Computational Methods in Engineering

This article predicts lifetime of high cycle fatigue loading using Chaboche-Lemaitre damage model. The Chaboche-Lemaitre damage model takes into account mean stress effect as well as compressive stresses effect, making crack to close. In the this paper, a numerical algorithm is offered to integrate this model implicitly and the obtained algorithm is implemented as a user material subroutine of the ABAQUS finite element software. To reduce computation time, Jump-in-Cycles procedure is used based on fatigue loading simulation. To verify the proposed algorithm, a V-notched specimen is chosen under a fatigue loading with different stress ratios, and its lifetime is compared with experiments. Next, an aviation industry part, main rotor spindle of an aircraft blades, subjected to a variable fatigue loading is analysed.

In this paper, buckling behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates is studied in line with the plates thikness. All  governing equations are presented incrementally, based on a First-order Shear Deformation Theory (FSDT) of plates and von Karman strain field. In order to find the critical buckling load, the axial load is applied to the plate incrementally and the equilibrium equations are solved by Dynamic Relaxation (DR) method. Parametric study of the effects of volume fraction of Carbon Nanotubes (CNTs), CNTs distribution, plate width-to-thickness ratio and aspect ratio of nano composite plates is done in detail. The results show that functionally graded distribution of CNTs causes a significant increase of critical buckling load.

In this paper, first the theory of Improved Applied Element Method (IAEM) is proposed and then an appropriate algorithm and software are developed for analyzing structures behavior until collapse by this method. Then, some examples of structural analysis by the above method and a software developed for this study are presented. The results show that IAEM has the ability to solve the discussed problems more accurately in less time than Finite Element Method (FEM). Moreover, the efficiency of the method for solving large displacements problems is enhanced in this research by introducing nonlinear response indicators. For modification of the stiffness matrix in the nonlinear range, a new method is presented that increases the accuracy of calculation up to 30%.

This study shows how to create different types of crack and discontinuities by using isogeometric analysis approach (IGA) and extended finite element method (XFEM). In this contribution, two unique features of isogeometric analysis approach are utilized to create discontinuous zones. Discontinuities consist of crack and cohesive zone. In isogeometric analysis method NURBS is used to approximate both geometry and primary variable. NURBS can create quadratic shapes exactly. Also, stress intensity factors are calculated in the vicinity of the crack tips for two dimensional problems and are compared with corresponding analytical and numerical counterparts. Extended finite element method is the other numerical method which is used in this work. The enrichment procedure is utilized in extended finite element method to create discontinuities. The well-known path independent J-integral approach is used in order to calculate the stress intensity factors. Also, in mixed mode situation, the interaction integral (M-integral) is considered to calculate the stress intensity factors. Results show that isogeometric analysis method has desirable accuracy as it uses lower degree of freedoms and consequently lower computational efforts than extended finite element method. In addition, creating the internal cohesive zone as one of the most important issues in computational fracture mechanics is feasible due to the special features of isogeometric analysis. The present study demonstrates the capability of isogeometric analysis parametric space to control the inter-element continuity and create the cohesive zone.

In present study, dynamic modeling and control of a tethered space robot system in trajectory tracking of its end effector is investigated. Considering variation of the tether length in the model, dynamics of the system is modeled using Lagrange’s method. Librational motion of the tether is controlled by adjusting the tether length similar to conventional manipulators,control of the robot is performed by its motors. It is clear that, in the trajectory tracking of the end effector, the tether length should be kept more or less constant, keeping them in a stable position. Limiting the tether length variation while using it as a tool for controlling the tether librational motion, is the main challenging part of the control system. To deal with this problem, a hybrid control  system is proposed to control the system. A nonlinear model predictive control approach (NMPC) is utilized to control the tether librational motion and a modified computed torque method (CTM) is used to control the manipulator motion. Initially the NMPC controller is developed for a simple tethered satellite system. Then it is combined with the CTM controller. The proposed controller is employed to control motion of a space robot’s end effector on a predefined trajectory. Performance of the controller is then evaluated by numerical simulations.

Using Vibro-Impact Nonlinear Energy Sinks (VI NESs) is one of the novel strategies to control structural vibrations and mitigate their seismic response. In this system, a mass is tuned on the structure floor, so that it has a specific distance from an inelastic constraint connected to the floor mass. In case of structure stimulation, the displaced VI NES mass collides with the  inelastic constraint and upon impacts, energy is dissipated. In the present work, VI NES is studied when its parameters, including clearance and stiffness ratio, are simultaneously optimized. Harmony search as a recent meta-heuristic algorithm is efficiently specialized and utilized for the aforementioned continuous optimization problem. The optimized attached VI NES is thus shown to be capable of interacting with the primary structure over a wide range of frequencies. The resulting controlled response is then investigated, in a variety of low and medium rise steel moment frames, via nonlinear dynamic time history analyses. Capability of the VI NES to dissipate siesmic input energy of earthquakes and their capabilitiy in reducing response of srtructures effectively, through vibro-impacts between the energy sink’s mass and the floor mass, is discussed by extracting several performance indices and the corresponding Fourier spectra. Results of the numerical simulations done on some structural model examples reveal that the optimized VI NES has caused successive redistribution of energy from low-frequency high-amplitude vibration modes to high-frequency low-amplitude modes, bringing about the desired attenuation of the structural responses.

In this paper, viscous dissipation and roughness effects on heat transfer and fluid flow are investigated in microchannels using perturbation method in slip flow regime. The flow is considered to be laminar, developing thermally and hydrodynamically, two-dimensional, incompressible and steady-state. The working fluid is air, flowing between two parallel plates. The equations obtained from developing Navier-Stokes and energy equations are solved numerically according to different orders of Knudsen number, with second-order velocity slip and temperature jump boundary conditions. The effects of thermal creep has been ignored. Tempreture and velocity fields are obtained and estimated for both constatnt heat flux and constant wall tempreture. The effects of roughness height, space between roughness elements, roughness elements length, Re number and Kn number on slip behavior of gas flow are investigated.The results indicate considerable effect of viscous dissipation and roughness on fluid flow and heat transfer in microchannel.

Although a significant portion of conditions encountered in geotechnical engineering, for investigating engineering behavior of soil, involves unsaturated soils; the traditional analysis and design approach has been to assume the limiting conditions of soils being either completely dry or completely saturated. In unsaturated soils the capillary force produce attractive forces between particles. Discrete Element Method (DEM) is an appropriate tool to consider the capillary effects. The calculations performed in DEM is based on iterative application of Newton’s second law to the particles and force-displacement law at the contacts. In the present study, the behavior of unsaturated soils in pendular regime is simulated utilizing DEM. Triaxial  compression tests were modeled as two-dimensional, considering capillary force effects. Finally, capillary effects on Macro parameters of a simulated granular soil (stress, axial strain, volumetric strain and void ratio) and Mohr Coulomb failure criteria parameters were studied.

Weighted Simulation-based Design Method (WSDM) is recently developed as an efficient method for Reliability-
Based Design Optimization (RBDO). Despite simplicity, this method degrades effectiveness to obtain accurate optimum design for
high dimension RBDO. Besides, its application range is restricted to RBDOs including only random design variables. In the
present study, local search strategy is employed to enhance the accuracy of conventional WSDOM, and to reduce the computational cost. Besides, a shifting strategy is proposed to increase the application range of WSDM for handling general RBDO problems. The efficiency of the proposed methods is investigated by solving some structural reliability problems.
Comparisonof the obtained results with exact solutions confirms accuracy and superiority of the proposed method for
solving various engineering problems.

In this article, the vibration analysis of a set of parallel Timoshenko beams connected by intermediate flexible connections, with arbitrary numbers, is studied. The moving load is a vehicle, which is modeled by a two-axle six degrees of freedom system, as a mass-spring-damper system, in a plane motion. For the solution, a new method is proposed which uses a change of variables strategy to decouple the system of differential equations. For this purpose, the stiffness matrix obtained from each column of intermediate connections should have the same normalized eigenvectors. The displacements and the bending moments of the beams and the vehicle due to changes in the stiffness of connections and changes in speeds will be examined. Finally, the validity of the results are measured.

In this study, for the first time natural convection heat transfer of Al2O3-water nanofluid with constant and variable
properties is investigated within square shape porous media using the lattice Boltzmann method. The horizontal walls of the
cavity are insulated, and left and right vertical walls are hot and cold, respectively. The Study have been carried out for Rayleigh
numbers of 103, 104, 105, 106, Darcy numbers of 10-2, 10-4, porosity coefficients of 0.4, 0.6, 0.9 and solid volume fraction of 0, 0.01,
0.02 and 0.03. In order to consider the effect of porous media, Darcy-Forchheimer model is used. The results show that the presence of the porous media decreases the velocity of nanofluid and consequently decreases the strength of the flow. With decreasing Darcy number and porosity coefficient, natural convection heat transfer weakens and the mechanism of natural convection of nano-fluids tends to that of thermal conduction. With increasing Rayleigh number, the strength of flow in cavity and average Nusselt number increases. In all cases studied, increase in volume fraction improves heat transfer. In constant properties model, by increasing solid volume fraction, average Nusselt number increases more than that of variable properties model. The results show that Lattice Boltzmann method has the ability to simulate flow in porous media.

In this paper, the solution of a non-linear model of Cell Manufacturing (CM) in certain and dynamic conditions is
studied, considering intracellular and extracellular costs, cell constructing costs, the cost of restoration and the cost of equipment
transportation per distance travelled. Since the number of cells in each stage of production is important, by optimizing the
number of cells, additional costs can be minimized. Therefore, the main objective of this study is to investigate the optimal
number of cells located. Bio-geographical Based Optimization (BBO) algorithm is applied in the CM for the first time in the
literature and the obtained results from this algorithm are compared with the results of well-known genetic algorithm. The results
shows the good performance of genetic algorithm. Finally, the conclusion and future research are provided.

The purpose of the present study is to investigate and analyze numerically, the effective mechanisms on the flow field and pollutant dispersion around a simple and long street canyon by means of Large Eddy Simulation (LES) approach using various inflow turbulence generation methods. For this purpose, four methods i.e. vortex, mapping, synthetic and no-inlet perturbation methods are used as inflow turbulence generators in LES. Results suggest that all methods are capable of capturing the two important structures of canyon vortex and corner eddy, which have great influences on air ventilation inside the street canyon. The magnitudes of concentration on the leeward wall of the first building are approximately four times as much as those
of windward wall of the second building. Among the various inflow turbulence generation methods, the vortex method is the most precise method and no-inlet perturbation method is the least precise method.

Many efforts have been done in recent years to decrease the required time for analysis of FKP (Forward Kinematics
Problem) of parallel robots.This paper starts with developing kinematics of a parallel robot and finishes with a suggested
algorithm to solve forward kinematics of robots. In this paper, by combining the artificial neural networks and a 3rd-order
numerical algorithm, an improved hybrid strategy is proposed in order to increase the accuracy and speed of forward kinematics
analysis of parallel manipulators. First, an approximate solution of the forward kinematics problem is produced by the neural
network. This approximate solution is then considered as the initial guess for the 3rd-order Newton-Raphson numerical
technique. By applying Stewart-Gough parallel manipulator, the efficiency of the proposed method is evaluated. It is shown that
replacing the Newton-Raphson algorithm by the 3rd-order one leads to a reduction of the iterations required to reach the desired
accuracy level and thus a reduction of the FKP analysis time. Finally, Stewart robot is used to simulate the movement of jaw.
This novel algorithm can be applied to any forward kinematics of serial or parallel robots.

In this paper, free vibration of carbon nanotube-reinforced functionally graded circular plates with hole has been
investigated. Distribution of carbon nanotubes are continuous and the gradual and graded changes of materials through the
plate thickness are considered as volume fraction. Considering the linear and non-linear variation of circular plates through the
radial direction and also considering the proposed function for the thickness, the plate thickness can be convex or concave.
Moreover, the motion equations of plate were obtained based on the third-order shear deformation theory. These equations are
coupled differential equations which can convert Ordinary Differential Equations (ODE) using the Trigonometric series
expansion of displacement fields such that they satisfy the axial symmetry condition. Solving the converted ODE equations is too
difficult. For this reason, the differential quadrature method is employed to solve these equations. The obtained results are
compared with the results reported by other researchers and an excellent agreement is observed between them. Finally, the effects
of different geometric parameters as well as different volume fracture of nanotubes on natural frequency have been studied.

For solving the dynamic equilibrium equation of structures, several second-order numerical methods have so far
been proposed. In these algorithms, conditional stability, period elongation, amplitude error, appearance of spurious frequencies
and dependency of the algorithms to the time steps are the crucial problems. Among the numerical methods, Newmark average
acceleration algorithm, regardless of existence of spurious frequencies, is very popular in the structural dynamics due to its
unconditionally stability status of the method. Recently, several first-order methods have been introduced for resolving the
accuracy and stability issues. However, in these methods stability, accuracy and error in inversion of the state matrix are known
as major issues. When the state matrix became singular or ill conditioned, numerical errors will occure in the computational
process. Many of the available first-order methods were to improve the stability and accuracy and also to remove the error of
inversion. Even though the introduced methods are conditionally stable, no investigation on errors, occuring during dynamic
loading, has been reported for them. The main purpose of this paper is to utilize a specific decomposition method based on
Singular Value Decomposition (SVD) for modifying PIM algorithm. Using the SVD inversion technique, the singularity problem
of the state matrix has been resolved. In this paper, the modified method is called PIMS. As well, by applying the developed
method for dynamic loading, the error of responses has been investigated. The results show that PIMS algorithm is stable and,
comparing with secoend order Newmark and other available first order methods, has more accuracy.

In this paper, wave propagation method was applied to detect damage of structures. Spectral Finite Element Method
(SFEM) was used to analyze wave propagation in structures. Two types of structures i.e. rod and Euler-Bernoulli beam were
modelled using spectral elements. The advantage of spectral finite element over conventional Finite Element Method (FEM), in
wave propagation problems, is its accuracy and lower computational time. Two examples of rod and Euler-Bernoulli beam with
embeded concentrated mass were presented to illustrate the superiority of SFEM to FEM. Finally, a cracked beam was modeled
and analyzed using spectral finite elements and the location of the crack was determined using time history response of beam
structure.