Modares Mechanical Engineering
Year:2019 | Volume:19 | Issue:1 |Papers Count:31

In this study, based on the nonlocal nonlinear Euler-Bernoulli beam model, the primary and superharmonic resonance of a single carbon nanotube (CNT) resting on a viscoelastic foundation under the magnetic axial loads and temperature as well as transverse harmonic forces was investigated. Using Galerkin approximation along with the trigonometric shape functions, the nonlinear partial differential governing equation is reduced to nonlinear ordinary differential equation. The frequency response of the single walled CNT is derived by implementing the multiple time scale method for the primary and superharmonic resonances. The effects of surface elasticity, change in temperature, magnetic field and the length-toouter diameter aspect ratio on the frequency response of CNT in the cases of primary and superharmonic resonances were analyzed. The results show that the nonlinearity according to considered geometrical and mechanical parameters in this study, may cause unpleasant jumping phenomenon accompanied by unstable region in the frequency response. In addition to the surface elasticity, magnetic field, smaller temperature changes, as well as larger aspect ratio have positive effects on weakening the jumping phenomenon and extending the stability level of single walled CNT.

In this research, the effect of using two solar fields in a solar thermal power plant was evaluated. The average price of natural gas in the last decade was 3. 5 dollar/MMBTU. Due to the complexities of the solar power plant, two methods were introduced to optimize the area of the solar fields. Then, for further evaluation of the solar power plant with two distinct solar fields, the plant was examined for two natural gas prices of 3. 5 and 9 dollar/MMBTU. The results of the study show that the use of two separate solar fields to produce high pressure steam turbines and low pressure over the use of a solar field reduces the cost of generating electricity. Although each solar field must produce different energy quantities, and the area of each of the fields is different, the size of the field coefficient of the field was the same for both solar fields.

In the different applications of thin plats in engineering industrial, some holes are created in the structure that can have different shapes such as circular, elliptical, and quasi-square. When the plate is subjected to loading, stress concentration around the hole causes the crack initiation in these areas that can results in a catastrophic failure. In this paper, mode II stress intensity factor (SIF) for two unequal aligned cracks emanating from a circle or a quasi-square hole in an infinite plane was investigated. The complex variable theory of Muskhelishvili and conformal mapping method were used. To obtain mapping function, Schwarts Christoffel integral was combined with some simple mapping functions. Accordingly, a new mapping function is presented and approximated to the sum of series expansion. Using this approximate mapping, SIF is calculated with high accuracy. Surfaces of the cracks and hole are traction-free. The plane is subjected to the pure shear at infinity. The analytical results are in good agreement with the literature. The obtained stress intensity factors have good accuracy for small cracks. The equation presented in this paper is applicable to the length of the different cracks and calculates the intensity coefficients of mode II for very small cracks with high accuracy. Results show that the shape of the hole is important only for the small cracks.

Appropriate changes to the blade tip pattern can effectively improve fan performance. In this research, the effect of two blade tip patterns and speed variation on aerodynamic performance of a ducted axial-flow fan was numerically investigated. In order to ensure the accuracy of the solving method, numerical results were compared with the experimental data from wind tunnel of the NACA Propeller-Research Center. Numerical results show that both the coefficients of pressure and torque increases with the appropriate groove at the tip of the blade. But due to the higher rate of increase in the coefficient of pressure than that of the torque, aerodynamic efficiency has also increased significantly. This increase has been observed in both patterns and in all operational speed of the fan. But, the increase in aerodynamic coefficients had rising trend up to 3000 rpm and, then, declined. The results determine the best pattern for the tip of the blade. In fact, the structure of the groove is such that it traps a rotating airflow with high kinetic energy at the tip, and this vortex, like a barrier, prevents air leakage. This causes reduction in losses due to mixing of the leakage flow and passage flow. With increasing fan rpm, the generated vortexes in tip groov are amplified, which, in addition to a further decrease in the leakage flow rate from the tip region, increases the viscosity and turbulence losses in the area.

An accurate estimation of the state of charge is necessary not only for optimal management of the energy in the electric vehicles (EV) and smart grids, but also to protect the battery from going to the deep discharge or overcharge conditions that degrades battery life and may create potentially dangerous situations like explosion. Despite the importance of this parameter, the state of charge cannot be measured directly from the battery terminals. In this research, an electric equivalent circuit model is simulated in the Simulink environment with two RC networks. This model has the advantage of providing a quick test for the extraction of parameters and dynamic characteristics of the battery model, but is not suitable for on-line applications in an EV. This is why algorithms need to be developed to estimate the SOC of the battery pack and the individual cells based on the measured data of each one. In this paper, for the validation of the neural network, a discharge rate of 0. 6A and in the adaptive neuro fuzzy inference system (ANFIS) network, the discharge rate of 0. 8, 0. 1, and 0. 45 was used. The comparison of ANFIS method with the neural method in this study showed that the ANFIS method is more accurate in estimating the state of charge and correlates the experimental points and the output of the network, so that ANFIS error in some states of charge is less than 2%.

Today, increasing the efficiency and optimization of energy systems in terms of economic and environmental conditions is of particular importance. So far, several methods have been proposed to increase the heat transfer in thermal systems, including the use of nanofluids and types of fluid flow turbulators. In this research, the application of both nanofluid and twisted tape to improve the heat transfer coefficient were numerically investigated. Different turbulence models were used to simulate fluid turbulence. The results showed that increasing the nanoparticle volume fraction, reducing the twisting ratio, and increasing the Reynolds number resulted in an increase in heat transfer. By reducing the twisting ratio from 15 to 5, the heat transfer rate increases from 8-16%. With rising Reynolds number from 10, 000 to 20, 000, maximum temperature differences decreases by 4. 5%. Moving downstream of the flow, the difference between the maximum temperature of the sections decreases. Increasing the heat transfer and intensifying the effects of the twisted tape to downward are the reasons for this decline.

Regarding the growing development of traffic perception systems, advanced driver assistance systems play a significant role in improving automotive safety. They should be able to guide intelligent vehicles through complicated driving scenarios. The complex nature of the driving process results in complicated control engineering methods. Modeling driver behavior based on psychological concepts would simplify the driving logic and human-machine interaction. In this research, psychological concepts and tire force limitations are formulated based on vehicle kinematics and kinetics as a function of speed and curvature. A multi-objective cost function is defined based on psychological concepts and tire force limits. The speed and the curvature, at which the cost function is minimal, are selected as the decided values. Saturated proportional controllers set the vehicle speed and path curvature on the decided values by adjusting the steering angle of the front wheels, accelerator pedal position, and brake force. The model performance is evaluated by a complicated driving scenario, which includes travelling in the same and opposite directions, presence of obstacles with different sizes and speeds, and high curvature paths. The model avoids face-to-face collisions with a time-to-collision close to 0. 72 s. Also, it can avoid obstacles in tight spaces as narrow as 30 cm. Simulation results indicate that the proposed driver model performs safely at the presence of moving obstacles and tight spaces.

By increasing the level of public awareness, more recyclable and natural materials are used. The aim of this research was to fabricate natural fiber reinforced composites and to investigate the effects of fiber length (5mm and 9mm), fiber mass percent (5%, 10%, 12. 5%, and 15%), and fiber surface treatment on tensile, flexural, and water absorption properties of the fabricated composite. The experiments were designed, by the Taguchi method. In this research, epoxy resin and kenaf fiber have been used. Tensile, flexural and water absorption tests were performed on the samples. The highest values were 37. 67 MPa for tensile strength, 4. 94 GPa for tensile modulus, 31. 78 MPa for flexural strength, and 6. 05 GPa for flexural modulus. The lowest percentage of water absorption was 0. 3%. Alkali treatment improved tensile, flexural, and water absorption properties. The optimum of fiber mass percent was 12. 5% to maximize tensile strength, tensile modulus, and flexural strength, 10%to maximize flexural modulus, and 5% to minimize water absorption. Except for the tensile modulus, the effect of fiber length on the mechanical properties of the composite is observed to be less pronounced than the other two factors. To maximize the tensile modulus, the fiber length is better to be 9 mm. In this study, the values obtained for the tensile strength and tensile modulus of the fabricated composite are more than the ones in the previous works. Finally, the strength and tensile modulus obtained experimentally were compared with the ones obtained via two micro-mechanical models, modified rule of mixture, and modified Halpin-Tsia model.

Determining yield and tensile strengths is of utmost importance for engineers in identifying and examining the mechanical properties of pipelines. However, performing a tensile test requires sampling and is, therefore, time-consuming. Thus, it is essential to use an accessible and convenient parameter in order to investigate the relationship between yield and tensile strengths. Hardness can prove to be the parameter we are seeking. The present study used 10 gas transmission pipelines (grade X70, straight seam welded, outer diameter: 1422. 2mm, and thickness: 15. 9mm) in order to perform chemical analyses, impact tests (base metal, weld, HAZ), microstructural examinations, using an optical microscope, indentation hardness tests (base metal, weld, HAZ), and tensile tests. The minimum, maximum, mean, probability density function, and standard deviation of hardness, yield strength in base metal, and tensile strength in weld and base metal were obtained and compared with API 5L standard. The data were used to determine the relationship between strength and hardness. The results prove to be a reliable measure in order to estimate the strength of base metal in pipelines, which reduces the costs and the time needed in order to achieve an optimal strength.

The dynamic response of shape memory alloy (SMA) systems and structures often exhibits a complex behavior due to their intrinsic nonlinear characteristics. The key characteristics of SMAs stem from adaptive dissipation associated with the hysteretic loop and huge changes in mechanical properties caused by the martensitic phase transformation. These exceptional properties have attracted attention of many researchers in various engineering fields from biomedicine to aerospace. One of the possible responses that may happen in SMA structures is the chaotic response, which can lead to a massive change in the system behavior. Moreover, such a system is highly sensitive to initial conditions. Therefore, its analysis is essential for a proper design of SMA structures. The present article discusses nonlinear dynamics and chaotic behavior in a one-degree-of-freedom (1DoF) oscillator connected to SMA at constant working temperature and pseudo elastic region. Equation of motion is formulated, using the Brinson constitutive model. Combination of structural equations of SMA and dynamical and kinematic relations, as well as forth-order Runge-Kutta scheme are employed to solve the equation governing the oscillator motion. Free and forced vibrations under the influence of harmonic stimulation force and in a wide range of excitation frequencies are presented in the form of various numerical examples. Different tools for detecting chaos, including, phase plane, time response, frequency response, Lyapunov exponent, and Poincare map are used to determine the type of motion. Numerical simulations demonstrate a wide range of periodic, quasi periodic, and chaotic responses for certain values of excitation frequencies, which is a reason for the proper understanding of the behavior of these systems.

Nowadays, due to mechanical, physical, thermal, electrical, and vibration properties, metallic multilayer rods have specific applications in industry. Bimetallic rods made from layers with two different materials have been considered by manufacturers in recent years for simultaneous use of the properties of several materials in a single work piece, such as high strength, corrosion resistance, wear resistance, and improved stress distribution. In this research, the tensile test was performed on steel wire and stainless steel pipes to obtain the stress-strain curve of each sample. Wire drawing dies have been used to make bimetallic rods. Then, two samples of the bimetallic rod were made by swaging with the reduction ratio of 9. 75% and 21%. Samples were cut by wire cut machine after production. For interlayer strength testing, dies were designed based on the punch method. The test results were used to calibrate the parameters of the adhesive element in the software. The simulation was performed, using Ansys 17. 0 software. Then the results were compared with experimental results. The effects of reduction ratio, internal diameter, sample length, and clad thickness were investigated. The experimental results were in good agreement with the simulation results. By increasing the reduction ratio, the force required for the separation of the two layers has increased, resulting in increased bonding strength between layers.

This article investigated design and construction of a 4-DOF delta parallel robot’ s components and additionally inverse kinematics and kinematics control of the robot. The initial and final version of the robot based on existing needs, the addition of gearboxes due to the low torque of motors, and flange transformations to connect the gearbox to the robot’ s base were also discussed. In the following, by simulating the robot in MATLAB software, the integrity of the inverse kinematic equation of the robot was investigated. In the other part, the design of the kinematic control in the joint space was discussed and the results were plotted in the graphs for a z-direction. By designing a suitable robot controller, tracing the desired path and comparing its results with other controllers become possible. By designing a conveyor for the robot and equipping it with a camera, detecting the objects that the robot moves them become possible with image processing. For the purpose of picking and placing the objects, the robot’ s end effector is equipped with a controlled suction. The results, through which the paths crossed, showed the designed PID controller for the robot was working correctly and the desired path was followed with small error.

Critical force and time are the two important output parameters in nanomanipulation of different particles. Various input parameters affect the critical force and time, among which dimensional parameters and velocity can be considered the most important ones. To accurately calculate the critical forces and time of the manipulation requires careful analysis of the effect of various input parameters. One of the new methods in affecting the sensitivity analysis of input parameters on problems are statistical sensitivity analysis methods, one of the most accurate methods of which is the Sobol method. Previously, research on the influence of various parameters on the 2D manipulation has been done. In this paper, for the first time, using Sobol statistical sensitivity analysis method, effects of various dimensional parameters, including length of cantilever, width of cantilever, thickness of cantilever, height of tip, the speed in direction of the x and y-axes, radius of the particle, radius of the tip needle, and length of particle have been studied on 8 output parameters, including critical force of sliding along the x-axis, rolling around the x-axis, sliding along the y-axis, rolling around the y-axis, and critical time of sliding along the x-axis, rolling around the x-axis, sliding along the y-axis, and rolling around the y-axis in 3D manipulation. The final obtained results demonstrate that “ cantilever thickness” and “ cantilever length” are the most influential parameters on critical forces, and “ tip height” and “ cantilever thickness” are the most influential ones on critical times.

Considering the hazards of noise pollutions and their increasing trend, nowadays, sound insulations are of the utmost importance. Some available insulating blankets in the market are made of foam and absorb moisture, while the other types of common insulations are fragile and vulnerable. Most of the insulations cannot be used in available construction materials and decrease the beauty of atmosphere. The insulations, which do not have the mentioned problems, are expensive. The current study aims at introducing an insulation, which does not have these problems and resists moisture at a reasonable price. This insulation is made of natural rubber and polyester fibers. It has a considerable flexibility and can be combined with other construction materials. In this experimental study, different samples of one-layer and two-layer natural rubbers with 2. 2 mm thickness for each layer were produced with and without fibers in compression molding method. They were tested in various frequencies and compared with the results of common XPS sound insulation. Each of the samples had a good performance in a specific frequency. All samples exhibited an acceptable behavior compared with their peers in the market. Each of the samples performed better at a certain frequency. In conclusion, the best performance is related to the two-layer rubber sample with fibers and the present insulation in the market is in the second rank.

Pulsed eddy current (PEC) technique is commonly used for the detection of sub-surface defects in electrically conductive metals. However, due to the limited penetration depth of eddy currents, the detection of sub-surface defects in ferromagnetic metals is limited while using PEC technique. In order to extend the application of PEC technique for the detection of subsurface defects in ferromagnetic metals, the penetration depth of eddy currents needs to be increased. For deeper penetration of eddy currents in the material, magnetic saturation of the tested specimen is a useful solution. In magnetic saturation state, the magnetic permeability of the ferromagnetic metal is decreased and stabilized and, as a result, the penetration depth of eddy currents is increased. In this paper, the performance of the PECT for detection of sub-surface pitting defects in the magnetized ferromagnetic specimen has been investigated through finite element modeling (FEM) and experimental studies. The tested specimen is a 10mm-thick steel plate, in which sub-surface pitting defects with various depths have been modeled. A probe consisting of a driver coil, a pickup coil, and a ferrite core is used to measure the time-varying PEC signals. Then, the time domain features of the differential PEC signals are extracted and used to detect the sub-surface pittings. The results indicate that PEC technique together with magnetization can effectively detect sub-surface pitting defects.

In recent years, due to the increase in the speed of rotary machineries, demands for enhanced lubrication and bearing design to overcome this challenge has increased. To satisfy these need, researchers have proposed additive contained lubricants such as Nano-lubricants and bearings with different designs such as noncircular lobed bearings. In this article, effects of preload and aspect ratio on static performance of noncircular lobed journal bearings of finite length lubricated with lubricant containing TiO2 Nano-particles for particle volume fraction of 0. 01 are studied. Using finite element method, the steady-state film pressure is obtained by solving the modified Reynolds equation based on the Nano-lubricants and Couple Stress model theories. With the help of film pressure, attitude angle, friction coefficient, friction force, and side leakage of noncircular lobed journal bearings are obtained. The results show that using lubricants containing TiO2 Nano-particles can enhance the performance of static characteristics of two, three, and four lobed journal bearings. According to results, increase in preload and bearing length will increase load carrying capacity noncircular lobed bearings. Based on results, choosing proper design parameters can have great impact on static performance of noncircular lobed journal bearings.

In this investigation, finite element method was used to model single discharge of ultrasonic vibrations and magnetic field assisted electrical discharge machining (MUEDM) process. Regarding good correlation between theoretical recast layer thickness obtained by process modeling and experimental recast layer thickness obtained by experiments with maximum error of 8. 6%, the developed numerical model was used to find the temperature distribution at workpiece surface and predict the created craters dimensions on workpiece surface. The influences of applying ultrasonic vibrations to tool electrode simultaneous with applying external magnetic field around gap distance of electrical discharge machining (EDM) process, on plasma flushing efficiency, recast layer thickness and created craters dimensions were found by numerical and experimental analysis. The experimental and numerical results showed that applying magnetic field around gap distance and ultrasonic vibrations to tool electrode, simultaneously, at EDM process increases plasma flushing efficiency and decreases recast layer thickness. Also, applying magnetic field around gap distance and ultrasonic vibrations to tool electrode, simultaneously, at EDM process, leads to higher depth and volume of created craters on machined surface and lower craters radius.

Shan-Chen model is the most common model for simulation of multiphase flows using lattice Boltzmann method. The entire multiphase Lattice Boltzman models are limited to regimes, where the temperature dynamics are either negligible or their effects on the flow are unimportant. The entire multiphase LBE models are limited to regimes where the temperature dynamics are either negligible or their effects on the flow are unimportant. The multiphase isothermal lattice Boltzmann equation (LBE) model and single phase thermal LBE (TLBE) model were described. In this research, by combining these two models, the thermal two-phase LBE model was proposed. The coupling of the two models is through a suitably defined body force term. Due to the external nature of this coupling, the new model will have the same stability as the isothermal two-phase model. For this purpose, the scalar thermal model was initially neutral and, then, the Shan-Chen model was expressed in homogeneous state. Also, droplet falling on a heated solid surface and positioning droplet on heated solid surface in different Rayleigh and Reynolds number and different diameter size of droplet were considered. Results show that the temperature in the multiphase flow, as a barrier, delays achieving a stable state, and the fake speed created at the interface area in the temperature field also affects.

Nanotechnology deals with objects and materials in nanometer scale and it is being expanded in the field of materials tools and systems. Nowadays, human knowledge in nanotechnology is going through a commercializing path in order to provide more services. Living creatures are built of cells with 10 μ m size. Some nanoparticles application in biology and medicine include drug and gene delivery, tissue engineering, and tumor destruction with heat. These procedures, which are done with nanoparticles manipulation, have two specific phase in general; in phase one, the amount of critical force and time are calculated based on dimensional and peripheral parameters. Now, it is tried to calculate nanoparticles displacement and velocity during the process in the phase two of nanoparticles manipulation. Also, in this paper, nanoparticles displacement and velocity were investigated in two dimensional space, using three main friction model namely coulomb, Hk, and lugre in phase two of nanoparticles manipulation. According to the results of this project, maximum speed and displacement was obtained, using lugre friction model and the minimum amounts in coulomb model. Also, with particles radius increase, displacement and velocity were reduced; this effect is engendered even without considering friction factor. Correspondingly, considering accuracy and validity, the coulomb model was the least accurate model and lugre was the most accurate one and the HK model was placed between these two models.

In this paper, the effect of the angle of injection on the film cooling effectiveness with sinusoidal wave pulsation is investigated at various frequencies. Four angles of injection are selected at 20, 25, 30, and 35 degrees. The pulsed flow is investigated at 3 frequencies of 2, 50, and 500 Hz. Geometry was simulated in Gambit and numerical analysis was done by Fluent software. The SST k-ω model was used for modeling turbulence. The results showed that the injection angle between 20 and 25 degrees in the frequencies studied had the most film cooling effectiveness of the central and lateral line, especially in the areas far from the edge of the hole. Higher frequencies (500 Hz) increase the effectiveness of the film cooling at the lower initial distances of the hole. At far distances, the lower frequency (2 Hz) is the most effectiveness. As the frequency increases, the difference in the cooling efficiency of the central and lateral lines decreases at different angles. As the frequency increases, the interruptions of the flow-off and the flow-on are reduced, and as a result, the instantaneous effectiveness also has a slower variation than the lower frequencies. The blowing ratio of 0. 5 had the most value in comparison with the blowing ratio of 0. 75 and 1 in all angles and frequencies.

Anthropomorphic robotic hand has always been one of the interesting topics for researchers in recent decades due to its application range, including space exploration, medicine, military, etc. In this paper, a new plan is designed to drive exoskeleton fingers and by means of which the fingers can not only mimic human-like movements, but also be lightweight and portable. In this way, before implementation of the new plan, the anatomy of index finger and related kinematic were studied to give a hand to the extraction of angle relationships among distal, middle, and proximal phalanges. In upcoming step, theories, and mathematical relations about replacing sheaths and its influence on bending joints, based on the coupling mechanisms, were explained and applied clearly. Additionally, considering extracted relationships and equations in prior section, a new model of robotic finger with mentioned properties was simulated in MSC ADAMS software. In following step, after linking the software with Matlab, the results of the simulation and comparing them with human finger in the configuration and generation of humanoid movements were discussed. In the last step, according to simulation results, an example was constructed and presented, using a 3D printer in accordance with the proposed mechanism.

Nowadays, polymeric foams have attracted special attention in scientific and industrial societies due to their unique properties such as high strength to weight ratio, excellent thermalinsulation, sound-insulation, and good mechanical properties. One of the main goals of the studies of polymeric foams is to increase the cell density and aligning with it, is to reduce the cell size of these materials. Researchers have shown that the extraordinary properties of polymeric foams such as superior thermal-insulation can be achieved by increasing the cell density/ decreasing the cell size. In this regard, firstly the most important processes for the production of polymeric foams (batch, extrusion, and injection molding processes) were studied in the present research. Then, cell nucleation stage as the most important process for achieving high cell density/ low cell size is studied in details. In the following, the most important researches in the field of polymeric foams were introduced in which, the highest cell densities/ lowest cell sizes were achieved. The investigations show that the most significant results (highest cell densities/ lowest cell sizes) are belonging to the batch process. Also, the use of nucleating agents, increasing the solubility of blowing agent into the polymer, and the use of nanoparticles are the most efficient solutions in order to achieve microcellular and nanocellular structures.

The weld residual stresses decrease the design stress in gas transportation pipelines. In this paper, two X70 steel pipes of 56 inch outside diameter were firstly girth welded. Experimental hole drilling test was conducted to evaluate the residual stress distribution in this joint. Then, the finite element simulation of the welding process was performed to evaluate the residual stress distribution precisely. The numerical results were verified by comparison with the obtained experimental measurements. The qualitative results achieved match properly with the experimental results. Simulation results (with a difference about 15% compared to experimental results) evaluated the maximum residual stress in hoop direction of pipe’ s external weld metal. The experimental data showed that the maximum tensile residual stress was located on the center line of the weld gap on the pipe outer surface alongside with the pipe hoop direction. Moreover, the maximum compressive (hoop and axial) residual stresses occurred on the pipe inner surface in heat affected zone. The variations of the hoop residual stresses on the inner and outer surfaces of the pipe had similar trend with tensile distribution at the center line of the weld gap. However, these stresses showed different trends (tensile stress on the outer surface, and compressive stress on the inner surface) with distancing from the weld center line.

In this research, the analysis of the effects of circular hole and thermal cycle fatigue on the mechanical properties in multi-layer polymer composite reinforced with nanoparticles are investigated. First, multi-walled carbon nanotubes with 0. 1% weight fraction of nanoparticles are added to the epoxy resin ML506. The. In order to homogenize particle in the resin, it is mixed with a magnetic stirrer for 30 minutes. The material is placed in an ultrasonic device for 40 minutes to homogenize the resin and nanoparticle completely. The resin reinforced with glass fibers constitute symmetric cross ply laminates stacking sequence [02/902]s, and nanocomposite samples are made with hand layup method. In this study, open-hole specimens with diameter of 2 and 4mm are investigated. To study the thermal cycles, nanocomposite samples of 3 levels of thermal cycles including 0, 180, and 360 cycles were investigated. The samples are exposed to a temperature range of 0 to 100oC. After that, the specimens undergo tensile testing. Using the tensile test, the modulus of elasticity and tensile strength are compared for the different thermal cycles and the diameter of the holes. By increasing the number of thermal cycles, the tensile strengths of nanocomposite samples are not significantly changed. Also, with increasing the diameter of the hole, the tensile strength is decreased. The elasticity modulus with increasing thermal cycles for all specimens have been minimal changes. Also, a linear regression model was developed, using MINITAB software for strength and elastic modulus in terms of number of thermal cycles and diameter to width ratio.

In this paper, extended complex variables method (ECVM) is presented in fluid flow problems for the first and second-order sensitivity analysis. The finite element method is used to solve the Navier-Stokes equations, and the complex variables method is implemented to it. In the complex variables method, a complex step that only includes the imaginary part is used, but in its development, it uses a complex step that includes both the imaginary part and the real part to achieve higher performance. In the first-order sensitivity calculation, the results are not dependent on the step size, but in the second-order sensitivity, the results of the sensitivity depending on the step size and inevitably the developed formulas should be used to obtain higher accuracy. The proposed method is first validated for a problem with a closed-form solution, and the convergence rate is investigated and, then, applied to a uniform flow past a cylindrical cylinder and, finally, the results are compared by finite difference method. The results show that the range of accuracy for second-order sensitivity in the extended complex variable method is doubled compared to the complex variable method and it can be reduced to 10-12. It means that the effectiveness of the proposed method has increased. The introduced method is applicable to a wide range of problems with simple and complex parameters.