. At the same time, obtaining reliable experimental data for testing models for calculating very branched hydraulic networks is very difficult. In this work, microfluidic technologies are used to solve this problem. Data of laboratory experiments, obtained using microfluidic models of branched networks with homogeneous and heterogeneous permeability, containing several tens of thousands of branches, as well as CFD simulation results in full 3D formulation employing the fine computational grids were used to validate the model. The Reynolds number ranged from 0.81 to 13. Conducted validation has shown a good qualitative and quantitative concordance of the results of network and hydrodynamic simulation, as well as the data of the microfluidic experiments. The error in determining the total pressure drop in the branched hydraulic network with heterogeneous permeability, containing 37,855 nodes and 74,900 branches, did not exceed 5%. It has been demonstrated that the speed of solving a single-phase flow problem in a highly branched chain using network simulation techniques is 60 times more of magnitude higher as compared to CFD simulation at virtually the same accuracy.