eng
Sharif University of Technology
Scientia Iranica
1026-3098
2345-3605
2020-02-01
27
1
203
214
10.24200/sci.2018.21093
21093
Application of AG method and its improvement to nonlinear damped oscillators
M. Mohammadian
mo.mohammadian@ut.ac.ir
1
M. Shariati
mahmoud.shariati44@gmail.com
2
Department of Mechanical Engineering, Kordkuy Center, Gorgan Branch, Islamic Azad University, Kordkuy, P.O. Box 488164-4479, Iran.
Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, P.O. Box 91775-1111, Iran.
In this paper, a new and innovative semi analytical technique, namely Akbari-Ganji’s method (AGM), is employed for solving three nonlinear damped oscillatory systems. Applying this method to nonlinear problems is very simple because in solving process only a trial solution, the main differential equation and its derivatives are required. The analytical solutions obtained by the AGM are utilized to study the impact of amplitude on nonlinear frequency and damping ratio. It is found that the AGM leads to acceptable results for the problems considered in this paper. Also, in order to obtain a more accurate solution, instead of using a trial solution with higher-order terms which may result in complicated and time consuming mathematical calculations, the solution obtained by AGM is improved via variational iteration method (VIM). The usefulness and effectiveness of the approach is demonstrated through comparison of the obtained results with those achieved by the numerical method. Hence, the AGM can be applied to nonlinear problems consisting of significant nonlinear damping terms and, if necessary, can be easily improved.
https://scientiairanica.sharif.edu/article_21093_b53fffd5af9a2ffb35fb21c8705ad667.pdf
Nonlinear frequency
Akbari-Ganji’s method (AGM)
Variational iteration method (VIM)
Semi analytical technique
Damped Duffing oscillator
Flexible beam with damping
Transversal vibration
Quintic nonlinear beam
eng
Sharif University of Technology
Scientia Iranica
1026-3098
2345-3605
2020-02-01
27
1
215
228
10.24200/sci.2019.21269
21269
Modeling particle deposition in the respiratory system during successive respiratory cycles
H. Nemati
1
M.S. Saidi
mssaidi@sharif.edu
2
V. Hosseini
vhosseini@sharif.edu
3
Department of Mechanical Engineering, Sharif University of Technology, Tehran, P.O. Box 11155-9567, Iran.
Department of Mechanical Engineering, Sharif University of Technology, Tehran, P.O. Box 11155-9567, Iran.
Department of Mechanical Engineering, Sharif University of Technology, Tehran, P.O. Box 11155-9567, Iran.
In this study, using a 5-lobe symmetric model, total, lobar and generational particle deposition in the lungs during successive cycles is investigated. It has been found that for the particle size between 0.05 and 2 μm and the tidal volumes greater than 1000 ml, considering the effect of successive cycles predicted more deposition fraction per cycle compared to a single cycle up to about 16 percent. The mentioned range of tidal volume is related to light or heavy physical activities. So, it can be understood that people exposed to particulate matter within the mentioned size range, when acting physically, are at more health risk compared not only to the resting state, but also to the same state calculations based on a single cycle. Finally, total and generational remaining mass fraction suspended in the respiratory tract after the completion of each cycle is calculated. This remaining mass fraction turned out to be negligible except for particles between 0.05 and 2 μm.
https://scientiairanica.sharif.edu/article_21269_f4b14976134f581bae1f2fda063908fe.pdf
particle deposition
respiratory system
lung
lobe
successive respiratory cycles
eng
Sharif University of Technology
Scientia Iranica
1026-3098
2345-3605
2020-02-01
27
1
229
238
10.24200/sci.2018.5512.1319
21094
Estimation of mixed-mode fracture parameters by gene expression programming
A. Khademalrasoul
ag.khadem@scu.ac.ir
1
A. Adib
arashadib@scu.ac.ir
2
Department of Civil Engineering, Engineering Faculty, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
Department of Civil Engineering, Engineering Faculty, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
The linear elastic fracture phenomenon has been characterized with stress intensity factors (SIFs). In this study a general function is obtained in order to predict the fracture parameters. Numerical calculation of the SIFs in a mixed-mode condition is a cumbersome task. In this research, more than 6800 numerical analyses using extended finite element method are conducted to simulate the fracture problem. States are considered for a plate with an arbitrary edge or center crack. Mixed mode SIFs were calculated using of interaction integral. Then, Gene Expression Programming (GEP) method is utilized to extraction of a function. Results show acceptable correlations between numerical calculations and genetic programming functions. R-square (R2) values are in a range of 0.91 to 0.96 that guarantees the accuracy of the inferred functions.
https://scientiairanica.sharif.edu/article_21094_63d40e8d833258a164c0e844b5eb6616.pdf
Fracture mechanics
Genetic programming
Stress intensity factors
Extended finite element method
eng
Sharif University of Technology
Scientia Iranica
1026-3098
2345-3605
2020-02-01
27
1
239
251
10.24200/sci.2018.5604.1369
21143
Improving heat transfer in a triplex tube heat exchanger containing phase-change materials by modifications of length and position of fins
M. M. Hossieni
mohammad_mh91@yahoo.com
1
A.B. Rahimi
rahimiab@yahoo.com
2
Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran.
Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran.
Heat thermal energy storage is a technique to improve thermal efficiency through reducing discrepancy between energy demand and supply. Latent heat thermal energy storage as a kind of thermal energy storage method has drawn considerable attention from researchers due to its high thermal energy density and constant operating temperature. This study numerically investigates the melting process in a triplex tube heat exchanger containing phase change material (PCM) RT82. A two-dimensional numerical model has been generated using the Ansys Fluent 16 software program to simulate melting process. In this study, conduction and natural convection have been considered. Selected arrangements of rectangular fins, including lengths and positions, were selected according to heat distribution while the total area of fins was kept constant. This new strategy was done to improve heat transfer in PCM which would result in decreasing its melting time. The select optimized model in this article reduces meting time to 28.4% in comparison with the model in Ref. [1]. Numerical results have been validated by numerical and experimental results of this reference and there has been a proper agreement between them.
https://scientiairanica.sharif.edu/article_21143_e09d1004466884eb1ff816795abaef8d.pdf
Phase change material
Triplex tube heat exchanger
Heat transfer enhancement
fins arrangements
eng
Sharif University of Technology
Scientia Iranica
1026-3098
2345-3605
2020-02-01
27
1
252
261
10.24200/sci.2018.5722.1444
21120
Studying buckling of composite rods made of hybrid carbon fiber/carbon nanotube-reinforced polyimide using multi-scale FEM
M. Ahmadi
masoud_ahmadi_pr@yahoo.com
1
R. Ansari
r_ansari@guilan.ac.ir
2
H. Rouhi
h_rouhi@guilan.ac.ir
3
Department of Mechanical Engineering, University of Guilan, Rasht, P.O. Box 3756, Iran.
Department of Mechanical Engineering, University of Guilan, Rasht, P.O. Box 3756, Iran.
Department of Engineering Science, Faculty of Technology and Engineering, East of Guilan, University of Guilan, P.C. 44891-63157, Rudsar-Vajargah, Iran.
In this paper, the buckling behavior of rods made of carbon fiber/carbon nanotube-reinforced polyimide (CF/CNT-RP) under the action of axial load is investigated based on a multiscale finite element method. A dual-step procedure is first adopted to couple the influences of micro- and nano-scale in order to obtain the equivalent elastic properties of CF/CNT-RP for various volume fractions of CF and CNT. The interphase effect between CNTs and the polymer matrix is taken into consideration. Also, dispersion of CF/CNT into the polymer matrix is assumed to be random. Then, rods with square and circular cross sections are considered whose stability characteristics are analyzed. The finite element modeling is performed using two models including a 3D brick model and a 2D beam model. Selected numerical results are given to study the effects of volume fraction of CNT/CF, interphase and geometrical properties on the axial buckling response of multiscale composite rods.
https://scientiairanica.sharif.edu/article_21120_35229ece51e9f88aebe66a8b0ab32c51.pdf
Multiscale composite rod
Hybrid carbon nanotube/carbon fiber reinforcement
Polyimide
buckling
Finite Element Method
eng
Sharif University of Technology
Scientia Iranica
1026-3098
2345-3605
2020-02-01
27
1
262
272
10.24200/sci.2018.50018.1466
21129
Intelligent navigation of a self-fabricated biped robot using a regression controller
P.B. Kumar
p.biplabkumar@gmail.com
1
C. Sahu
mechchinu@gmail.com
2
D.R. Parhi
dayaldoc@yahoo.com
3
Robotics Laboratory, Department of Mechanical Engineering, National Institute of Technology, Rourkela-769008, Odisha, India.
Robotics Laboratory, Department of Mechanical Engineering, National Institute of Technology, Rourkela-769008, Odisha, India.
Robotics Laboratory, Department of Mechanical Engineering, National Institute of Technology, Rourkela-769008, Odisha, India.
With increasing demand towards use of biped robots in industrial automation and other related applications, navigation and path planning has emerged as one of the most challenging research topic over the last few decades. In this paper, a novel navigational controller is designed and implemented in a self-fabricated biped robot. After fabricating the biped equipped with a large set of sensors, a regression controller is implemented in it for obstacle avoidance and path optimization purpose. The obstacle distances detected by the sensory network of the biped are fed as input parameters to the regression controller and the output obtained from the controller is the necessary heading angle required to avoid the obstacles present randomly in the environment. The biped is tested in a simulation environment for obstacle avoidance and target following behaviour. Along with that, to validate the simulation results, a real-time experimental set up is designed under laboratory conditions. The results obtained from both the environments are compared in terms of navigational parameters and a good agreement between them is observed. Being a relatively new area of research, the navigation of bipeds can serve as a pioneer act towards industrial automation.
https://scientiairanica.sharif.edu/article_21129_c0c1aae339d603979fc7ae95308fc13d.pdf
Biped Robot
Basic Regression
Navigation
Path planning
V-REP
eng
Sharif University of Technology
Scientia Iranica
1026-3098
2345-3605
2020-02-01
27
1
273
286
10.24200/sci.2018.5100.1095
21046
Adaptive control of a cable-actuated parallel manipulator mounted on a platform with differential wheels under payload uncertainty
M. H. Korayem
hkorayem@iust.ac.ir
1
M. Yousefzadeh
ma.yousef@gmail.com
2
Robotic Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran.
Robotic Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran.
Cable-actuated parallel Manipulators (CPMs) are widely employed for object handling applications. In order to displace the carried object along the ground to an unlimited distance, the CPMs can be mounted on wheeled mobile robots (WMRs). The derivation of the dynamic equations of motion for this integrated system is presented using Lagrange method. Since in load carrying task, the inertia of the moving load is the main source of uncertainty, an adaptive control approach is considered for the CPM, whereas the WMR uses a feedback linearized sliding mode approach. In order to maintain the end-effector of the CPM in within its relative workspace in the WMR frame, the convergence rate in the two controllers should be similar. Decentralization of the control law can be accomplished if the inertia of the CPM motors are negligible compared with the other inertias of the system. This assumption is shown to be applicable if an introduced index is small enough to have noticeable effect on the tracking error.
https://scientiairanica.sharif.edu/article_21046_caedfb69034b101f04c3f167a3c25a88.pdf
Cable-Actuated Parallel Manipulators
Mobile Robots with Differential Wheels
Non-Holonomic Constraints
Adaptive Control
sliding mode control
eng
Sharif University of Technology
Scientia Iranica
1026-3098
2345-3605
2020-02-01
27
1
287
294
10.24200/sci.2018.50154.1540
21206
Numerical and experimental study of the effect of the process parameters on the void evolution in the cold extrusion of rods
M. Rajabzadeh Gatabi
rajabzadehgatabi@nit.ac.ir
1
H. Afrasiab
afrasiab@nit.ac.ir
2
A. Moazemi Goudarzi
mgoodarzi@nit.ac.ir
3
Department of Mechanical Engineering , Babol Noshirvani University of Technology, Babol, Iran.
Department of Mechanical Engineering , Babol Noshirvani University of Technology, Babol, Iran.
Department of Mechanical Engineering , Babol Noshirvani University of Technology, Babol, Iran.
Elimination of defects such as voids and internal cavities is required in metal forming processes to avoid premature failure of mechanical components during service. In this paper, the effect of different parameters on the void closure behavior is studied in the cold extrusion of rods. A three dimensional nonlinear dynamic finite element model is developed for this purpose. Experiments are also performed on aluminum samples to verify the accuracy of the finite element model. Results of the developed model are in good agreement with experimental findings. It is observed that voids contract in all directions during the direct extrusion which is in contrast to some other metal forming processes like forging and rolling. Effect of parameters such as die semi-angle, friction coefficient and void location on the void evolution is systematically investigated and discussed. The results of this study can help industries using metal extrusion for optimized design and control of the process to reduce voids and porosity and increase the strength of their product.
https://scientiairanica.sharif.edu/article_21206_cf3fc80e2535c3766e386a3b220001d3.pdf
Void evolution
Cold extrusion
Finite Element Method
Die geometry
Void location
eng
Sharif University of Technology
Scientia Iranica
1026-3098
2345-3605
2020-02-01
27
1
295
301
10.24200/sci.2018.50340.1644
20587
Analysis of change in the state of hydraulic drive of machines in operation according to the diagnostic results
N.G. Grinchar
1
P.A. Sorokin
2
V.A. Karpychev
3
K.A. Sergeev
4
Department of Track Machines, Construction Machines and Robot Systems, Russian University of Transport, 127994, 9 Obrazcova Str., Moscow, Russian Federation.
Department of Track Machines, Construction Machines and Robot Systems, Russian University of Transport, 127994, 9 Obrazcova Str., Moscow, Russian Federation.
Department of Machine Science, Design, Standardization and Certification, Russian University of Transport, 127994, 9 Obrazcova Str., Moscow, Russian Federation.
Department of Non-Traction Rolling Stock, Russian University of Transport, 127994, 9 Obrazcova Str., Moscow, Russian Federation.
Technical diagnostics is a sphere of knowledge embracing theory, methods and means for defining the technical state of the objects. It is necessary for provision of security, functional reliability and efficiency of the technical object operation, as well as for reduction of the costs for its technical maintenance and reduction of the idle time losses caused by failures and premature shutdowns for maintenance. Therefore the objective of the paper is to analyze the change in the state of hydraulic drive of machines while in operation according to the diagnostic results. In order to achieve the set objective the authors used various experimental methods. The paper considers mutual influence of maintenance and technical diagnostics of hydrostatic drives of construction, track and some other mobile machines. It is shown that introduction of technical diagnostics allows transferring from the system of planned preventive repairs to the system of servicing the machines according to their actual technical state, which allows completely using the resource of a series of expensive aggregates. The authors described several main basic characteristics of change in the volume effectiveness of the hydraulic sets while in operation.
https://scientiairanica.sharif.edu/article_20587_1f33547aa3b27d70cf3458d3e127cc77.pdf
Diagnostic parameter
Hours in operation
Hydraulic drive
Economic expenditures
Performance capability
eng
Sharif University of Technology
Scientia Iranica
1026-3098
2345-3605
2020-02-01
27
1
302
309
10.24200/sci.2018.50465.1710
21041
Effect of processing time on microstructure of surface and corrosion resistance of coatings resulting from plasma electrolytic oxidation on titanium alloy in hydroxyapatite nano-particles electrolyte
B. Barooghi
b.barooghi@gmail.com
1
M. Sheikhi
mohammd.sheikhi@gmail.com
2
A. Amiri
amiramiri.aa@gmail.com
3
Department of Mechanical Engineering, Shahid Rajaee Teacher Training University, Tehran, P.O. Box 1678815811, Iran.
Department of Mechanical Engineering, Shahid Rajaee Teacher Training University, Tehran, P.O. Box 1678815811, Iran.
Department of Mechanical Engineering, Islamic Azad University, North Tehran Branch, Tehran, Iran.
In this study, the effect of coating processing time on microstructure of surface and corrosion resistance of coatings resulted by plasma electrolytic oxidation (PEO) was investigated on substrate of TiAl6V4 alloy. The coating processes in hydroxyapatite nano-powder electrolytic were carried out in same conditions of constant voltage of 600V and three different times of 125, 250 and 350 seconds. Studying the microstructure of coatings identified that the coating formed in 125 (s) had more compact and steady structure with fine surface cavities and less porosity. X-ray diffraction pattern of coating demonstrates that this coating is consists of oxide phases of titanium (rutile and anatase) and hydroxyapatite. Also, the study of corrosion resistance of coatings by Potentiodynamic polarization and electrochemical impedance spectroscopy in corrosive solution of chloride sodium 3.5% showed that the coating formed in 125 s has the most noble corrosion resitance potential and the least ICorr and finally the highest resistance to corrosion.
https://scientiairanica.sharif.edu/article_21041_11383805a256531347702dcc32ba91f7.pdf
corrosion resitance
TiAl6V4
Plasma Electrolytic Oxidation
eng
Sharif University of Technology
Scientia Iranica
1026-3098
2345-3605
2020-02-01
27
1
310
329
10.24200/sci.2018.50714.1832
21074
Parameter converting method for bifurcation analysis of nonlinear dynamical systems
H. Asghari
hossein.h.asghary@gmail.com
1
M. Dardel
dardel@nit.ac.ir
2
Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, P.O. Box 484, Postal Code 47148-71167, Mazandaran, Iran.
Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, P.O. Box 484, Postal Code 47148-71167, Mazandaran, Iran.
For detecting behavior of a dynamical system, bifurcation analysis is necessary with respect to change in parameters of system. In this work, based on the solution of ordinary differential equations from initial value and parameters, a simple method is presented, which can efficiently reveal different bifurcations of system. In addition to its simplicity, this method does not required to have deep physical and mathematical understanding of the problem, and because of its high precision and the speed of solutions, does not need to reduce the order of models in many complex problems or problems with high degrees of freedom. This method is named parameter converting method (PCM), which has two steps. In the first step the parameter is varied as a function of time and in the second step, time is expressed as inverse of this assumed function. With this method bifurcation and amplitude-frequency diagrams and hidden attractors of some complex dynamics will be analyzed and the sensitivity of the multi potential well systems to initial conditions is studied. With this algorithm, a simple way to find the domain of high-energy orbit in bistable systems is obtained.
https://scientiairanica.sharif.edu/article_21074_b586add3f67251a127671742ea16a6e3.pdf
Parameter converting method
sweeping parameter
bifurcation
Poincare’ map
continuation
nonlinear dynamics
time continuation method
unlimited steady solution method
eng
Sharif University of Technology
Scientia Iranica
1026-3098
2345-3605
2020-02-01
27
1
330
340
10.24200/sci.2018.51214.2065
21098
Modeling, control, and simulation of a SCARA PRR-type robot manipulator
M.E. Uk
me.uk@sherpa-eng.com
1
F.B. Sajjad Ali Shah
faris.ali.shah@outlook.com
2
M. Soyaslan
msoyaslan@sakarya.edu.tr
3
O. Eldogan
eldogan@sakarya.edu.tr
4
Faculty of Technology, Department of Mechatronics Engineering, Sakarya University, Sakarya, Turkey.
Faculty of Technology, Department of Mechatronics Engineering, Sakarya University, Sakarya, Turkey.
Faculty of Technology, Department of Mechatronics Engineering, Sakarya University, Sakarya, Turkey.
Faculty of Technology, Department of Mechatronics Engineering, Sakarya University, Sakarya, Turkey.
In this study, a SCARA PRR-type robot manipulator is designed and implemented. Firstly, the SCARA robot was designed according to the mechanical calculations. Then, forward and inverse kinematic equations of the robot are derived by using D-H parameters and analytical methods. The software is developed according to obtain cartesian velocities from joint velocities and joint velocities from cartesian velocities. The trajectory planning is designed using the calculated kinematic equations and the simulation is performed in MATLAB VRML environment. A stepping motor is used for prismatic joint of the robot, and servo motors are used for revolute joints. While most of the SCARA robot studies focus on RRP-type servo control strategy, this work focuses PRR-type and both stepper and servo control structures. The objects in the desired points of the workspace are picked and placed to another desired point synchronously with the simulation. So the performance of the robot is examined experimentally.
https://scientiairanica.sharif.edu/article_21098_78d1e2ef66a1f50e243fc0c00b688f8a.pdf
SCARA robot
Real-time control
Modelling
Simulation
PRR
Servo motor
eng
Sharif University of Technology
Scientia Iranica
1026-3098
2345-3605
2020-02-01
27
1
341
349
10.24200/sci.2018.51294.2100
21099
Comparative study of damage behavior of synthetic and natural fiber-reinforced brittle composite and natural fiber-reinforced flexible composite subjected to low-velocity impact
M. Vishwas
vishwasm.nitk@gmail.com
1
S. Joladarashi
sharnappa@nit.ac.in
2
S.M. Kulkarni
smk@nit.ac.in
3
Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal, Mangaluru 575025, India.
Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal, Mangaluru 575025, India.
Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal, Mangaluru 575025, India.
In the present study, comparative study on the damage behaviour of Glass-Epoxy (GE), Jute-Epoxy (JE) laminates with [0/90]s orientation and Jute-Rubber-Jute (JRJ) sandwich is carried out using ABAQUS/CAE finite element software. The GE, JE laminate and JRJ sandwich with thickness of 2 mm is impacted by a hemispherical shaped impactor at a velocity of 2.5 m/s. The mechanisms in which the brittle laminate gets damaged are analyzed using Hashin’s 2D failure criteria and flexible composites are analysed by ductile damage mechanism. The energy absorbed and the incipient point of each laminate was compared. It was observed from the results that there is no evidence of delamination in JRJ as opposed to GE and JE. The compliant nature of rubber contributes in absorbing more energy and it is slightly higher than GE. Also it was observed that there is no incipient point in JRJ sandwich which means there is no cracking of matrix since rubber is elastic material. Thus the JRJ material can be a better substitute for GE laminate in low velocity applications. The procedure proposed for the analysis in the present study can serve as benchmark method in modelling the impact behaviour of composite structures in further investigations.
https://scientiairanica.sharif.edu/article_21099_fc44c3b694db62bbdc293cd611568fd8.pdf
rubber
Damage
Energy absorbed
Glass fiber
Jute fiber
Low velocity impact
Stiff and Flexible Composites
eng
Sharif University of Technology
Scientia Iranica
1026-3098
2345-3605
2020-02-01
27
1
350
360
10.24200/sci.2018.20829
20829
Design of mixed flow pump impeller blade using mean streamline theory and its analysis
D. Zindani
1
A.K. Roy
2
K. Kumar
ganikganesh@gmail.com
3
Department of Mechanical Engineering, Birla Institute of Technology, Mesra, Ranchi, 835215, India.
Department of Mechanical Engineering, Birla Institute of Technology, Mesra, Ranchi, 835215, India.
Department of Mechanical Engineering, Birla Institute of Technology, Mesra, Ranchi, 835215, India.
Given the importance of blade design in effective performance of the mixed flow pump, the present work demonstrates the designing of the mixed flow pump impeller blade using almost unexplored Mean stream line theory. The Mean stream line theory, though been used sparingly but has found to give comparable results to that of other templates of design. The design process has been carried out in AUTOCAD 2013 and Solid Works Premium 2014 software. The analysis for equivalent stress, equivalent elastic strain, Total deformation and the directional deformation have been carried out in ANSYS 2014 for different construction material of the blade i.e., stainless steel, titanium alloy, bronze, and copper alloy. Total deformation was found to be maximum for impeller blade made from titanium alloy whereas the equivalent stress and strain was least for titanium alloyed impeller blade. Further, a comparison analysis has been carried out for the equivalent stresses in blade designed using mean stream line theory and free vortex theory. It was observed that the equivalent stress in impeller blade designed using free vortex theory was lesser than that designed using mean stream line theory.
https://scientiairanica.sharif.edu/article_20829_c6ce09db0545e717365b32d512884859.pdf
Mixed flow pump impeller blade
AUTOCAD
Solid Works Premium
ANSYS
Mean stream line theory
free vortex theory