eng
Shahid Chamran University of Ahvaz
Journal of Applied and Computational Mechanics
2383-4536
2383-4536
2020-04-01
6
2
183
199
10.22055/jacm.2019.28695.1498
14296
مقاله پژوهشی
Viscoelastic Micropolar Convection Flows from an Inclined Plane with Nonlinear Temperature: A Numerical Study
S. Abdul Gaffar
abdulsgaffar0905@gmail.com
1
P. Ramesh Reddy
prreddy.mits@gmail.com
2
V. Ramachandra Prasad
rcpmaths@gmail.com
3
A. Subba Rao
asrsvu@gmail.com
4
B. Md. Hidayathulla Khan
bmdhkh@gmail.com
5
Department of Information Technology, Mathematics Section, Salalah College of Technology, Salalah -211, Oman
Department of Mathematics, Madanapalle Institute of Technology & Science, Madanapalle - 517325, India
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore – 632014, India
Department of Mathematics, Madanapalle Institute of Technology & Science, Madanapalle - 517325, India
Department of Mathematics, Sir Vishveshwaraiah Institute of Science and Technology, Madanapalle – 517325, India
An analytical model is developed to study the viscoelastic micropolar fluid convection from an inclined plate as a simulation of electro-conductive polymer materials processing with nonlinear temperature. Jeffery’s viscoelastic model is deployed to describe the non-Newtonian characteristics of the fluid and provides a good approximation for polymers. Micro-structural is one of the characteristics of non-Newtonian fluid that represents certain polymers, which constitutes a novelty of the present work. The normalized nonlinear boundary value problem is solved computationally with the Keller-Box implicit finite-difference technique. Extensive solutions for velocity, surface temperature, angular velocity, skin friction, heat transfer rate and wall couple stress are visualized numerically and graphically for various thermophysical parameters. Validation is conducted with earlier published work for the case of a vertical plate in the absence of viscous dissipation, chemical reaction and non-Newtonian effects. This particle study finds applications in different industries like reliable equipment design, nuclear plants, paint spray, thermal fabrication, water-based gel solvents, polymeric manufacturing process, gas turbines and different propulsion devices.
http://jacm.scu.ac.ir/article_14296_bb014b40dd323f5984e72b340333153b.pdf
Viscoelastic fluid
Micropolar Fluid
Nonlinear Temperature
Retardation time
Vorticity
eng
Shahid Chamran University of Ahvaz
Journal of Applied and Computational Mechanics
2383-4536
2383-4536
2020-04-01
6
2
200
208
10.22055/jacm.2019.28835.1509
14550
مقاله پژوهشی
Exact Solution for Nonlinear Local Fractional Partial Differential Equations
Djelloul Ziane
djeloulz@yahoo.com
1
Mountassir Hamdi Cherif
mountassir27@yahoo.fr
2
Dumitru Baleanu
dumitru@cankaya.edu.tr
3
Kacem Belghaba
belghaba@yahoo.fr
4
Laboratory of Mathematics and its Applications (LAMAP), University of Oran1, Oran, Algeria
Laboratory of Mathematics and its Applications (LAMAP), University of Oran1, Oran, Algeria
Department of Mathematics, Cankaya University, Ankara, Turkey | Institute of Space Sciences, Magurele-Bucharest, Romania
Laboratory of Mathematics and its Applications (LAMAP), University of Oran1, Oran, Algeria
In this work, we extend the existing local fractional Sumudu decomposition method to solve the nonlinear local fractional partial differential equations. Then, we apply this new algorithm to resolve the nonlinear local fractional gas dynamics equation and nonlinear local fractional Klein-Gordon equation, so we get the desired non-differentiable exact solutions. The steps to solve the examples and the results obtained, showed the flexibility of applying this algorithm, and therefore, it can be applied to similar examples.
http://jacm.scu.ac.ir/article_14550_b9fbc3b03e787b53897af757aa0fa2c9.pdf
Adomian decomposition method
Sumudu transform method
Local fractional derivative operator
Local fractional
Nonlinear local fractional gas dynamics equation
Nonlinear local fractional Klein-Gordon equation
eng
Shahid Chamran University of Ahvaz
Journal of Applied and Computational Mechanics
2383-4536
2383-4536
2020-04-01
6
2
209
218
10.22055/jacm.2019.28936.1521
14531
مقاله پژوهشی
Effect of Corrugated Baffles on the Flow and Thermal Fields in a Channel Heat Exchanger
Houari Ameur
houari_ameur@yahoo.fr
1
Department of Technology, University Centre of Naama - Ahmed Salhi (Ctr Univ Naama), Po. Box 66, 45000, Algeria
The performance of corrugated baffles inserted in a rectangular channel heat exchanger is investigated. The fluid flows and thermal distribution are determined via numerical simulations. The working fluid has a shear thinning behavior. The influence of the baffle design is explored, we interest to the “wavy” shape. The corrugation angle of baffle (<em>α</em>) is changed from 0° (i.e. a straight baffle) to 45°. Also, the height (<em>h</em>) of the corrugated baffle is changed and three cases are considered, namely: <em>h/H</em> = 0.4, 0.5 and 0.6, where “<em>H</em>” is the channel height. In comparison with the unbaffled channel, the overall performance factor has increased from 1.27 up to 1.53 when the corrugation angle is increased from 0° to 45°. Concerning the corrugation height, the predicted results allowed us to select the case <em>h/H</em> = 0.5 as the best configuration from the cases studied.
http://jacm.scu.ac.ir/article_14531_785a8f150d172eb143fc866195246a40.pdf
Heat exchanger
Corrugated baffles
Baffle design
Laminar flow
Non-Newtonian fluids
eng
Shahid Chamran University of Ahvaz
Journal of Applied and Computational Mechanics
2383-4536
2383-4536
2020-04-01
6
2
219
234
10.22055/jacm.2019.28965.1527
14428
مقاله پژوهشی
Efficient Solution of Nonlinear Duffing Oscillator
Iman Khatami
iman.khatami81@gmail.com
1
Ehsan Zahedi
zahedi_ehsan@yahoo.com
2
Mohsen Zahedi
seyyed.mohsen.zahedi@gmail.com
3
Department of Mechanical Engineering, Chabahar Maritime University, Iran
Department of Biosystems Engineering, Shiraz University, Iran
Faculty of Computer Engineering, University of Isfahan, Iran
In this paper, the efficient multi-step differential transform method (EMsDTM) is applied to get the accurate approximate solutions for strongly nonlinear duffing oscillator. The main improvement of EMsDTM which is to reduce the number of arithmetic operations, is thoroughly investigated and compared with the classic multi-step differential transform method (MsDTM). To illustrate the applicability and accuracy of the new method, six case studies of the free undamped and forced damped conditions are considered. The periodic response curves of both MsDTM and EMsDTM methods are obtained and contrasted with the exact solution or the numerical solution of Runge Kutta 4<sup>th</sup> order (RK4) method. This approach can be easily extended to other nonlinear systems and therefore is widely applicable in engineering and other sciences.
http://jacm.scu.ac.ir/article_14428_f7aa848cda780cf38498e06079a75b23.pdf
Efficient multi-step transforms method
Duffing oscillator
Nonlinear equation
Differential transformation method
eng
Shahid Chamran University of Ahvaz
Journal of Applied and Computational Mechanics
2383-4536
2383-4536
2020-04-01
6
2
235
247
10.22055/jacm.2019.28849.1513
14509
مقاله پژوهشی
Implicit RBF Meshless Method for the Solution of Two-dimensional Variable Order Fractional Cable Equation
Akbar Mohebbi
a_mohebbi@kashanu.ac.ir
1
Marziyeh Saffarian
marziyesafarian11@gmail.com
2
Department of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, Iran
Department of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, Iran
In the present work, the numerical solution of two-dimensional variable-order fractional cable (VOFC) equation using meshless collocation methods with thin plate spline radial basis functions is considered. In the proposed methods, we first use two schemes of order O(τ<sup>2</sup>) for the time derivatives and then meshless approach is applied to the space component. Numerical results obtained from solving considered model on regular and irregular domains, demonstrate the accuracy and efficiency of the proposed schemes.
http://jacm.scu.ac.ir/article_14509_1912c71c376dc776522713124f8da483.pdf
Variable order fractional cable equation
Meshless method
Radial basis functions
Thin plate spline
eng
Shahid Chamran University of Ahvaz
Journal of Applied and Computational Mechanics
2383-4536
2383-4536
2020-04-01
6
2
248
258
10.22055/jacm.2019.28827.1507
14533
مقاله پژوهشی
On the Influence of Riveting Process Parameters on Fatigue Life of Riveted Lap Joint
Pedram Zamani
p.zamani@mail.um.ac.ir
1
Khalil Farhangdoost
farhang@um.ac.ir
2
Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
In this paper, influence of riveting process parameters, namely, riveting force, sheet thickness, friction coefficient and clearance fit are investigated on residual stress field and fatigue life of single riveted lap joint of AA2024 type. According to the effect of riveting induced residual stresses on fatigue life of riveted lap joint, these parameters are optimized to maximize the residual stress field. For this purpose, finite element simulations are performed for various combinations of the parameters according to Taguchi design of experiments. Afterwards, the parameter combination that maximize the residual stress field and the most effective parameters are obtained. The joint with maximum residual stress field is considered to have a semi-elliptical crack emanating from the rivet hole as an initial defect. Stress intensity factors are calculated by implementing two approaches: First, formulation overview that considers the effect of residual stress field, geometry and secondary bending, and second, the finite element method. The fatigue life of the joint is estimated using the obtained stress intensity factors and Paris-Erdogan rule. Finally, good accordance is found between results of these two approaches.
http://jacm.scu.ac.ir/article_14533_911a0f6ba088b183cbbc6bc5f6fd2076.pdf
Single lap joint
Residual stress
Stress intensity factor
Taguchi method
Fatigue life
Paris-Erdogan rule
eng
Shahid Chamran University of Ahvaz
Journal of Applied and Computational Mechanics
2383-4536
2383-4536
2020-04-01
6
2
259
270
10.22055/jacm.2019.29520.1608
14580
مقاله پژوهشی
Unsteady Hydromagnetic Flow of Eyring-Powell Nanofluid over an Inclined Permeable Stretching Sheet with Joule Heating and Thermal Radiation
Bharath Kumar
bharathkmr094@gmail.com
1
Suripeddi Srinivas
srinusuripeddi@hotmail.com
2
Department of Mathematics, School of Sciences and Languages, VIT-AP University, Amaravati, Andhra Pradesh, 522 237, India
Department of Mathematics, School of Sciences and Languages, VIT-AP University, Amaravati, Andhra Pradesh, 522 237, India
The present analysis deals with an unsteady magnetohydrodynamic flow of Eyring-Powell nanofluid over an inclined permeable stretching sheet. Effects of thermal radiation, Joule heating, and chemical reaction are considered. The effects of Brownian motion and thermophoresis on the flow over the permeable stretching sheet are discussed. Using Runge-Kutta fourth-order along with shooting technique, numerical and graphical results were obtained for the governing flow equations. The influence of various parameters on flow variables have been examined in detail. The results reveal that the temperature of the fluid enhanced with increasing Brownian and thermophoresis parameters. The increase of fluid velocity with the local Grashof number, the solutal Grashof number has been noticed. Further, the nanoparticles concentration decreased for a given increase in Brownian motion and chemical reaction parameters, while it increased with an increase in the thermophoresis parameter.
http://jacm.scu.ac.ir/article_14580_81175fa2eddf2a1c75c8edac8f860396.pdf
Chemical reaction
Eyring-Powell nanofluid
Hartmann number
Inclined stretching sheet
Joule heating
eng
Shahid Chamran University of Ahvaz
Journal of Applied and Computational Mechanics
2383-4536
2383-4536
2020-04-01
6
2
271
283
10.22055/jacm.2019.29948.1650
14699
مقاله پژوهشی
Numerical Simulation of Non-Newtonian Inelastic Flows in Channel based on Artificial Compressibility Method
Reisan Y. Yasir
reasan75@gmail.com
1
Alaa H. Al-Muslimawi
alaamath73@gmail.com
2
Bashaeer K. Jassim
bashaeir90@yahoo.com
3
Department of Mathematics, College of Science, University of Basrah, Basrah, Iraq
Department of Mathematics, College of Science, University of Basrah, Basrah, Iraq
Department of Mathematics, College of Science, University of Basrah, Basrah, Iraq
In this study, inelastic constitutive modelling is considered for the simulation of shear-thinning fluids through a circular channel. Numerical solutions are presented for power-law inelastic model, considering axisymmetric Poiseuille flow through a channel. The numerical simulation of such fluid is performed by using the Galerkin finite element approach based on artificial compression method (<em>AC</em>-method). Usually, the Naiver-Stoke partial differential equations are used to describe fluid activity. These models consist of two partial differential equations; a continuity equation (mass conservation) and time-dependent conservation of momentum, which are maintained in the cylindrical coordinate system (axisymmetric) flow in current study. The effects of many factors such as Reynolds number (<em>Re</em>) and artificial compressibility parameter (ß<sub>ac</sub>) are discussed in this study. In particular, this study confirms the effect of these parameters on the convergence level. To meet the method analysis, Poiseuille flow along a circular channel under an isothermal state is used as a simple test problem. This test is conducted by taking a circular section of the pipe. The Findings reveal that, there is a significant effect from the inelastic parameters upon the the velocity temporal convergence-rates of velocity, while for pressue, the change in convergence is modest. In addition, the rate of convergence is increased as the values of artificial compressibility parameter (ß<sub>ac</sub>) are decreased.
http://jacm.scu.ac.ir/article_14699_fe042cf6c8c12d9b83d37e24cc9df375.pdf
Finite element method
Galerkin method
Naiver-Stoke
Non-Newtonian
Artificial compressibility method
eng
Shahid Chamran University of Ahvaz
Journal of Applied and Computational Mechanics
2383-4536
2383-4536
2020-04-01
6
2
284
295
10.22055/jacm.2019.30017.1659
14665
مقاله پژوهشی
Effect of Coating Materials on the Fatigue Behavior of Hip Implants: A Three-dimensional Finite Element Analysis
Ayham Darwich
a.darwich@au.edu.sy
1
Hasan Nazha
hasannazha15@gmail.com
2
Monzer Daoud
monzerdaoud@hotmail.com
3
Faculty of Biomedical Engineering, Al-Andalus University for Medical Sciences, Tartous, Syria
Faculty of Technical Engineering, University of Tartous, Tartous, Syria
Department of Mechanical Engineering, École de Technologie Supérieure (ÉTS), Montreal, Canada
This study aims to validate, using finite element analysis (FEA), the design concept by comparing the fatigue behavior of hip implant stems coated with composite (carbon/PEEK) and polymeric (PEEK) coating materials corresponding to different human activities: standing up, normal walking and climbing stairs under dynamic loadings to find out which of all these models have a better performance in the prosthesis-bone systems. A 3D finite element models of hip implants, femur, coating layers with polymeric (PEEK) and composite (carbon/PEEK) coating materials are created for FEA. The cyclic loads are applied on the prosthesis head. Fatigue life durations are calculated based on the Goodman mean-stress fatigue theory. The fatigue safety factor for the coated implant is increased more than 12.73% at least compared to the uncoated implant. The carbon/PEEK composite material with 0, +45, -45, and 90 degrees fiber orientation (configuration I) has the highest fatigue life and fatigue safety factor. The numerical result show that the carbon/PEEK composite material (configuration I) seems to be a good solution to increase the values of fatigue safety factor of coating layers due to highest fatigue life and fatigue safety factor. It distributes the applied load and transfers it to the bone, reducing stress-shielding effects and prolong the bone-prosthesis system life span.
http://jacm.scu.ac.ir/article_14665_ff5fa2d4a2b55ceaf5c2de49b243b588.pdf
Hip implants
Coatings
PEEK
Carbon/PEEK
Fatigue behavior
Finite element analysis
eng
Shahid Chamran University of Ahvaz
Journal of Applied and Computational Mechanics
2383-4536
2383-4536
2020-04-01
6
2
296
306
10.22055/jacm.2019.29024.1543
14453
مقاله پژوهشی
Slip Effects on Ohmic Dissipative Non-Newtonian Fluid Flow in the Presence of Aligned Magnetic Field
P. Renuka
prenuka.maths@gmail.com
1
B. Ganga
gangabhose@gmail.com
2
K. Kalivanan
vananmaths@gmail.com
3
A.K. Abdul Hakeem
abdulhakeem6@gmail.com
4
Department of Mathematics, Erode Sengunthar Engineering College, Erode - 638 057, India
Department of Mathematics, Providence College for Women, Coonoor - 643 104, India
Department of Mathematics, Vivekananda College, Madurai - 625 234, India
Department of Mathematics, SRMV College of Arts and Science, Coimbatore - 641 020, India
The present paper deals with the effects of Ohmic dissipative Casson fluid flow over a stretching sheet in the presence of aligned magnetic field. The present phenomenon also includes the interaction of thermal radiation and velocity slip. The governing boundary layer equations are transformed into a set of ordinary differential equations using the similarity transformations. The dimensionless velocity and temperature profiles are solved analytically using hypergeometric function and numerically by using fourth order Runge-Kutta method with shooting technique. It is noted that the increasing values of Eckert number increases the temperature profile and decreases the local Nusselt number.
http://jacm.scu.ac.ir/article_14453_59762e7463c4b61369230d184fd00277.pdf
Aligned magnetic field
Casson Fluid
Slip
Thermal radiation
Ohmic dissipation
eng
Shahid Chamran University of Ahvaz
Journal of Applied and Computational Mechanics
2383-4536
2383-4536
2020-04-01
6
2
307
319
10.22055/jacm.2019.29503.1605
14545
مقاله پژوهشی
Mesoscopic Simulation of Forced Convective Heat Transfer of Carreau-Yasuda Fluid Flow over an Inclined Square: Temperature-dependent Viscosity
Ali Jalali
a_jalali@pnum.ac.ir
1
Amin Amiri Delouei
a.amiri@ub.ac.ir
2
Mojtaba Khorashadizadeh
mojtaba.khorashadi@yahoo.com
3
A.M. Golmohamadi
golmohamadi-a@mashhad.ir
4
Sajjad Karimnejad
karimnejad.sajjad@gmail.com
5
Department of Mechanical Engineering, Payame Noor University (PNU), P.O. BOX 19395-3697, Tehran, Iran
Department of Mechanical Engineering, University of Bojnord, Bojnord, Iran
Department of Mechanical Engineering, Payam Noor University, Mashhad, Iran
Department of Mechanical Engineering, Payam Noor University, Mashhad, Iran
Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran
<span>In the current study, non-Newtonian flow pattern and heat transfer in an enclosure containing a tilted square are examined. In order to numerically simulate the problem, the mesoscopic lattice Boltzmann method is utilized. The non-Newtonian Carreau-Yasuda model is employed. It is able to adequately handle the shear-thinning case. The simulation results of flow and heat transfer have been successfully verified with the previous studies. Several parameters such as Nusselt number, Drag coefficient, and Carreau number are investigated in details. Considering the temperature-dependent viscosity, it is seen that with increasing the</span><span>temperature-thinning index, the drag coefficient increases, but the Nusselt number decreases. By rotating the square obstacle, the results display that increasing the angle of inclination from zero to 45 degrees, increases both the drag coefficient and the Nusselt number. Also, the highest rate of heat transfer occur at the angle of 45 degrees (diamond); however it has a negative impact on the Drag coefficient.</span>
http://jacm.scu.ac.ir/article_14545_89eaabd8976162ca5e5e9028936102f5.pdf
Carreau-Yasuda model
Temperature-dependent viscosity
Inclined square
Lattice Boltzmann method
eng
Shahid Chamran University of Ahvaz
Journal of Applied and Computational Mechanics
2383-4536
2383-4536
2020-04-01
6
2
320
331
10.22055/jacm.2019.29782.1634
14667
مقاله پژوهشی
A Modified Energy Balance Method to Obtain Higher-order Approximations to the Oscillators with Cubic and Harmonic Restoring Force
Md Alal Hosen
alal_ruet@yahoo.com
1
Gamal Ismail
gamalm2010@yahoo.com
2
Ahmet Yildirim
yahmet49ege@gmail.com
3
M.A.S. Kamal
ozeldersmatematikizmir@gmail.com
4
Department of Mathematics, Rajshahi University of Engineering and Technology, Rajshahi-6204, BANGLADESH
Department of Mathematics, Faculty of Science, Sohag University, Sohag, 82524, EGYPT
Department of Mathematics, Ege University, Bornova-İzmir, TURKEY
Graduate School of Science and Technology, Gunma University, Kiryu 376-8515, JAPAN
This article analyzes a strongly nonlinear oscillator with cubic and harmonic restoring force and proposes an efficient analytical technique based on the modified energy balance method (MEBM). The proposed method incorporates higher-order approximations. After applying the proposed MEBM, a set of complicated higher-order nonlinear algebraic equations are obtained. Higher-order nonlinear algebraic equations are cumbersome to investigate especially in the case of a large initial oscillation amplitude. This limitation is overcome in the proposed method by using the iterative procedure based on the homotopy perturbation method. The approximated results agree well with the numerically obtained exact solutions. These third-order approximate solutions are found to be almost the same as exact solutions, which cannot be found using the existing energy balance method. Highly accurate result and simple solution procedure are advantages of this proposed method, which could be applied to other nonlinear oscillatory problems arising in nonlinear science and engineering.
http://jacm.scu.ac.ir/article_14667_4cbfbc6281d4e4a80d1dfce81a4baf65.pdf
Analytical technique
Strongly nonlinear oscillator
Nonlinear algebraic equations
Energy balance method
Iterative procedure
Homotopy perturbation method
eng
Shahid Chamran University of Ahvaz
Journal of Applied and Computational Mechanics
2383-4536
2383-4536
2020-04-01
6
2
332
343
10.22055/jacm.2019.29070.1552
14643
مقاله پژوهشی
Experimental Investigation and Optimizing Geometrical Characteristics and Surface Quality in Drilling of AISI H13 Steel
Farshid Jafarian
fjafarian@mahallat.ac.ir
1
Hojjat Samarikhalaj
h.samarikhalaj@gmail.com
2
Faculty of Engineering, Mahallat Institute of Higher Education, Mahallat, Iran
Department of Mechanical Engineering, Amirkabir University of Technology, 424 Hafez Ave., 15914 Tehran, Iran
The aim of this paper is to investigate and optimize surface quality and geometrical characteristics in drilling process of AISI H13 steel, because they are critical items for precision manufacturing. After conducting the experiments, two regression models are developed to extensively evaluate the effect of drilling parameters on process outputs. After that, evolutionary multi-objective optimization algorithm is employed to find the optimal drilling conditions. Non-dominated Sorting Genetic Algorithm (NSGA-ІІ) is developed and regression functions are taken into account as objective functions of algorithm to simultaneously optimize the surface roughness and deviation of circularity. The optimization results are successfully in agreement with experimental findings and finally the set of optimal drilling conditions is reported that can be selected by process engineer according to the priority and application. It is shown that, an increase in Cutting speed and liquid coolant intensity decreases the surface quality, while higher depth of cut, tool diameter and reed rate improve it. It is also found that tool diameter and depth of cut are the most effective input parameters on deviation of circularity. Finally, it can be concluded that, the implemented approach in this research provides an efficient method for other manufacturing processes to increase the performance and reduction of production costs.
http://jacm.scu.ac.ir/article_14643_e6741aba3677a38fc8a767f214ac0b81.pdf
NSGA-ІІ
Multi-Objective Optimization
Drilling Process
Hardened Steel
eng
Shahid Chamran University of Ahvaz
Journal of Applied and Computational Mechanics
2383-4536
2383-4536
2020-04-01
6
2
344
356
10.22055/jacm.2019.29567.1616
14461
مقاله پژوهشی
A Parameter Uniform Numerical Scheme for Singularly Perturbed Differential-difference Equations with Mixed Shifts
P. Mushahary
417ma2094@nitrkl.ac.in
1
S. R. Sahu
515ma1013@nitrkl.ac.in
2
J. Mohapatra
jugal@nitrkl.ac.in
3
Department of Mathematics, NIT Rourkela, Odisha, 769008, India
Department of Mathematics, NIT Rourkela, Odisha, 769008, India
Department of Mathematics, NIT Rourkela, Odisha, 769008, India
In this paper, we consider a second-order singularly perturbed differential-difference equations with mixed delay and advance parameters. At first, we approximate the model problem by an upwind finite difference scheme on a Shishkin mesh. We know that the upwind scheme is stable and its solution is oscillation free, but it gives lower order of accuracy. So, to increase the convergence, we propose a hybrid finite difference scheme, in which we use the cubic spline difference method in the fine mesh regions and a midpoint upwind scheme in the coarse mesh regions. We establish a theoretical parameter uniform bound in the discrete maximum norm. To check the efficiency of the proposed methods, we consider test problems with delay, advance and the mixed parameters and the results are in agreement with our theoretical findings.
http://jacm.scu.ac.ir/article_14461_880cc645745f67e899fdeb388bcc42c3.pdf
Singularly perturbed problem
Differential-difference equation
Mixed shifts
Shishkin mesh
Hybrid scheme
Uniform convergence
eng
Shahid Chamran University of Ahvaz
Journal of Applied and Computational Mechanics
2383-4536
2383-4536
2020-04-01
6
2
357
372
10.22055/jacm.2019.29527.1609
14642
مقاله پژوهشی
An Analytical Approach of Nonlinear Thermo-mechanical Buckling of Functionally Graded Graphene-reinforced Composite Laminated Cylindrical Shells under Compressive Axial Load Surrounded by Elastic Foundation
Ngoc Ly Le
lyln@utt.edu.vn
1
Thi Phuong Nguyen
phuongnt@utt.edu.vn
2
Hoai Nam Vu
vuhoainam@tdtu.edu.vn
3
Thoi Trung Nguyen
nguyenthoitrung@tdtu.edu.vn
4
Minh Duc Vu
ducvm97@gmail.com
5
Faculty of Fundamental Science for Engineering, University of Transport Technology, Hanoi, 100000, Vietnam
Faculty of Civil Engineering, University of Transport Technology, Hanoi, 100000, Vietnam
Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, 700000, Vietnam | Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, 700000, Vietnam
Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, 700000, Vietnam | Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, 700000, Vietnam
Faculty of Civil Engineering, University of Transport Technology, Hanoi, 100000, Vietnam
This paper deals with an analytical approach to predict the nonlinear buckling behavior of functionally graded graphene-reinforced composite laminated cylindrical shells under axial compressive load surrounded by Pasternak’s elastic foundation in a thermal environment. Piece-wise functionally graded graphene-reinforced, composite layers are sorted with different types of graphene distribution. The governing equations are established by using Donnell’s shell theory with von Kármán nonlinearity terms and three-term solution of deflection is chosen for modeling the uniform deflection of pre-buckling state, linear and nonlinear deflection of post-buckling state. Galerkin method is applied to determine the critical axial compressive buckling load expression, post-buckling load-deflection and load-end shortening relations of the shell. The effects of environment temperature, foundation, geometrical properties, and graphene distribution on buckling behavior of shell, are numerically evaluated.
http://jacm.scu.ac.ir/article_14642_69ac3298ee953e35f2aabf8424171fff.pdf
Functionally graded graphene-reinforced composite
cylindrical shell
compressive axial load
thermo-mechanical buckling
elastic foundation