مجله مهندسی مکانیک امیرکبیر
سال پنجاه و یکم شماره 1 (فروردین و اردیبهشت 1398)

In this paper, a C1 finite element (FE) formulation of Mindlin-Reissner microplate based on strain gradient elasticity theory is developed. The general form of the stiffness matrix and force vector of the microplate element is firstly extracted, and then specialized on a four-node quadrilateral element with 36 degrees of freedom. Deformation of rectangular microplates with simply-supported edges, clamped edges, and three edges simply-supported and the fourth edge free, and under uniform external pressure is then studied. For the case of microplate with simply-supported boundaries, comparison between the FE and the corresponding exact solution is made, which shows extremely close results. For the next two examples, a convergent solution by means of mesh refinement is obtained. Moreover, for the case of thin plates and for large values of the thickness-to-material length ratio, the results of gradient-based FE analysis are coincident with those of the Kirchhoff plate model based on classical elasticity. Numerical simulations show that the introduced element is able to capture the size effect phenomenon at micron scale. When the plate thickness is in the order of the material length parameter, the value of deflection is lower than that predicted by the models based on classical elasticity.

In most industries, such as Petrochemical and Nuclear power plants design of pipelines which operate under high pressure is important. Especially when the pipelines are subjected to external cyclic loads for example during earthquakes. The situation becomes more severe when chemical reactions cause corrosion in pipe walls. In this case, ratcheting effect due to the cyclic mechanical load is magnified due to the corroded region and it becomes a major concern. In this paper the ratcheting behavior of corroded elbows have been investigated using finite element based software ABAQUS and numerical solution method. Two forms of corrosion: spherical and cubic geometric shapes are used with two depths of one and two millimeters on the sensitive areas such as symmetry axes in the intrados, crown and extrados of the elbow Finally results suggests the corrupting influence of corrosion in term of ratcheting and consequently increase this corrupting influence with increase depth of corroded and also its reliance to the geometry of applied corrosion. So the ratcheting on corroded place with cubic shapes is larger than spherical shapes. The results show that the ratcheting in the circumferential direction is too large compared with the axial direction.

This research deals with experimental investigation on energy absorption and deformation of thin walled square columns under multi-indentation loading. The main goal of this research is to examine the effect of number and diameter of indenters and distance between them on the energy absorption parameters. First, square aluminum specimens with specific lengths were prepared and also an adjustable fixture for applying multi-indentation loading was fabricated. Then the indentation loading were applied on the specimens during a quasi-static condition with a constant loading rate. During loadings, the specimens were located between an almost rigid platen and the adjustable indenters. The load-displacement diagrams of specimens were obtained and the energy absorption parameters were calculated. The results indicate that the amount of absorbed energy in multi-indentation process increases significantly respect to single-indentation. By increasing the distance between indenters in multi-indentation loading, the load- displacement diagram shifts upward and moves toward the twice of single-indentation diagram. Also, by increment of diameter of indenters and distance between them, the amount of absorbed energy increases 20-60% due to formation of bigger plastic hinges.

Despite the development of some advanced concepts in fracture mechanics during recent decades, the prediction of crack initiation and its growth in materials is still a major challenge. The main difficulty is because of the continuum based mathematical formulation, which assumes that a body remains continuous as it deforms. In fact, the classical theory is formulated using spatial partial differential equations. This presents a characteristic limitation to the classical theory, as the spatial derivatives in the governing equations lose their meaning due to the presence of a discontinuity, such as a crack. To overcome this problem, Peridynamic theory could be used to improve the analysis of cracked structures. Basically, the peridynamic theory is a reformulation of the equation of motion in solid mechanics that is better suited for modeling bodies with discontinuities, such as cracks. The theory uses spatial integral equations that can be applied to a discontinuity. The present study uses this approach to study the effects of applying tensile loads on crack paths in a plate with two parallel initial cracks located in an anti-symmetric manner. The results are compared with other investigations and it is shown that the velocity of applying load has significant effect on crack path and branching.

The medium caliber armor piercing projectiles have high kinetic energy and in practice, it is impossible to prevent these projectiles from penetration through different types of targets, directly. So this is essential to demonstrate a solution to repel these projectiles by studying on behavior of the targets. Air targets, generally made of fiber-metal laminates called GLARE, are one of the most important targets for medium caliber projectiles. In this study, numerical simulation of oblique penetration of medium caliber armor piercing projectile through the flat target of GLARE5 as well as curve targets with 6.3cm and 20cm curvature radius of the same material has been investigated via Abaqus software and consequence damage studied. Simulating failure behavior of the composite, 3D unidirectional composite model has been used and in order to do, a user-defined-subroutine VUMAT written and used with the Abaqus software. Also, because of high kinetic energy of the projectile, projectile damage has been accounted. Method of simulation has been verified by an experimental equation and the influence of target curvature on the penetration investigated. Results have shown that the increasing of the target curvature has not monotonic outcome of decreasing or increasing of the target damage.

In the fiber metal laminated shell with determination the proper fiber angle orientation is achieved the arrangement with maximum performance. For this purpose in this study the fiber angle orientation of composite layers of the fiber metal laminate circular cylindrical shells are changed frequently and each cases being subjected to lateral load and the tension of all composite layers are calculated for all cases. Then the fiber angle orientation that cause to maximum stiffness based on maximum tension fracture criterion is selected. For this purpose an analytical program linked to the numerical program is used and calculated result. The buckling analysis is applied to determine the performance of design process. The results of buckling analyses show that determination of the optimum fiber angle orientation causes to improvement of the fiber metal laminated shell stability. Comparing the effect of variation of the fiber angle orientation, variation of the metal layer properties and variation of the thickness shell on the buckling load is the another innovation of this study and it is determined that for various amount of metal volume fraction with change in which item the maximum stability is achived.in order to improve the result accuracy high order shear deformation theory is utilized for buckling analysis.

In this work, buckling and free vibration analyses of double-bonded micro composite plates reinforced by boron nitride and carbon nanotubes rested in an orthotropic foundation in presence of initial stresses and electro-magneto-thermal multi-physics fields are investigated based on sinusoidal shear deformation theory. The relation between electro-magneto-thermo-mechanical parameters are presented based on most general strain gradient theory and the governing equations of motions are obtained using Hamilton’s principle. With solving the governing equations of motions of double-bonded nanocomposite micro plates the effect of various parameters such as mass scale length parameter, lengthto- thickness and width ratios, orthotropic elastic constants, temperature changes and boron nitride and carbon nano tubes volume fractions are considered. The obtained results of this work demonstrate that the natural frequencies and critical buckling load enhance with increasing the mass scale length parameter, orthotropic elastic constants and nanotubes volume fractions and lead to delay the resonance phenomenon. While increasing the temperature changes lead to reduce the micro structure stiffness, natural frequencies and critical buckling load. It can be said that this application can be used in micro electro mechanical and nano electro mechanical systems and provide a great background for more studies.

This paper presents an analytical method for the application of piezoelectric patches to repair a rotating cracked beam. The beam equations of motion are obtained based on the Timoshenko beam theory including the effects of shear deformation and rotary inertia. The criterion applied for the repair is to modify the first natural frequency of the cracked beam towards that of the healthy beam applying a piezoelectric patch. Due to this, an external voltage is applied to actuate a piezoelectric patch bonded on the beam that decreases the effect of the crack on the vibration characteristics of the beam. First, the coupled equations of motion are discretized by applying the assumed modes method. Then, the cracked beam is modeled as numbers of healthy segments connected by two linear springs at the crack locations (one, extensional and the other, rotational). The compatibility requirements on the crack section and on the ends of the piezoelectric patch are considered to obtain the relationships between any two spans. Finally, applying the semi-analytical differential transform method, the natural frequencies and mode shapes of the system can be calculated. Numerical simulations are performed to assess the effects of different conditions on the repair moment coefficient. The presented model is validated by comparing the results with those available in the literature where, the natural frequencies are in a reasonably good agreement with the reported results.

In this paper, free vibration analysis of two-dimensional functionally graded annular sector plates with two piezoelectric layers on elastic foundation using the Rayleigh-Ritz method is investigated applying the third order shear deformation theory of plates. Despite the existence of more complex equations, the third-order shear deformation theory of plates leads to more accurate results, this is due due to the effects of transverse shear deformation and inertial rotation,.The material properties of the annular plate is graded two-dimensionally in both of the circumferential and thickness directions. The volume fraction power law distribution is used to model the two dimensional functionally graded plate properties. The sinusoidal function is used to determine the electrical potential of the piezoelectric layers. The assumed potential function satisfies the Maxwell electrostatic equations. To obtain the natural frequencies of the plate, the Lagrangian function is defined by subtracting the kinetic and potential energies of the plate and then the Hamilton’s principle and the Ritz method is applied to obtain the natural frequencies of the plate. Finally, the results are validated by various references and the effect of various parameters including the sector angle, ratio of thickness to radius of the plate and foundation coefficients on the natural frequency of the structure has been discussed.

In This paper, the behavior of a functionally graded micro-resonator that is excited by thecombination of DC electrostatic force and AC harmonic force, Casimir force, the uniform temperaturechange is investigated based on the Euler-Bernoulli beam theory and the nonlinear von-Karman strain. Itis assumed that material properties follow exponential law distributions through the thickness direction.The principle of minimum total potential energy and the modified couple stress theory are used to derivethe nonlinear governing differential equation of micro-beam. Static differential equations are solvedby using the differential quadrature method. The effects of temperature change, material length scaleparameter and power distributions model on pull-in voltage are investigated. Applying perturbationmethod with multiple scales technique and numerical integration of the second order nonlinear ordinarydifferential equation, an approximation for the response of the micro-beam to the primary-resonanceexcitation is obtained.

The main objective of this paper is to propose an optimal fuzzy controller for suppressing the resulting vibration of an earthquake in a five floor building facilitated with magneto rheological damper. To this end, by utilizing the Hamilton’s principle, equations of motion of the system are derived based on a distributed parameter model. The mode shapes of the system are found by finite element simulations. A magneto rheological damper is used for each floor. To find the rule base of the fuzzy controller, a single degree of freedom vibratory system is considered and the rules derived from open loop simulations are utilized for controlling the vibration of the building. Spencer’s model is employed for analyzing the behavior of the magneto rheological damper. By recognizing the magneto rheological damper behavior as well as having the rule based obtained from single degree of freedom simulations, a fuzzy controller is designed to suppress the vibration of the building. Finally, the genetic algorithm is used to improve the performance of the proposed controller. Comparing the results of semi-active vibration control with passive-on and passive-off control strategies reveals that the suggested fuzzy controller can effectively reduce the amplitude of the vibration of the building.

Principal parametric resonance in rotating blades with varying rotating speed is investigated in this paper. In the presented model, the lagging-axial coupling motion due to Coriolis force is considered. The governing equations of motion are the available equations in the literature based on the exact geometrical formulation for unshearable blades. The rotating speed of the blades is considered as a mean value perturbed by a small harmonic variation. The variation frequency of the perturbed value is considered twice the one of the lagging frequencies and/or one of the axial frequencies which causes the principal parametric resonance. The direct method of multiple scales is implemented to study the dynamic instability produced by the principal parametric resonance. A closed form relation which defines the stability region boundary under the condition of the principal parametric resonance is derived using the method of multiple scales. The current results are validated by comparison with the available results in the literature. After validation of the results, a comprehensive study has been adjusted for illustration of the rotating speed effects and mode number influences on the parametric stability region.

A variety of mechanical phenomena can be simulated by modeling bilinear oscillators which have different stiffness in pressure and tension. In this paper, bilinear oscillators with unlimited stiffness in compression say impact oscillators, and the eigenset which is homogenous solution of equation without external load are investigated. The results show that this set and the corresponding subsets are stable with respect to variation in initial conditions. In addition, among all periodic collections of impact times which are proportional to the period of external load, only the eigenset can support resonance, especially the multi-harmonic resonance. The rest of the resonances should produce the nonperiodic impact times. This phenomenon shows that the usual assumption that the times between impacts are proportional to the period of external load is not always confirmed. Furthermore it is shown that in half frequency of the main resonance (the first sub-harmonic resonance), the impact times are close to the eigenset and unlike linear increase of multi-harmonic resonances, the envelope of the oscillations increases as a square root of time.

The optimal design of path planning for unmanned aerial vehicles with many potential applications ranging from mapping to supporting rescue operations will improve their performance. Hence, the aim of this paper is to determine the optimal trajectory of quadrotor robot based on minimizing engine torque in point-to-point motion. First, the dynamic equations of quadrotor motion are derived in state space form by using Newton’s method. In this investigation, the computational method to solve the trajectory planning problem is based on the indirect solution of open-loop optimal control problem. The Pontryagin’s minimum principle (PMP) is used to obtain the optimality conditions, which is lead to a standard form of a two-point boundary value problem. Finally, to evaluate the efficacy of the proposed method, numerical simulation is performed for a quadrotor and the optimal trajectory is designed based on minimize torque. The results illustrate the power and efficiency of the method to overcome the high nonlinearity nature of the problem such as path optimization of multi-rotor helicopters (tri, quad, hexa, octa, etc.).

High-speed planetary gears, or more generally, gyroscopic systems are not preserve energy and therefore subjected to instability. In this research, the dynamic equations for double- helical planetary gear system in 3-D space and considering 6-DOF for each member are extracted. Then, the system stability in the range of critical speed is investigated. In the extraction of equations, the constant mesh stiffness is assumed and the gyroscopic effects due to rotating carrier are considered. The critical speeds of gyroscopic systems occur at speeds in which one or more natural frequencies are zero. To calculate the critical speeds, the eigenvalue problem of the system is solved by numerical methods. In order to validate the equations and the process of extraction of critical speed, the obtained results for a high-speed spur planetary gear system are compared with the results of the existing research. Finally, by plotting the variations of the real and imaginary parts of the Eigenvalues of the double-helical planetary gear system versus a range of carrier speeds investigate the system stability near critical speeds. The results of the current study indicate that the double- helical planetary gear system is stable at some critical speeds and in others subjected to divergence instability.

In this paper, three models for tire friction force are identified using experimental data of scaled test rig. In this setup, a scaled tire is forced to be in contact with a high inertia disk and the friction force between the tire and disk is measured in terms of the slip during braking. For identification of the models, tire’s rotational speed, tire’s slip and tire’s normal force are used as the inputs and the tire’s longitudinal force is considered as the output. The experimental data required for identification are collected by force and rotational displacement sensors. By using the measured data, the parameters of tire friction force models are calculated using nonlinear least square method. The identified models are evaluated by data not used in the identification process. The results show that the identified models follow the system outputs with acceptable errors. Among the identified models, the Dugoff model has the better accuracy compared with the Fiala and semi-linear models. As an application, a nonlinear dynamic model of the setup including the identified friction force model is employed to design a nonlinear controller for anti-lock braking system.

In this paper application of the multipoint aerodynamic model for parameter estimation in spin maneuver as a high-angle-of-attack and high-angular-rate fight regime was concentrated. The identification technique used to illustrate the approach is maximum likely hood with the equation error approach. The multipoint model comprises a set of new parameters describing the aerodynamic force distribution along individual surface components of the aircraft so using this method will be useful for spin aerodynamic modelling. The aim of this study is to demonstrate that this model allows coupling among the three force and three moment components, this means that the parameters associated with the six-component equations are thus treated simultaneously. Another advantage of this approach is that the model allows each individual force generating surface element of the aircraft to contribute independently to the total force and moment rather than some average of these contributions relative to the center of mass. The method is applied to measurements from spin fight test data conducted with a light general aviation aircraft and the results compared with conventional aerodynamic model. The results indicate that the method is capable of reproducing, with reasonable accuracy, the force and moment measurements obtained from a fight other than the one used in the parameter estimation.

In this paper, based higher shear deformation theory, electro-elastic equation of functionally graded material axisymmetric thick-walled cylinders in general form is presented. The displacements, stresses and electrical potential in clamped-clamped cylindrical shells analytically are calculated. The presented approach leads to the definition of new formulation to study thick shells based on shear deformation theory. The mechanical equilibrium equation obtained by energy method and for finding electrical equilibrium equation used Maxwell and Gauss equations. The governing equation solved in general form (independent of the order of shear deformation theory) by the coupled electro-mechanical using eigen vectors In this study, all mechanical and electrical piezoelectric material properties, were considered to follow an identical power law in the radial direction. The results obtained in the present paper have been compared with findings of plane elasticity theory. For investigating the effect of higher order approximations on displacements and stresses and electrical potential, a comparison between the results of first and third-order shear deformation theory have been studied. The numerical results show that the higher-order approximations must be applied in electro-elastic analysis of cylindrical shells made of functionally graded piezoelectric material. Finally, some numerical results are presented to study the effects of mechanical and electrical loading on the stresses, displacements and electrical potential of the cylinder.