مجله مهندسی مکانیک امیرکبیر
سال چهل و نهم شماره 4 (زمستان 1396)

In this paper, the closed-form stress intensity factors are calculated at the deepest point of a circumferential semi-elliptical crack located at the inner surface of a cylinder. The cylinder is subjected to pressure (internal and external) and the inner surface of the cylinder is subjected to convection cooling. To solve the problem, initially, a weight function is derived for the deepest point of the circumferential semi-elliptical crack using two reference loads. Then, the steady state solution of the thermoelasticity problem is derived and, finally, the stress intensity factors are extracted using the weight function method. For some special cases of loading, the results of the present theory are compared with available solutions in the literature indicating an acceptable agreement. Moreover, the effects of crack relative depth and aspect ratio and heat transfer type on the thermal stress intensity factors are studied. The extracted results demonstrate that for some cases of loading and crack geometry, shallow cracks are more critical than deep ones and the solution of conduction heat transfer is more conservative than the forced convection one.

In this work, stresses, strains, creep damage and remnant life for rotating thick walled hollow cylinder made of alloy steel using the theta projection concept and Larson miller parameter are investigated. Loading is composed of internal and external pressure, a distributed temperature field and a centrifugal body force. Using stress-strain, strain-displacement and equilibrium relations a second-order non-homogenous differential equation containing creep strains for radial displacement is obtained. With ignoring amounts of creep strains, thermo-elastic solution of constitutive equation at zero time is achieved. With considered creep strains in mentioned differential equation and differentiating with respect to a time, a differential equation consist of radial and circumferential creep strain rates for radial displacement rate is obtained. By combining theta projection model and Prandtle-Reuss relations and substituting instead strain rates in last differential equation and then numerically solving that, radial displacement rate and stresses are calculated. Using Larson effective stress at each point and Miller parameter and Rabinson's rule, creep damage and remnant life redistributions along the thickness of cylinder are achieved. It has been found that maximum and minimum creep damage is occurred at inner and outer surfaces of cylinder respectively.Also remaining life at outer surface is more than inner surface.

In this paper, the performance of the Expanded Metal Tube absorbers under axis impact loading was investigated. A cylindrical expanded metal sheets is used as an energy absorber. Thin-walled expanded metal sheets, despite their low weight, have high energy absorption capacity. The cellular direction of expanded metal sheets will have a large impact on the absorber behavior. In this study, a sheet with angle α=0 is used to create a cylindrical Expanded Metal Tube absorber. In this study, to evaluate the performance of energy absorption caused by the collapse and to achieve maximum energy absorption, a numerical study of the effect of the cross-section size and making the absorber a multi-layer one on the energy absorption behavior has been discussed. Numerical studies have been performed by the ABAQUS Finite Element Method software. The output of ABAQUS software is displayed in form of the force-displacement diagram. In this study, numerical investigation of collapse, force-displacement and the effective parameters have been carried out. From the results obtained, it was observed that increasing the size of the cross-section and making the absorber multi-layer , will have a significant effect on the initial maximum crushing force and energy absorption capacity and making the absorber a multi-layer improves the crushing efficiency.

Due to the growing use of oil journal bearings, as an effective support for the rotating parts of industrial machines, analysis of their performance is of importance. The shear stresses and the frictional forces, proportional to the speed of the lubricant layers in different points of the bearing clearance space, causes variation in the temperature of the lubricant, journal and bearing shell. However the bearing design parameters also have effects on the lubricant temperature. So, in the present work, the effects of design parameters such as the journal speed and the preload factor of the noncircular lobe journal bearing on the temperature variations which result in variation of the pressure distribution of the lubricant as well as changes in the load carrying capacity and attitude angle of the noncircular two lobe journal bearings are investigated. Then the bearing performance parameters are calculated using the final thermal pressure distribution of lubricant. Comparing the performance of two lobe bearings, with the thermal effects and without them, shows that the lubricant viscosity and the pressure distribution in the bearings decreases by increasing the rotational velocity of the journal. Also the results indicate that the effects of lubricant temperature changes on the bearing performance decreases by increasing the amount of the bearing preload.

In this article, free vibration analysis of double-bonded Timoshenko micro beams rested in an elastic foundation under various physical fields is investigated based on modified couple stress theory. Properties and distribution of carbon and boron nitride nanotubes are used based on experimental and analytical equations, which They have a lower error and do not use in other studies. The governing equations of motions are derived based on Hamilton’s principle. The effects of various parameters such as electric field, magnetic field, material length scale parameter and elastic foundation modulus on the natural frequency of the micro structures are studied. The results of this work show that different physical fields on the microbeams have more influence on the dimensionless natural frequencies, so the effect of the CNTs on the natural frequencies for micro beams is more than the BNNTs. Moreover, if the double-bonded micro beams are considered simultaneously as CNT and BNNT, the increase of natural frequency is less than when two micro-beams become only as CNT or BNNT. Also, it is shown that the effect of elastic foundation is more important than the electric and magnetic fields as well as material length scale parameter on the natural frequency of microbeams.

In this article, free vibration analysis of functionally graded cylindrical nanoshell on the basis of the modified couple stress theory is investigated. The nanoshell is embedded in an elastic Pasternak medium, which is obtained by adding a shear layer to the Winkler model. In addition, the boundary conditions at two ends of cylindrical nanoshell are simply supported. It is assumed that the functionally graded cylindrical nanoshell, is made of aluminum and ceramic, follows the volume fraction definition and law of mixtures, and its properties change as a power function through its thickness. Governing equations and boundary conditions are obtained by applying the Hamilton’s principle and are based on first-order shear deformation. Navier solution is used for predicting the natural frequencies of functionally graded cylindrical nanoshell. Finally, the effect of parameters such as material length scale, circumferential wave number, the length to radius ratio, shear correction factor, power low index and elastic foundation coefficients of Winkler and Pasternak on natural frequency of functionally graded cylindrical nanoshell are identified. The results show, there is a very good agreement between the results of molecular dynamics simulations by previous researchers with the results of this study.

In this article, the random vibration analysis of a delaminated beam is performed for the first time by considering the thicknesswise location of the delamination and the Young’s modulus as the stochastic parameters. First, the delaminated beam is divided into four intact sub-beams. Then by introducing a beam element and based on the beam’s classical theory, the kinetic and potential energies of each sub-beam are derived. The considered higher order element has three nodes, one at each end and one at the midpoint and each node has two degrees of freedom, namely, deflection and slope. Using the mentioned energies, the stiffness and mass matrixes of the element are obtained. Next, by assembling the above stated matrices and considering the continuity conditions for adjoining elements at the delamination boundaries, the total stiffness and mass matrices are obtained. In employing the continuity conditions, the deflection and slope of these elements are taken to be equal. At the end, by applying the boundary conditions the governing differential equations of motion are obtained in matrix form. Then by modeling the stochastic parameters as random fields, the governing deterministic differential equation of the system is transformed into a stochastic differential equation. The continuous random fields are discretized by mid-point and local average discretization methods. Finally using the Monte Carlo simulation method in each iteration loop, each stochastic differential equation is transformed into a deterministic differential equation. For free vibration analysis, the eigenvalue problem is solved to investigate the frequencies and mode shapes of the system. Consequently, having the eigenpairs of the system, the statistical properties of free vibration characteristics of the beam such as expected values, standard deviations and probability density functions are obtained and the effect of different parameters of the beam and delamination are studied. Also in order to verify the obtained equations and the written computer programs, the deterministic frequencies of the beam are compared with other results and very good agreement is observed.

In this paper, linear and nonlinear free vibration of one functionally graded magnetoelectro- elastic rectangular plate is studied. The boundary conditions in all side of plate have been considered as simply supported. Also the equations of motions have been derived calculation the kinetic energy and potential energy based on the third order shear deformation theory using Hamilton principle. Considering the top surface of the plate as an pizeomagnetic material and the bottom surface as a piezoelectric material, the bottom and upper surfaces of the plate are subjected to electric and magnetic potentials. The electric and magnetic behaviors of the plate are modeled by using Gauss’s laws. Then, the equations of motions have been transformed from partial differential equations to ordinary differential equations by using Galerkin Method. Then, Using Lindeshtot- Poincare method a closed form expression for linear and nonlinear natural frequency has been obtained. for validation of the proposed model, some numerical examples have been presented and comparisons between the obtained results with the results in literature have been down. It is shown that good agreement exist between obtained results and previous works. Then, to study the effects of several parameters on the nonlinear vibration response of functionally graded magneto-electro-elastic rectangular plates

In this paper, whirling and stability analyses of a rotor made of functionally graded materials are investigated. The rotor is modeled based on Timoshenko beam theory and gyroscopic effects are considered. Diameter and mechanical properties of the rotor are considered to be variable in longitudinal direction and the rotor is considered to be subjected to axial load and torsional torque. In order to generalization of the modeling of bearings, each of them is replaced with foursprings; two translational and two rotational acting on two perpendicular directions. Using Newton’s second law, the set of governing equations and external boundary conditions are derived and solved numerically using differential quadrature method (DQM). Convergence and accuracy of the presented solution are confirmed and effect of various parameters including power index, angular velocity ofspin, value and sign of applied axial load and torsional torque on the forward and backward frequencies and stability of the rotor are investigated. Numerical results show that all forward and backward frequencies and therefore critical speeds decrease by increase in power law, applying axial pressure load and torsional torque and increase by applying axial tension force.

Cold roll forming process is a process that a strip passes through a collection of rotary rolls to be converted to a desired profile. Hat channel section is one of the roll forming products that has many applications in various industries especially in automotive industry. In the present study proper flower pattern for production of hat channel section is determined. Proper flower pattern in the cold roll forming process can prevent some defects such as bowing and wrinkling. Flower pattern of hat channel section was predicted by ABAQUS 3D simulation. Longitudinal strain is one of the results of simulation which was used as a criterion for product quality evaluation. Results of simulations were verified by experimental tests for first forming stand of hat channel section which were done in the present study. In the experimental part of present study, effect of roll angle was investigated on the bow defect of product. Experimental and numerical results of this study have a good agreement. Numerical and experimental of this study showed that bow defect increases by increasing bending angle.

In this paper, the dynamic instability of swept wings by using the geometrically exact fully intrinsic beam equations is investigated. Due to the lack of existence of sweep angle effects in the aeroelastic formulation of these equations, this study is aimed to add the effect of sweep angle to the aforementioned formulation and this is one of the aspects of innovation in this paper. The fully intrinsic equations involve only moments, forces, velocity and angular velocity, and in these equations, the displacements and rotations will not appear explicitly. For this reason, the important advantages of these equations are complete modeling without any simplifying assumptions in large deformations, low-order nonlinearities and thus less complexity. In order to determine the stability of the wing, first the resultant non-linear partial differential equations are discretized by using the central finite difference method, and then linearized about the static equilibrium. Afterward, using the eigenvalueanalysis of linearized equations, the stability of the system versus different parameters is evaluated. The obtained results are compared with those available in the literature, and good agreement is observed. Finally, it is observed that by using the fully intrinsic equations, the instability of the swept wings can be determined accurately.

In this paper, based on the duality between the predictive control and general estimation problem, two new predictive filters, named generalized predictive filter and generalized predictive Kalman filter, are developed. The major advantage of the new filters over the existing predictive filters are that their structure are very simple and their application as a recursive filter is not complicated. Unlike the Kalman filter, these proposed predictive filters assume that process noise and model error are not equivalent and there are no limitations about the form of model error so that this model error can appear in a nonlinear form or even a colored noise. By minimizing a quadratic cost function consisting of a measurement residual term and a model error term respect to the process model error, the optimal model error is determined. Compensation of this model error in the time update state model provides accurate estimates even in the presence of dynamic uncertainty. Combination of Kalman filter and generalized predictive filter improves the performance and robustness of Karman filter. The validity of the suggested filters is illustrated by a numerical example and their performance and robustness are compared with those of KF and the fading Kalman filter.

An optimal control is designed for damping the unwanted vibrations of an electrostatically actuated micro-system. The goal is using feasible methods to decrease the settling time and overshoot of the response. This configuration consists of an electro-statically actuated micro-plate attached to the end of a micro-cantilever. The DC voltage is applied between the micro-plate and the opposite electrode micro-plate. This DC voltage causes an electrostatic force. In this model micro cantilever is considered as a continuous medium for which Euler-Bernoulli beam theory can be implemented. The plate is considered as a rigid body, and the electrostatic force is a nonlinear function of the displacement and the applied voltage underneath the micro-plate. The equation of motion is derived using Newton’s second law. In order to extract the corresponding state space and control the system in a closed loop way, exact method is used to reduce related partial differential equation of the systems into a set of two ordinary differential equations and the resultant state space is linearized about the operating point. The linearized state space is then optimized using the linear-quadrant regulator. Efficiency and applicability of the mentioned controller is investigated using comparative analyzing method.

In this paper, bimetal tubes extrusion process through conical dies has been analyzed by upper bound method using stream functions. The bimetal tube is in un-bonded conditions initially and the proposed deformation model, investigates the bonding at the interface of two metals in the deformation zone. For this propose, the deformation region has been divided into three deformation zones where the position of the start point of bonding at the interface of two metals is determined. For each deformation zone, an admissible velocity field has been proposed and the internal power, shear and frictional powers and the total power have been calculated. The total power, which is expressed by deformation zone boundaries and the position of the start point of bonding, is optimized and the extrusion force has been calculated. Analytical results are compared with the results given by experimental data of other researchers and also by finite element method that show a good agreement. Finally the effect of various extrusion conditions such as reduction in area and semi die angle upon the extrusion force and the position of the bonding start point at the interface have been investigated.

One of the most common non-traditional forming process, is the tube hydroforming, which is widely used for to form various tubular parts. To produce final product without any failure, tube hydroforming process is strictly dependent on load path, internal pressure-axial feed. Major modes of failure which may be occur in tube hydroforming process are necking, bursting, buckling and wrinkling. Predicting and preventing each of these failures are very important and leads to defects-free products. In this study, geometrical criteria for detecting wrinkling in numerical methods such as finite element analysis are reviewed. This type of identifying the wrinkling can be pointed out such as the first derivative or geometric slope and length to area indices criteria. In this paper, a new geometric method as a center of volume is introduced. In this case, the center of volume of wrinkled part is not equal with the wrinkled-free one. In order to verify, the results of this new criterion were compared with the results of previous measures and experimental tests in published articles.

Weld residual stress is one of the most sensitive issues in the safety and reliability of structures such as nuclear reactor components. In order to prevent the corrosion caused by corrosive environments, the inner surface of containers made of carbon steel, is cladded in a layer of austenitic stainless steel. In this study, a steel plate of carbon steel A516-G70, will be cladded by the shielded metal arc welding method. In order to validate the results, hole drilling method is used to determine residual stresses. Finally, the residual stresses in samples with two and three layer cladding are examined. By giving the sources of error in testing, the results have a relatively good compliance. The results indicate that, the maximum amount of residual stresses in the clad layer, are tensile and in the stress limit, it is in submission of base metal and cladding layer. Also, by increasing the number of layers in the cladding layer thickness and steel plate, residual stresses are reduced. However, at the surface of the cladding layer stresses have inconsiderable changes. And on the border between the cladding layer and the plate, residual stress increases by increasing the number of layers.

Production of rectangular sheet parts by traditional deep drawing methods is associated with many problems. The absence of axisymmetry and the difference between the length and width of the part makes the forming of these products difficult. In this paper, forming of rectangular cups in a single step which is not possible by traditional methods for the desired depth and corner radius, has been examined by hydrodynamic deep drawing process with radial pressure. In this research, after designing and manufacturing of die and forming of rectangular parts, the obtained results from simulation were compared and verified by those of experiments. Moreover, the effect of forming pressure on thickness distribution has been investigated. The study illustrated that increasing forming pressure up to an optimum value improves formability and thickness distribution. In addition, in order to remove flange area and to improve formability, optimization of the sheet dimensions has been performed using sensitivity analysis. It was concluded that optimizing the blank shape can improve thickness distribution, eliminate final flange trimming and decrease one stage of manufacturing, resulting in decreasing production time and cost. Finally, it was illustrated that it is possible to adequately form rectangular cups in one stage using optimized blanks.

Creating melt joints in aluminum is an obstacle in introducing this metal into structures. This is due to the fact that fusion welding methods of aluminum leaves mechanical and metallurgical defects in the final produced parts. Friction stir welding is a non-melting replacement fabrication method, which creates welded joints from a semi-solid material state. In this paper, friction stir lap welding of 7075 aluminum alloy is studied both numerically and experimentally with the aim of investigating the shear strength of the welded joint. The shear strength which is calculated by the simulation is maximum 14 to 15 % lower to the acquired experimental results, which shows that the simulation process can appropriately be utilized to predict the shear strength of the welded joints for different cases. In addition, the results show that the maximum shear strength is equal to 165 Mpa which is obtained for a case in which the rotational speed is 1250 rpm, the linear speed is 50 mm/min and the tilt angle is set to 3˚.