Design of support system is One of the most important issues in tunnels design. Therefore, in order to safe design of support system, determination of internal loads has a special importance. In this paper, Analytical and Numerical Methods were used to determine of internal loads, and in 2D and 3D states, the results of these Methods were compared with the assumption of no slip and full slip conditions. Findings prove that in different sections of support system, the axial force obtained from full slip condition is more uniform than that of no slip condition, and the bending moment of full slip condition is higher than that of no slip condition. According to results, an increase in stiffness contrast between support system and ground results in an increase in the internal loads. Moreover, by increasing of the tunnel radius, the bending moment decreases and axial force increases.

Backlash between meshing gears in gear rotating systems leads to vibro-impact phenomena which mostly causes excessive vibration and noise. The gear rattle is a noise which is produced by the vibroi-mpact in gearboxes, and which might be audible in specific driving conditions in the interior of the vehicle. In this paper a non-linear mathematical model of a simple gearbox system is developed to understand and control the problem. The Analytical and Numerical activities were performed for minimizing gear rattle. It is shown that Analytical prediction agrees well with the Numerical results.

The dynamic design of tunnels and their dynamic response under various seismic and vibration loads is an essential issue that researchers have studied in recent years. The most suitable Methods for investigating the effects of seismic and vibrational loads on tunnels and underground structures are Analytical Methods and Numerical simulations. The problem is first modeled and then analyzed in Numerical Methods such as the finite element method or boundary element method. Based on comparing the research results in this field, it can be concluded that due to the low flexibility of Analytical Methods in solving problems with geometry and properties of complex materials, the need to use Numerical Methods is more felt because of its advantages in solving complex problems. This study aimed to investigate the effect of vibrations on tunnels and underground structures, which are special considerations in the design.

In this paper, a new method for fracture analysis of notched cylindrical cases under explosive loading of High Explosive internal charge has been presented to determine fracture time, fracture radius, fragment velocity and acceleration. Also the fracture dynamics has been simulated by explicit and nonlinear LS-DYNA code. In Numerical simulation the behaviour of metallic case has been modeled by JOHNSON-COOK model, and of HE charge by HIGH-EXPLOSIVE-BURN. Mie-Gruneisen and JWL equations of state have been used for the materials. Finally, the results of the Analytical model, the Numerical simulation and extended Taylor's model have been compared, and the effects of some paremeters on the fracture time, fragment velocity, and expansion radius have been discussed.

In situ soil properties are spatially variable parameters causing soil deposits to be heterogeneous. Heterogeneity consists of two components: (i) A deterministic trend and (ii) The residual component. This paper presents the eect of dierent components of soil heterogeneity on the ultimate bearing capacity of a vertically loaded shallow foundation resting on clay deposits. The Numerical model used in this study is based on nite dierence simulations, employing FLAC 5.0. Results of Numerical analysis are compared with other simple and Analytical solutions. For heterogeneous soil deposits, considering both linear and bi-linear deterministic trends, nite dierence tools were found to be able to reect salient features of heterogeneity in bearing capacity estimation. An equivalent homogeneous analysis solution is introduced, in order to allow for heterogeneity, by adopting a representative depth for shear strength measurements. Stochastic variation of shear strength is shown to induce under conservatism by solely relying upon deterministic estimations.

In this paper, recommended spiral passive micromixer was designed and simulated. spiral design has the potential to create and strengthen the centrifugal force and the secondary flow. A series of simulations were carried out to evaluate the effects of channel width, channel depth, the gap between loops, and flowrate on the micromixer performance. These features impact the contact area of the two fluids and ultimately lead to an increment in the quality of the mixture. In this study, for the flow rate of 25 μl/min and molecular diffusion coefficient of 1×10-10 m2/s, mixing efficiency of more than 90% is achieved after 30 (approximately one-third of the total channel length). Finally, the optimized design fabricated using proposed 3D printing method.

Slope stability studies is one of the most considerable parameter of safety and economical factors of open pits.Because the pit walls usually consist of different characteristics of lithology and structure, using only one slope for all walls is not enough and reasonable.So they need carefull geological and geotechnical studies to determine the geotechnical limits of the pit.By using MRMR Methods, SlopeW 2004 and FLAC 4.0 softwares and comparing the results,optimum slopes for North western wall of Chadormalu Iron mine have been calculated.On the basis of all available data,the following geotechnical domains have been distinguished for North western wall of Chadormalu Iron mine:• Lithology and Structure• Pit Wall Orientation• Rock Mass Rating and conditionsNorth western open pit wall is bounded by metasomatite, albite metasomatite, and ore. The structure of this domain is distinguished by steep normal faults with great displacement and brecciate limestone.The results of geotechnical boreholes, modeling and studies indicate that the overall slope of this domain could be increased from 52, to 60 degrees.

The various Methods are published for satellite orbit propagation and the Numerical integration is one of the most common Methods. The Numerical integrators can be divided into two main Methods, Single-Step and Multi-Step Methods. In this paper, the results of Runge-Kutta method as the most common Single-Step method and prediction-estimation-correction-estimation method as the most common Multi-step method are compared. In this paper, it is proved that if the error-controlled integration Methods are used, the difference between Single-step and Multi-step Methods would be at sub-millimeter level. In this paper, the Lagrange method is introduced as a semi-Analytical method too and the Lagrange coefficients are developed from central field to full gravitational field of Earth. By this development, the Lagrange method can be used in LEO satellite orbit determination. The results show that the accuracy of the Lagrange method for LEO satellite orbit determination is about 5 millimeter over one day.

In this paper, the free vibration of homogeneous micro / nano beams coated by a functionally graded layer is investigated based on the Eringen's nonlocal elasticity theory. In order to extract the equations of motion, the first-order shear deformation beam theory (Timoshenko's beam theory) has been used. The obtained equations of motion are solved using two different Analytical and Numerical Methods for different boundary conditions. In the Analytical method, the equations of motion are first solved and the general functions for the displacements are obtained. The functions include a number of unknown parameters and constants. Then, by considering the boundary condition equations at both ends of the beam, a set of algebraic equations is extracted. Finally, the natural frequencies are obtained form the nonzero solution of the algebraic equations. In the Numerical solution, the generalized differential quadrature method is used to solve the equations of motion. In the results section, first, the validity of present Methods should be confirmed. Hence, the results obtained from this article are compared with the corresponding results presented in the litterature. Then, the results of the two Analytical and Numerical Methods are compared, which confirms the consistency of the results of both two Methods. The effects of thickness of porous layer and also the percentage of porosity of porous layer on the natural frequencies of beams are studied.

Flexural toppling is a mode of failure that may occur in a wide range of layered rock strata in both natural and excavated rock slopes. As illustrated in Figure 1, a typical flexural toppling can be occurring in a rock slope when columns of rock are separated by steeply dipping discontinuities and bended forward.