Journal of Applied and Computational Mechanics
Volume:6 Issue: 4, Autumn 2020

In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to pick multiple solutions together by any discrete method like finite difference method, finite element method etc. Here, we propose a new technique based on homotopy perturbation method and variational iteration method. We compare numerically the approximate solutions computed by Adomian decomposition method. We study the convergence analysis of both iterative schemes in C^2 ([0,1]). For small values of λ, solutions exist whereas for large values of λ solutions do not exist.

The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of the equation.

The inclusion of complex obstacles within solar channels is the aim of this article. Two obstacles of the form ꞌ+ꞌ interlaced within a two-dimensional and rectangular channel are the subject of our study. The fluid is Newtonian, turbulent, incompressible and has constant properties. The Reynolds number varies from 12,000 to 32,000 with a constant temperature along the upper surface of the channel. The thermal and dynamic analysis of the channel's internal structure has been carefully processed. Different fields of speed and heat, with various profiles of frictions and heat exchange coefficients, have been included in this research. Future work will involve more complex geometries and using nanofluids to assess the optimum conditions for heat transfer enhancements.

The present research investigates the torsional aeroelasticity of the blade of an H-type vertical axis wind turbine subject to stall and post-stall conditions in various Reynolds regimes, which is experienced by the blade in a full revolution. In order to simulate the aerodynamics, a new model based on a combination of the Double Multi Streamtubes (DMST) model and the nonlinear multi-criteria Cl-a equations, which is depended on the local Reynolds number of the flow, has been proposed. The results indicate that using of multi-criteria function dependent on the Reynolds number for the Cl-a curve has improved the prediction of the torsional behavior of the blade in azimuthal rotation of the blade compared to using single-criterion functions and linear aerodynamics. The blade’s aeroelastic torsion has been studied for various TSR values.

In this paper, the vibration of microbeams due to a temperature pulse has been investigated. The thermoelastic coupled equations for microbeam resonator have been derived via the modified theory of couple stress in connection with the generalized thermoelasticity with relaxation time. The analytical expressions for studied fields due to modified couple stress for the microbeam have been obtained by applying the Laplace transform method. In addition, some comparisons have been displayed in graphs to estimate the effects of different parameters such as the couple stress parameter and pulse of temperature on the considered fields. Numerical conclusions demonstrate that the estimation of deflection expected by the new theory is lower than that of the classical one. Comparisons are made with the results of different models in the absence and presence of couple stress theory. Particular cases of interest are also derived.

Green’s function, an analytical approach in inhomogeneous linear differential equations, is the impulse response, which is applied for deriving the wave equation solution in composite materials mediums. This paper investigates the study of SH wave’s transmission influenced by concentrated point source disturbance in piezomagnetic material resting over heterogeneous half-space. Green function approach is used to solve differential equation and obtain the dispersion relation in determinant form and match with existing classical Love wave equation for the authenticity for the article. The properties of SH wave throughout the considered framework and their state of relying on varied geometrical and physical parameters are scrutinized. The simulated outcomes of disparate physical quantities viz., dimensionless phase velocity, elastic parameter, group velocity, initial stress, piezomagnetic/heterogeneity parameter and stress distribution of SH wave in the considered structure are investigated and used to regulate the behavior of dispersion characteristics of smart material waveguides.

In the current research project, the thermal performance of a series of newly designed mixers has been investigated. Each mixer has two concentric cylinders comprising two annular slot flow channels around a solid cylindrical rod at the center. In each mixer, the first cylinder around the central solid rod has either spherical or pyramidal protrusions throughout the outer surface. It has been observed that with varying mass flow rate of cold and hot water (1 kg/m3-sec to 5 kg/m3-sec), 17% increase in rate of heat transfer for cold water & 73% for hot water has been observed with a variation in mass flow rate of 1-3 kg/m3-sec with all combination of angles of holes in spherical protrusions. In the case of pyramidal protrusions, the rate of heat transfer has been raised from 16% for cold water & 88% for hot water at varying a mass flow rate of 1-3 kg/m3-sec in all combinations of angles of the top vortex in each protrusion. The effect of imparting the centrifugal force has raised the rates of heat transfer in the range of 24-36% at varying rpm from 60-180 rpm of the central cylinder, with the highest with 120 rpm. A comparison of the heat transfer rates reveals that with increasing the mass flow rates, rpm, angle of the holes in spherical protrusions and angle of the traversed angle at the top corner of each pyramidal protrusion didn’t contribute linearly in terms of rising in the rate of heat transfer.

In this research, the numerical and experimental analysis of the carbon fiber composite lattice conical structure has been performed to assess the buckling stability of the structure before and after the lateral impact. In the experimental analysis, the carbon fiber composite lattice conical structure was constructed with the winding method and using elastic molds and metal mandrel. In order to investigate the buckling stability of the structures before each lateral impact, they are subjected to be compressive-axial loading. The rest of the structures first subjected under the axial-compressive loading, then in the next step, a compressive loading is applied to determine the effect of the impact on the compressive strength of the damaged structures. In the numerical analysis, the Abaqus software is used to modeling and performing the mentioned analysis. Finally, the comparison of the results shows that the effect of the lateral impact causes how many reductions will be occurred in the buckling strength. So, it should be considered during the design of the applied structures. On the other hand, the low difference between the numerical and experimental simulations shows that the experimental and numerical methods can be used to analyze the structures with different geometric characteristics and material.

Optimization of the volume/weight in the gear train is of great importance for industries and researchers. In this paper, using the particle swarm optimization algorithm, a general gear train is optimized. The main idea is to optimize the volume/weight of the gearbox in 3 directions. To this end, the optimization process based on the PSO algorithm occurs along the height, length, and width of the gearbox to achieve the smallest possible gearbox. The constraints are divided into three types named geometrical, design and control constraints. The optimization process is presented for two and three-stage gear trains and by choosing different values for the gear ratio, input power and hardness of gears. The practical graphs for the optimum value of the weight/volume and all necessary design parameters of gearbox such as the number of stages, position, modulus of gears, face width of gears, and diameter of shafts are also presented. The results are validated by comparing with the results reported in the previous publications.

Human beings have always made their tools and instruments they need using patterns in nature. Mimicking nature has become the foundation of a new science called Biomimetics. In the present article, multiple forms and levels in nature were utilized to design and create a mouse. The rivers are a good source for choosing the shape of a mouse with lots of stones abraded through the centuries which also have smooth surfaces. In this research, a significant number of stones fitted to hand size were collected and then the best ones were scanned by an optical scanner. The point cloud model obtained was used to design and create the mouse and determine the geometric parameters of the mouse. After extracting the 3D model of the point cloud using a rapid prototyping technique with the Fused Deposition Modeling (FDM) method, some mouse models were designed ambidextrously for left-handed and right-handed people. Considering the results of the mouse evaluation by 30 people who were provided with the mouse, it can be concluded that the created mouse provided a high rate of satisfaction.

In this paper, we derive a novel numerical method to find out the numerical solution of fractional partial differential equations (PDEs) involving Caputo-Fabrizio (C-F) fractional derivatives. We first find out the approximation formula of C-F derivative of function tk. We approximate the C-F derivative in time with the help of the Legendre spectral method and approximation formula of tk. The unknown function and their derivatives in spatial direction are approximated with the quasi wavelet-based numerical method. We apply this newly derived method to solve the nonlinear distributed order reaction-diffusion in which time-fractional derivative is of C-F type. The accuracy and validity of the proposed method is exhibited by giving a solution to some numerical examples. The obtained numerical results are compared with the analytical results and conclude that our proposed numerical method achieves accurate results. On the other hand, the method is easy to apply on higher-order fractional partial differential equations and variable-order fractional partial differential equations.

A comprehensive set of ten artificial neural networks is developed to suggest optimal dimensions of type ‘C’ Bi-lobe tanks used in the shipping of liquefied natural gas. Multi-objective optimization technique considering the maximum capacity and minimum cost of vessels are implemented for determining optimum vessel dimensions. Generated populations from a genetic algorithm are used by Finite Element Analysis to develop new models and find primary membrane and local stresses to compare with their permissible ranges using PYTHON coding. The optimum design space is mathematically modeled by training ten artificial neural networks with design variables generated by the Taguchi method. The results are compared with actual design data and the 93% achieved accuracy shows the precision of the developed design system.

In this paper, the stress intensity factor (SIF) expression for defected butt welds containing undercut and inclined lack of penetration (LOP) subject to far-field tensile stress is derived. Some of the standards such as ISO 5817 and BS EN 25817 have specified allowable limits for the length of the undercut and LOP defects and for the height of the weld. In addition, EN 29692 standard has determined an acceptable range for the groove angle. In this paper, the effect of these acceptable geometries on stress intensity factor (SIF) of butt welded joint is investigated through following steps: i) elastic analyses to predict crack tip stress intensity (KI, KII) and shape factors, ii) approximation of shape factors by Response Surface Method (RSM). These expressions provide design guidelines for welded butt joint containing unavoidable undercut and inclined lack of penetration (LOP) defects.

The dynamic analysis of the biomechanical model of the head load impact using the Differential Transform Method is presented in this paper. In many parts of the world, the problem of traumatic brain injuries (TBI) has led to neurodegenerative dementing disorders and diseases as a result of head load impact from sporting activities, accidents involving the head, etc. have serious effects on humanity. The head load impact and its control have been modeled as a rigid linkage head-neck manipulator. This rigid link manipulator is governed by a system of nonlinear ordinary differential matrix equations with three degrees of freedom which requires special techniques for its solution. The system of equations was solved using Differential Transform Method (DTM) and the results were compared with results obtained in earlier studies and validated with the fourth-order Runge-Kutta numerical method (RK4). Good agreements are reached in all these results. From the model, the effects of head loads, head mass, neck mass, upper and lower linkage lengths, head and neck moments of inertia were investigated. As the head loads increased, there were increases in both axial and angular displacement of the head motion and the neck region. The study provides a theoretical basis for the design and understanding of the effects of head load carriage on vital organs that are susceptible to pains, damages, and even failure.

This study introduces the free vibration analysis of multilayered symmetric sandwich Timoshenko beams, made of functionally graded materials with two edge cracked, using the finite element method and linear elastic fracture mechanic theory. The FG beam consists of 50 layers, located symmetrically to the neutral plane, whose material properties distribution change along the beam thickness, according to power and exponential laws. The constituent of each layer of the beam is different, but each layer is isotropic and homogeneous. Natural frequency values of a cantilever beam are calculated using a developed MATLAB code. There is good agreement between the present results and the published results from the literature. A detailed study is carried out to observe the effect of crack location, crack depth ratio, power law index and material distribution on the first four natural frequencies.

In this study, weight optimization of the prismatic core sandwich panel under transverse and longitudinal loadings has been independently investigated. To solve the optimization problems corresponding to the mentioned loadings, a new Improved Constrained Differential Evolution (ICDE) algorithm based on the multi-objective constraint handling method is implemented. The constraints of the problems are buckling load and yield stress. By comparing the results of the ICDE with those obtained by the other evolutionary algorithms based on the penalty function method in the previous studies, it is discerned that the results of the transverse loading obtained in this study are equal to those of the previous works, but the results of the ICDE in the longitudinal loading are better.

Computational fluid dynamics is implemented to investigate the influence of the wheel contact patch on the global car aerodynamics. Two main aspects of the problem are the contact step and patch shape. Three important parameters: step height, cut angle, and tire tread shape are taken into consideration. For validations of the numerical results, the experimental data are also considered. The obtained results show that the step height may not significantly affect the global flow field. But when the cut angle increases, the flow separations on the two sides of the front wheel patch will be suppressed successively, which generates two critical points and a sudden drag decrease is achieved. Besides, tiny differences in tread shape can effectively change the flow rate of the underbody and make a huge drag discrepancy in the results. In conclusion, the cut angle and tire tread shape carefully must be dealt with in aerodynamic applications of automotive engineering.

In the present paper, a numerical investigation of transport phenomena is considered in electrically-conducting nanofluid flow within a porous bed utilizing Buongiorno’s transport model and Runge-Kutta-Fehlberg fourth-fifth order method. Induced flow by non-isothermal stretching/shrinking sheet along with magnetic field impact, dissipation effect, and slip conditions at the surface are also included. The numerical results show the existence of two branches of the solution for a selected range of the governing parameters. The physical significance of both branches of solutions is ensured by performing a stability analysis in which a linearized eigenvalue problem is solved. The multiple regression analysis with the help of MATLAB LinearModel.fit package has also been conducted to estimate the dependence of the parameters on Nusselt number.

In the present paper, we get exact solutions of Magnetohydrodynamic (MHD) of the fractionalized three-dimensional flow of Newtonian fluid with porous and heat transfer through the traveling wave parameter. The governing equations are produced dependent on established Navier-stokes equations which can be diminished to ordinary differential equation by wave parameter ξ=ax+by+nz+Utα/Γ(α+1). The new exact solutions are established for three various cases. In special cases the solution for Newtonian fluid with and without MHD and porous effects can also be found from the general solution by putting M+Φ→0 and solutions for simple Newtonian fluid can also be obtained by putting α→1 in general solutions. Finally, the effect of the parameter of interest on the stream motion, as well as difference among the Newtonian fluids is examined by 2D and 3D graphical interpretations.

In the present analysis, the Dufour and Soret effects on unsteady heat-mass transfer of a viscous incompressible Powell-Eyring fluids flow past an expanding/shrinking permeable sheet are reported. The fluid boundary layer develops over the variable sheet with suction/injection to the non-uniform free stream velocity. Under the symmetry group of transformations, the governing equations along with three independent variables, are converted into a system of PDEs with two independent variables. Finally, by employing the order-reduction technique the PDEs are transformed into ODEs, which are then solved numerically. The results are presented graphically and analyzed. The main advantage of this technique is that without any prior knowledge, one can easily find the scaling transformations, expanding velocity, suction/injection velocity, and free-stream velocity. From computed numerical results many important findings are obtained. Most importantly, thermal and concentration overshoots are found for larger values of Dufour and Soret numbers, respectively. Also, thermal and concentration crossing over found for different values of Soret and Dufour numbers, respectively.

A laminar, two dimensional, steady boundary layer Newtonian conducting fluid flow passes over a permeable shrinking sheet in the presence of a uniform magnetic field is investigated. The governing equations have converted to ordinary nonlinear differential equations (ODE) by using appropriate similarity transformations. The main idea is to transform ODE with infinite boundary condition into other sets of variables in a way that infinite boundary condition becomes a finite boundary condition. The effects of physical parameters affecting the velocity and temperature are shown. The results show that with increasing the magnetic and suction parameters, the normal velocity component of fluid increases over the sheet whereas the tangential velocity component of fluid decreases. Moreover, when the suction parameter, the Prandtl and Eckert numbers increase, the rate of the heat transfer increases. However, when the magnetic parameter increases, the rate of heat transfer reduces. Finally, the solution shows that the results of the analytical method using a special technique have an excellent agreement with numerical solutions.

Numerous techniques in designing zones happen at high temperature and functions under high temperature are in a way that involves non-linear radiation. In weakly conducting fluids, however, the currents induced by an external magnetic field alone are too small, and an external electric field must be applied to achieve an efficient flow control. Gailitis and Lielausis, devised Riga plate to generate a crossed electric and magnetic fields which can produce a wall parallel Lorentz force in order to control the fluid flow. It acts as an efficient agent to reduce the skin friction. So, in this paper, we start the numerical investigation on the three-dimensional flow of nanofluids with the inclusion of non-linear radiation past a Riga plate. To this end, the numerical investigation is conducted on the three-dimensional flow of nanofluids with the inclusion of non-linear radiation past a Riga plate. Water (H2O) and Sodium Alginate (NaC6H9O7) are the base fluids, whereas Magnetite (Fe3O4) and Aluminium oxide (Al2O3) are the nanoparticles. The mathematical formulation for Sodium Alginate base fluid is separated through the Casson model. Suitable transformations on governing partial differential equations yield strong non-linear ordinary differential equations. Numerical solutions for the renewed system are constructed by fourth-order Runge-Kutta method with shooting technique. Various deductions for flow and heat transfer attributes are sketched and discussed for various physical parameters. Furthermore, the similarities with existing results were found for the physical quantities of interest. It was discovered, that the temperature ratio parameter and the radiation parameter enhance the rate of heat transport. Moreover, the NaC6H9O7 - Al2O3 nanofluid improves the heat transfer rate. Likewise, H2O-Fe3O4 nanofluid stimulates the local skin friction coefficients.

Heat sinks are used in industrial equipment to dissipate the excess heat from their heat-generating parts to the ambient. In the last few years, efforts on manufacturing electronic or mechanical devices with less weight, space, and lower cost were spent. Heat dissipation from the heat sink is stalling a big problem which many researchers are trying to solve. The aim of this study is to brief the previous investigation attempted enhancing the heat sinks thermal performance and to provide help to understand the cooling ability of their specific geometries. The various enhancement techniques used for optimizing the hydrothermal design of a pin fin, flat fin, micro-channel, and topology optimized heat sinks were summarized. The way in which the heat sinks’ thermal performance is affected by orientation, shapes, perforation, slot, interruption, and space between fins and their arrangement under free and forced convection condition also reviewed.

Functionally graded materials are commonly used in thermal environment to change the properties of constituent materials. The new numerical procedure of functionally graded skew plates in thermal environment is presented in this study based on the C0-form of the novel third-order shear deformation theory. Without the shear correction factor, this theory is also taking the desirable properties and advantages of the third-order shear deformation theory. We assume that the uniform distribution of temperature is embedded across the thickness of this structure. Both the rule of mixture and the micromechanics approaches are considered to describe the variation of material compositions across the thickness. Numerical solutions and comparison with other available solutions suggest that this procedure based on novel third-order shear deformation theory is accuracy and efficiency.

This article concentrates on the effect of MHD heat mass transfer on the stagnation point nanofluid flow over a stretching or shrinking sheet with homogeneous-heterogeneous reactions. The flow analysis is disclosed in the neighborhood of stagnation point. Features of heat transport are characterized with Newtonian heating. The homogeneous-heterogeneous chemical reaction between the fluid and diffusing species is included in the mass diffusion equation. The MHD stagnation boundary layer flow is explored in the presence of heat generation/absorption. Numerical convergent solutions are computed via the spectral quasi-linearization method (SQLM). The physical aspects of different parameters are discussed through graphs.