Modares Mechanical Engineering
Year:2018 | Volume:18 | Issue:8 |Papers Count:29

The aim of this paper is simulation of shaped charge process using Eulerian analysis. To this end, the finite element analysis was used to simulate the process of shaped charge. In this simulation, whole of the model has been considered from Eulerian elements. Verification of finite element method has been confirmed by comparing simulation with experimental tests and Birkhoff model. Comparison of penetration depth in finite element analysis with experimental samples has shown that the results are in good agreement with each other. Also comparing parameters such as liner collapse velocity, velocity distribution in jet length and jets profile has indicated that the simulation results are close to Birkhoff model. It should be noted that ABAQUS finite element software is used in this simulation to analyze the process of shaped charge.

In this contribution, behavior of gas phase distribution in a two phase gas-liquid stirred vessel with Rushton turbine was studied by computational fluid dynamic (CFD) technique at different operational conditions. Multiphase flow regime in the in the two phase gas-liquid vessel was modeled by Eulerian-Eulerian multiphase flow approach. Due to complex hydrodynamics and turbulent flow in the agitated vessel, RNG k-ε was used to simulate turbulence flow behavior. With study of operational conditions by means of Aeration and impeller Reynolds dimensionless numbers, distribution of gas phase volume fraction was studied in the vessel. The results showed minimum hold up of the gas phase exists between vessel bottom up to impeller and maximum gas phase hold up is formed in the impeller zone. Also, it was observed due to the formation of larger vortex areas with increase in impeller Reynolds number the mixing quality in the vessel improves. Furthermore, it was shown that increase in Aeration and impeller Reynolds numbers enhances gas phase holdup in the vessel. Study of impeller Power number showed that with increase in Aeration number the amount of mixing power is reduced at constant Reynolds number. Also, it was observed that increase in Reynolds number enhances power consumption at constant Aeration number.

In this research work, using the recently introduced entropic constant speed kinetic model and employing the Pseudo-Potential model of Shan and Chen (SC), two phase flow of incompressible and immiscible fluids through porous media is studied. Applications of the entropic kinetic models in simulating multi-phase and multi-component flows have been thoroughly investigated, during the past decade. Lack of an entropy function, in a kinetics based model, implies that the existence of a unique equilibrium state, under all flow conditions and for all positions and times, cannot be guaranteed by the model. Hence, simulation of two multi-phase flows with high density ratios, using the conventional kinetic models (which do not satisfy the second law of thermodynamics) may not yield proper results, due to numerical instabilities. In this research, performing numerical simulations, the accuracy and stability of the recently introduced constant speed kinetic model and the conventional lattice Boltzmann models have been compared with each other. The present simulations include the verification of the Laplace Law and the contact angles and two phase flow through simple channels. In addition to the above, two phase flow in porous media has been simulated and the relative permeability vs wettability has been reported. The obtained results are in excellent agreement with previous results reported by others researchers.

The main purpose of this paper is to the distributed formation tracking for fractional order multi agent systems with the leader-follower approach. First, it discusses the Lyapunov candidate function used to check the stability of the controlled system. The introduced candidate function is based on the properties of the matrix representing the desired system graph of the system. In this phase, the Lyapunov direct method is used to determine the stability of fractional order systems. Then, using sliding mode control, a decentralized controller design for tracking in fractional multi agent systems is presented in which it introduces and verifies the introduced control inputs. In the model, the input system is also considered as a disturbance type, and the control efficiency designed in turbulence mode is shown. In this section, it is shown that the controller introduced in the previous section has a desirable efficiency due to the sliding mode control. In the second section, the stability of the system, such as the first section, is investigated. at the end of this paper, several simulation examples are developed for controlling the performance of the controller.

In this paper, an adaptive wavelet neural network tracking controller is studied for solving control and stability problem of a class of uncertain nonlinear systems. The considered systems in this paper are of the discrete-time form in pure-feedback structure and include the backlash and external disturbance. The backlash nonlinearity input appears non-symmetric in the systems. These systems are more general than those in the previous work. There are major difficulties for stabilizing such systems and in order to overcome the difficulties, by using prediction function of future states, the systems are transformed into an n-step-ahead predictor. The wavelet neural networks are used to approximate the unknown functions and unknown backlash in the transformed systems and the adaption laws are to update neural weights and to compensate for the unknown parameter of backlash. Based on the Lyapunov theory, it is shown that the proposed controller guarantees that all the signals in the closed-loop system are bounded and the tracking error converges to a small neighborhood of zero. The simulation of a Single-link robot arm system is provided to verify the effectiveness of the control approach in the paper. Finally, in order to validate, the results of the proposed method are compared with the results of PID and sliding mode controller.

Quadrotor is one the most popular models of unmanned aerial vehicles with four actuated propellers which has a simple, light weight, small mechanical structure and high maneuverability. However, its nonlinear under-actuated dynamics needs more advanced controllers for rejection of external disturbances, balancing and precise trajectory tracking. In particular, the under-actuated subsystem of the quadrotor's dynamics needs a fast response without overshoot and steady state error. In this paper, fuzzy fractional-order proportional-integral derivative (FOFPID) controller is designed for quadrotor control system using fuzzy and fractional order systems to improve response speed, tracking accuracy and system robustness respect to the conventional PID controller. Controller architecture of the under-actuated subsystem of the quadrotor's dynamics is designed based on the inner-outer loop control theory which is employed explicit and analytical inverse kinematic of system to connect the inner and outer loops. Also, dynamics of the motors and actuators saturation are considered in the quadrotor’ s dynamics model and their effects are studied on the controllers' performance. In order to evaluate tracking performance of controllers, trajectory of an eight aerial maneuver is designed and controllers’ performance is assessed in the absence and presence of wind disturbance. Trajectory tracking accuracy of the controllers is studied according to the maximum absolute error and integral of absolute error criterions and is compared that shows the proposed FOFPID controller has successfully improved performance of the quadrotor system.

The tube spinning process is one of the forming processes to fabricate conical seamless tubes. This process is done warm or cold, with or without mandrel. In this article, the possibility of forming of an Al-6061 conical tube by hot die-less spinning process has been investigated. An estimation of tangential force and required power can be obtained by analytical methods. So, the ideal work and upper bound methods have been utilized to derive equations for calculation of tangential force and required power of forming. An identical result was acquired for the two methods. The proposed equations can be used in design stage of the process. Furthermore, final thickness and initial length of the tube have been calculated by using of geometrical relations and constant volume law. The proposed formulation has been compared by experimental results. The final thickness and initial length of the tube are in good agreement with experimental results. An error of 0. 5% and 5. 5% were observed for final thickness and initial length, respectively. The obtained equation for the final thickness is a cosine function of the conical angle. Hence, it predicts higher final thickness in comparison with the sheet spinning process.

In this paper, the separation black powder from air flow experimentally have been studied by spiral-channels dust separator and the efficiency and pressure drop of spiral-channels dust separator has been investigated by CFD simulations in different operating conditions. Powder particles have been tested from a sample of powders of Saveh Strengthening Station, whose average particle size has been determined by DLS and SEM images processing, 0. 327 micrometers. CFD simulation of spiral-channels dust separator has been done with FLUENT software. The RNG k-ε turbulent model as an optimal turbulence model has been used. The difference between the experimental and the simulation results was revealed around 16% and 7. 15% for efficiency and pressure drop parameters respectively. To illustrating the effect of operating condition, the various flow rate and solids mass fraction were investigated and results showed that maximum efficiency is the highest input volumetric flow rate. Also, the results showed that this system has the efficiency of more than 80% for separating Black Powder particles and with increasing 40% of the volumetric flow rate, the separation efficiency increased up to 10%. If, by increasing the mass fraction of solids by 5 times, the efficiency increased only by 3%. The pressure drop of the separator increased up to about 50% with increasing the volumetric flow rate from 80 to 140 m3/hr.

One of the most important constraints on manufacturing productivity is the machining vibrations. This vibrations may cause increase in machining costs, lower accuracy of products and decrease tool life. The effective solution for increasing cutting process stability and vibration suppression is to improve structural dynamic stiffness. There has been presented different techniques for enhancing dynamic stiffness of structures using passive and active vibration control methods. Although passive vibration control methods are always stable, they exhibit limited performance. In active control methods, vibrations can be effectively damped over a various conditions. The aim of this research is to enhance the dynamic stiffness of an industrial boring bar by using active damping. Cutting process mainly exposed to parameter perturbations and unknown external disturbances, therefore, designing an active vibration control system for cutting process is a challenging problem. In this research an extended state observer based control strategy was proposed that can overcome these uncertainties. The proposed strategy was implemented into an active vibration control system for a boring bar. Moreover, the direct velocity feedback is successfully implemented in the vibration control loop. The results of impact tests indicate that the control algorithms have a great performance in suppressing vibrations and increasing the structural dynamic stiffness. Voltage impact results show that ADRC controller spends less control effort than direct velocity feedback controller.

Impact damage is one of the most important failure types for aircraft structures, which can come from variety of reasons. Such impacts can realistically be predictable for the duration of the life of the aerospace structure and can cause internal damage that is often challenging to identify and can produce rigorous drops in the strength and stability of the structure. By combination of monolithic Aluminum alloys with composites, structures will be achieved that has weight lighter than monolithic aluminum alloys and better fire and fatigue resistance. These structures, that called fiber metal laminates, are developed as a suitable alternative to monolithic aluminum in aerospace structures. In this research, impact resistance of multi-walled carbon nanotubes (MWNTs) /glass aluminum reinforced laminates (GLAREs) is investigated at variety concentrations of 0. 1, 0. 2, 0. 3 and 0. 5 wt% of MWNTs. Here, anodizing method is used for preparation of aluminum surface. The results showed that by adding MWNTs to GLAREs, energy dissipation is increased in charpy impact test. Investigation showed maximum energy dissipation at 14. 36% in 0. 3 wt% of CNTs. Also different fracture modes observed for different concentration of carbon nanotubes.

Aluminum alloys have become widespread in the various industries due to the characteristic of high strength-to-density ratio. These alloys do not have a suitable formability at ambient temperature so they formed at high temperatures. The main hot forming methods used for aluminum alloys include deep drawing and gas forming. Both of these methods have their own advantages and disadvantages. In this study, a combined process involving deep drawing and gas forming has been used. In this process, the first step is to create a pre-formed deep drawing and in the second stage, the final piece is produced by gas forming process. The purpose of this study is to optimize the levels of the main process parameters for the shaping of cubic parts of aluminum sheet 5083 sheet. These parameters include the temperature and blank-holder force of deep drawing stage and the temperature and gas pressure at the gas forming stage. The best levels of process parameters were selected using the Taguchi experimental design method. The results show that the temperature at 350 ° C and the blank-holder force of 1000 N for deep drawing, as well as the temperature of 485 ° C and the gas pressure of 0. 6 MPa for the gas forming stage, can be achieved with the least degree of thinning in the specimen. The maximum thinning achieved is 22%.

Rotating machinery is a type of mechanical systems that is widely used in industry. The shafts connection method, vibration control and stabilizing in these systems, have consistently been important. In this research, the robust control of a shaft system with torsional vibration has been considered. The system includes three elastic shafts, which are misaligned with each other. The misaligned shafts are connected through Cardan joints. Herein, the governing equations of torsional vibration for three-axis Cardan systems with nonlinear behavior have been derived. Then, according to the system uncertainties, robust control was used and three controllers with H∞ optimum method, H2/H∞ consolidated method and  – synthesis robust stability method have been designed. The design was done after identifying the system parameters that are sensitive to uncertainty. The implementation results of designed controllers have been presented in the form of frequency response curves. Comparison and analysis of the results of three controllers show that H∞ and   synthesis have both are performance and robust stability criteria, while H∞ method, which is needed to determine the weighting functions, is harder. In addition, the reduced order   synthesis controller can guarantee the robust performance.

Fluid flow over a cylinder is appeared in differenet engineering fields. In this article, laminar, two-dimensional, incompressible and viscous CuO-water nanofluid flow around a circular cylinder with angular oscillation in unsteady regime at Reynolds numbers of 100, 150 and 200 in amplitudes of θ _A=π ⁄ 4, π ⁄ 2 and different oscillation frequency ratios of F=0. 5, 1, 2 and volume fractions of nanoparticles in the range of 0≤ φ ≤ 0. 03 is simulated numerically. Governing equations include continuity, momentum and energy equations have been solved numerically for a combined grid via finite volume method. Effective thermal conductivity and dynamic viscosity of nanofluid were estimated by Corcione empirical model. The effects of volume fraction of nanoparticles and oscillation parameters on the average heat transfer coefficient were investigated and concluded that at vortex Lock-on region, the amount of heat transfer coefficient increased significantly. The main target of this article is to determine the preference of two mechanisms of heat transfer enhancement include adding nanoparticles to the base fluid and applying oscillation to the cylinder surface. Evaluation of this two mechanisms indicates that using nanofluid in compared with applying rotational oscillation to the cylinder, leads to more heat transfer enhancement rate. Results show that heat transfer coefficient enhancement due to rotational oscillation of the cylinder at θ _A=π ⁄ 4 and F=1 compared with the stationary cylinder in water flow is between 4. 25 and 15. 83%. Moreover, the amount of heat transfer enhancement of nanofluid at φ =0. 03 compared with the base fluid in stationary cylinder is between 20. 49 and 31. 26%.

In this study, the fingering instability in displacement of Newtonian fluid by viscoelastic fluid through heterogeneous media is investigated using spectral method and Hartley transforms. The White-Metzner model has been used as the constitutive equation. This model can be presented the shear-thinning and elastic behaviors of viscoelastic fluid very well. The heterogeneity of the media is considered in two different types. In the first case, the permeability of medium exponentially decreases in the transversely section. This case is named decreasing heterogeneity. In the second case, the permeability of the medium will initially be increasing and it reaches to its maximum at the middle of the cross-section and then decreases. This type of heterogeneity is called parabolic heterogeneity. The results are included concentration contours, mixing length and sweep efficiency. It can be seen that in the first case, the degree of heterogeneity has little effect on the structure of fingers. However, increasing in this parameter leads to decrease in mixing length and increase in sweep efficiency. But, in the latter case, with the change in the degree of heterogeneity, the finger structure will be strongly affected. In addition, in this case, increasing the degree of heterogeneity will increase the mixing length and reduce the sweep efficiency. Also, in both cases, the flow becomes more unstable by the shear thinning property of viscoelastic fluid. Although it seems this effect is less in medium with parabolic heterogeneity.

Considering broad applications of sheets, specially circular sheets in the industry and the widespread use of nanotechnology to pass from limitations of each branches of science, particularly mechanics of materials and also importance of vibration (or buckling) due to temperature changes or thermal loads, in this thesis, development of relative relations of circular single layer nanographene sheets’ vibrations due to temperature changes, were studied. Nonlocal thin plate theory of Eringen is employed to investigate effects of thermal environment on the behavior of circular single-layer graphene sheet freely vibration containing a circular perforation of arbitrary size and location. In order to analytically solve the equation of motion, the separation of variables method in conjunction with the translational addition theorem for Bessel functions is used. The results of changing various geometric and physical parameters and different kinds of restrains and boundary conditions on the natural frequency of a single layer circular graphene sheet were examined and discussed. In some cases, thermal buckling phenomenon was observed.

Experimental studies indicates that the mechanical behavior of materials at micro and nano scales are size-dependent. Since the classical continuum mechanics theories cannot capture the size effect, employment of different non-classical theories has received a considerable attention among researchers. In this study, the finite element formulation is presented to investigate the bending of square microplates with circular hole subjected to uniform pressure based on the three-dimensional strain gradient elasticity theory. For this account, the 8-node C^1 continuous hexahedral element is introduced in which, in addition to the values of displacement components, some related higher-order mix derivatives are further considered as nodal values. The governing equations are derived based on the strain gradient theory and three-dimensional elasticity model and the finite element formulation is presented using the introduced element. Note that by considering some specified values for coefficients of strain gradient theory, the numerical results can be obtained for modified strain gradient theory and modified couple stress theory. To demonstrate the efficiency of the proposed finite element, the convergence and accuracy of the results are firstly checked and then the impacts of geometrical parameters on the bending of microplates with circular hole are studied.

In this paper, a constrained predictive controller is designed using Laguerre functions to control the depth and steering of an autonomous underwater vehicle considering underwater disturbances. Due to under-actuated nonlinear coupled dynamics, parameters uncertainty, external underwater disturbances autonomous underwater vehicles are complicated. Moreover, the underwater autonomous vehicle investigated in this study includes constraints on actuators leading a more complex problem. In this study, first, the nonlinear dynamics of the autonomous underwater vehicle utilized for the controller design has been modeled. Then, Laguerre orthogonal functions were used in the constrained predictive controller design for reducing computational time and accelerating optimization process. Optimized, online, high precision, implementation capability, consider constraints purposefully and robust properties against disturbances can be mentioned as the most important advantages of designed controller. In addition, predictive control method is robust against disturbances. To monitor the methods’ performance, the autonomous underwater vehicle was modeled and then a comparison between the controller's calculation time with and without the Laguerre functions was also represented. At the end, the simulation results obtained from this controller, using Laguerre functions, showed the efficiency and effectiveness of the proposed solution.

Coatings are used in various industries in order to improve the surface properties of materials. Delamination of coatings from their substrate, at the root of channel cracks, is one of the common failure modes in these structures. In this paper, discrete element method is used in order to simulate the initiation and propagation of damages, caused by the mismatch between the thermal expansion coefficients of coating and substrate. Coating and substrate are considered to be brittle elastic in which, substrate is stiffer than the coating, but the thermal expansion coefficient of coating is considered to be much greater than substrate. The interface properties are also considered to be the geometric average between the coating and substrate. Temperature reduction is applied to the whole structure as loading. The effect of elastic mismatch and coating thickness was investigated. The results showed that, by increasing the elastic mismatch and decreasing the coating thickness, the temperature reduction, need to delamination initiation at the interface, increased. Also, changing in the damage propagation pattern was happened by changing in the elastic mismatch. In coatings with high elastic mismatch, damage propagation was happened inside them but by increasing the stiffness, damage propagation happened at the interface.

The investigations of changes in bed surface of sediment due to the fluid flow and tracing sediment motion are complex and attractive for the researchers. In the recent decade, modeling of fluid flow using the Lagrangian methods, e. g. Smoothed Particle Hydrodynamics (SPH), is of interest. In this study, the open-source two dimensional SPHyiscs code is used to model the two phase Newtonian and non-Newtonian flows using the μ (I) visco-plastic model, which is obtained according to particle properties including inertia and friction coefficient. First, and in order to study the visco-plastic model, the one phase code is extended to non-Newtonian and the SPH results are compared with the experimental model of the collapsing granular column, where a harmonic interpolation is used for the viscosity of particles. In this stage, the comparison of the SPH model with the experimental data shows a good agreement. Then, the numerical method is utilized for the simulation of Newtonian dam-break fluid flow over a movable bed. The proposed model treat sediments as a non-Newtonian fluid using μ (I) model, by implementing the harmonic interpolation for the viscosity coupled with the Owen’ s relation at the interface. Results show that the proposed model has a capability for simulating two-phase water sediment systems.

Dynamic motion of a 2D SD7037 airfoil is investigated numerically in presence of a slip boundary condition. The dynamic motion of the airfoil is a harmonic oscillation, where the frequency and the amplitude of oscillations were adequate to airfoil to undergoing dynamic stall phenomenon. Dynamic stall occurred when the dynamic motion of the airfoil causes dynamic stall vortices, resulting in leading edge and trailing edge vortices which lead to rising the aerodynamic loads significantly. Analyzing the phenomena is challenging especially when a slip boundary condition exists near the airfoil wall. This particular condition is the general property of super-hydrophobic surfaces. These surfaces could potentially prevent the blade from icing. The main characteristic of these coatings is the appearance of a slip velocity on the wall. The slip velocity can affect the airfoil aerodynamics which is the main purpose of this paper. In this regard, a 2D airfoil with the Reynolds number of Re≈ 4×〖 10〗 ^4 is analyzed using computational fluids dynamics (CFD). The Transition-SST model is applied. The results showed that not only the slip condition affects the aerodynamic loadings, but also the dynamic stall regimes changed considerably. So that for slip lengths higher than 100 micrometers, the maximum magnitude of the lift coefficient damped by 16%.

The waste heat management in heavy industry significantly increase productivity in this sector. Organic Rankine cycles (ORCs) are appropriate technology for the conversion of low quality thermal energy to electrical power. The Organic Rankine Cycle(ORC) applies the principle of the steam Rankine cycle, but uses organic working fluids with low boiling points can be used to recover heat from lower temperature heat sources. In this study the performances of three different organic Rankine cycles (ORCs) systems including the basic ORC (BORC) system, the single-stage regenerative ORC (SRORC) system and the double-stage regenerative ORC (DRORC) system using five different working fluids under the same waste heat condition are optimized by thermo-economic method using genetic algorithm. The results indicate that the R113 has the best performance between fluids. The optimized turbine inlet temperature and pressure in comparison with when exergy efficiency uses only, decreases. By changing basic Rankine cycle to the single-stage regenerative and the double-stage regenerative cycles, 12. 5% and 18. 75% change in specific power cost occurs respectively. Also results indicate that, as superheat degree in turbine inlet increases, the specific power cost increase and the exergy efficiency of system decreases.

The precise finite element model is an efficient tool for vibrational analysis. It should be mentioned that, in structural dynamic analysis finite element models of system should be able to accurately predict system characteristics such as natural frequencies. Contrary to static analysis, in structural dynamic analysis, it is not possible to overestimate system characteristics or apply safety factor for predicted characteristics; that means that the exact values of system characteristics such as natural frequencies, should be derived in structural dynamic. According to this, constructing a reliable model in the structure dynamic always has great degree of importance in vibrational analysis. In this study, it has been tried to extract a reliable finite element model for a row of a sample turbine of RollsRoyce brand using empirical results. So, the material properties of the disk and the connection between the disk and the blade are corrected and updated using experimental modal analysis results. Also, it has been tried to propose new method to model and update the disk and blade joint. Finally, reliable finite element model could be used for more analysis such as derivation of Campbell diagrams of system.

The issue of fire safety in tunnels is very essential because the closure tunnels increase consequences of accidents significantly. Therefore, it is necessary to control fire development and smoke propagation with appropriate measures when fire occur. The ventilation system is used to control smoke propagation and the suppression system is used to prevent fire spread in tunnel. In the present study, fire in the tunnel with operating ventilation and suppression systems are simulated using an open source fire dynamic simulator (FDS). The results show that increase water flow rate leads to increase cooling effect of suppression system, also, increasing the water flow rate from 320 to 1280 liters per minute lead to increase the reduction of radiation flux at the downstream of fire from 40% to more than 75%. With the activation of suppression system with a median diameter of 100 and 1000 micrometers, the temperature difference with the environment decreases by about 70% and 34%, respectively. In the case of downstream area, with decrease in size of droplet diameter from 1000 to 100 micrometers, the radiation attenuation increases from 58% to 93%. Air flow leads to transport the droplets to downstream and increase the air flow rate leads to decrease radiation attenuation of suppression system for upstream area. The relative position of activated sprinklers affect the cooling and radiation attenuation ability of system. The suppression system by reducing the smoke temperature enables the ventilation system to resist the smoke backlayering with a lower velocity than the critical ventilation velocity.

Due to higher demands for tailor welded blanks (TWBs) applications in transportation industry, it is worthy to understand their forming characteristics in manufacturing processes, especially the deep drawing, in order to produce products with higher qualities. Due to differences between the base materials strength as well as existence of the welding zone, the formability of TWBs is frequently less than the base metals. Comparison of weld line movement and drawing depth in TWBs designed and produced by laser welding and friction stir welding are the aims of this study. Because of creation of limited heat affected zone area and suitable keyhole, laser welding is more appropriate for TWBs production comparing to the other welding processes. The parameters of the friction stir welding process are very important due to having high influence on complicated plastic zone variation, material flow pattern and temperature distribution in TWBs sheets. In this paper, having designed the experiments, the effect of blank holder force and linear welding velocity on drawing depth and weld line displacement of TWBs have been investigated. Moreover, the harnesses of the weld zone in both processes have been examined. Results show that by increasing the linear velocity of laser welding, the amount of weld line displacement and drawing depth will be increased. Furthermore, the higher linear velocity of friction stir welding will result into the higher weld line displacement and drawing depth. Likewise, the harnesses of the laser welding zone are higher than those ones for friction stir welding zone.

At present paper, an equivalent model with different dimensions and also with different dimensions and material in comparison with main body for strain rate sensitive structures subjected to high rate loading is presented by using the novel finite similitude method. The finite similitude method provides performing a test on the model instead of the original sample. This method is used to obtain the properties of model and to reverse the obtained results for model to main body by using the principles of nature (the law of conservation of mass, the law of conservation of momentum, the law of conservation of energy and the law of conservation of entropy) which is always true for any system. The relationships for both pure dimensional and simultaneously dimensional/material scaling of strain rate sensitive structures are presented. To evaluate the efficiency of the proposed relationships, the numerical results are obtained for impacted circular plates. It should be mentioned that the numerical results are obtained by using the finite element software LS-Dyna in which the strain rate effects are considered into account by using the Cowper-Symonds and Johnson-Cook constitutive equations. The results indicate that the scaled plate to one tenth of its original dimensions and also made of different material in comparison with original plate predicts the response characteristics of the original plate with a very good accuracy.

In this study first the meshless local Petrov-Galerkin (MLPG) method by Radial Basis Function (RBF) has been explained entirely. In this way the governing channel flow expression that is based on the Laplace equation is expanded. In MLPG method, the problem domain is represented by a set of arbitrarily distributed nodes and Quadrature radial basis function is used for field function approximation and local integration is used to calculate the integrals. In the following, MLPG method is verified by exact solution in a numerical example. The Results show that MLPG method presented high accuracy and capability for solving the governing equation of the problem. Finally the velocity field is approximated in middle of nodes by RBF (MatLab code was adopted) in the uniform flow in a sloped channel problem. The MLPG results are compared with the isogeometric analysis (IA) method in the tutorial numerical example of Fluid flow modeling in channel, the velocity contours is detected, and their accuracy is demonstrated by means of several examples. The results showed good conformity compared to available analytical solution. The obtain results explain that Application of meshless method in Fluid flow modeling in channel show the applicability and efficiency of the meshless local Petrov-Galerkin method by Radial Basis Function method.