فصلنامه مدل سازی در مهندسی
پیاپی 34 (پاییز 1392)

The vibration analysis of cracked post-buckled beam is investigated using the differential quadrature method. Crack، assumed to be open، is modeled by a massless rotational spring. The beam is divided into two segments and the governing nonlinear equations of motion for the post-buckled state are derived. The solution consists of static and dynamic parts، which both result in nonlinear differential equations. Application of differential quadrature to the static differential equations results in a nonlinear algebraic system of equations، which will be solved utilizing an arc length strategy. Next، the differential quadrature is applied to the linearized dynamic differential equations of motion and their corresponding boundary and continuity conditions. Upon solution of the resulting eigenvalue problem، the natural frequencies and mode shapes of the beam are extracted. Several numerical case studies on cracked beams are conducted to ensure the integrity and accuracy of the proposed method. The results confirm the efficiency and accuracy of the differential quadrature method in dealing with this class of engineering problems.

This paper presents a numerical study on the mixed convection in an enclosure، with a heat source at its center filled with a water–CuO nanofluid. Central heat source and the wall heat source have Th and Tc respectively. For this purpose we used a Fortran program based on Finite Volume Method and SIMPLER algorithm. The effects of parameters such as volume fraction for 0، 0. 02 and 0. 04، Richardson number for 0. 01، 0. 1، 1، 10 and 100، Grashof equal to 104، as well as aspect ratio 0. 2، 0. 4 and 0. 6 are examined. The results show that the Nusselt number decrease with Richardson number for all aspect ratio with and without Brownian motion effects. At Richardson number equal to 100 average Nusselt number increase with volume fraction while at other Richardson number it increase from 0 to 0. 02 and it has not change after 0. 02. When we consider the effect of Brownian motion average Nusselt number show grater increase at all cases under study. Maximum increase in average Nusselt number is 9. 31 with effect of Brownian motion.

This paper deals with motion planning of Tractor-trailer robots، which are car-like robot dragging several trailers with no driving force. Each trailer has a nonholonomic kinematic constraint which increases the complexity of the path planning problem. We solved this problem by implementing the Equivalent Size concept، which depending on the size، number، and link-point positions of trailers، transforms a tractor-trailer path planning problem into a single car-like robot path planning problem. In this paper a new path planning algorithm is proposed for car-like robots which utilizes the Fast Marching Method (FMM)، which is a numerical method for solving the Eikonal differential equation، and the concept of Virtual Obstacles. The algorithm is fast، works independent of the shape of obstacles، and is easy to implement. To evaluate the quality of the solutions the algorithm is compared with the grid search and nonholonomic RRT algorithms. The results showed that the new method has by far lower runtime compared to the other algorithms، while producing short and smooth paths.

In this study، it is tried to simulate the behavior of pedestrians by using Social Force model، which is one of the presented model in the microscopic simulation. Because of the fact that this model is close to the real world، its results are more realistic. The aim of this study is to evaluate this model in Tehran’s sidewalks. In order to do this، sidewalks of 22 districts of Tehran were observed، and in the end، 6 districts (1، 4، 13، 16، 19، 22) were chosen since they had better conditions for shooting films. The procedure was that the real behavior of people was considered using the films، then، the data related to velocity and density were extracted. Based on the results achieved from statistical analysis، the Correlation coefficient between the data of the field study and modeling the velocity and density parameters are 0. 916 and 0. 907 which show an acceptable level of Correlation between the field study and the simulation. Moreover، based on the linear regression analysis done in the SPSS software program، it was observed that the variable constant amount in both velocity and density parameters equals to zero and the amount of the independent variable for the velocity parameter equals to 0. 956 and for the density parameter equals 1. 03. Also، the adjusted R square coefficient of the velocity parameter is 0. 839 and for the density parameter is 0. 870.

In current years، some attempts have been done to eliminate the grid of numerical solving processes. These attempts were created the groups of calculation methods which are known as meshless methods. MLPG methods are one of the efficient meshless methods in solving different problems. In this study، the MLPG meshless algorithm was used to Modeling and simulation of thermomechanical stresses and residual stresses in resistance spot welding between two sheets. In this method، a unit step function is used as a test functions in local weak-form. The Analyzed domain is divided to small subdomains with a circular shape. The numerical results of MLPG method are compared with the result of finite element method. The results of meshless method are similar to FEM simulation.

Steady flow of a non-Newtonian fluid over a stretching sheet under influence of a constant transverse magnetic field has been investigated based on the power-law model. Velocity of the sheet varies linearly along the flow direction. PDE type equations of motion of fluid were transformed to a nonlinear ODE type equation using similarity transformation. A numerical scheme based on finite difference and shooting method has been proposed to solve the governing equations. Effects of characteristics of flow، fluid and magnetic field have been investigated. Results show that the magnetic field acts as a drag force and decreases the boundary layer thickness. Finally، considering the Newtonian model for a non-Newtonian fluid causes considerable errors up to 100% especially for the skin friction coefficient.

The aim of this study is friction modeling and optimization of a “vibration modal analysis simulator”. This device has been used for observation and measurement of natural frequencies and mode shapes ofvibrating components and parts under the free or forced vibration conditions. In this paper to obtain linear vibrating motion with less measurement errors and optimum friction factor، the new prototype has been designed using the genetic algorithm. Mass linear motion is modeled by viscous friction agent so that optimized friction factor C with six sub-designation factors is calculated. Obtained results with respect to precursor’s availability، fabrication ability and from the economical point of view are more amenable and applicable than the preliminary devices and show a 70% reduction in friction factor.