نشریه روش های عددی در مهندسی
سال چهل و دوم شماره 2 (زمستان 1402)

Modeling of crack and discontinuity related problems has had a great influence on numerous industries for a long time. Simulation of discontinuity behavior in different scales, especially in atomistic scales, can lead to better insight of the crack/discontinuity initiation and propagation phenomena and prediction of its behavior in larger scales. On the other hand, modeling based on fully refined scales requires huge computational effort compared to other methods due to the higher number of degrees of freedom. Concurrent multiscale methods have been developed to overcome the high computational cost issues of refined models, while preserving sufficient accuracy. Studies have shown that concurrent multiscale methods are capable of simulating all atomic behaviors in order to establish a compatible solution with larger scales, and to accurately resemble the laboratory results. In the present review, concurrent multiscale methods, which could be categorized into homogenization and partitioned-domain methods, are briefly investigated and compared. These methods have been widely used for modelling of cracks, discontinuities and impurities in different types of problems in the past two decades. To create a suitable basis for comparing the main concurrent methods, the problem of edge crack propagation is redesigned and modeled, and the simulation results and their computational accuracy are compared.

In this paper, a new method has been proposed for the topology optimization of trusses. The method takes advantage of the equation of equilibrium between internal and external forces in the flexibility method of structural analysis. The internal forces are written as the multiplication of cross-sections of members into their stresses. The stress constraints (i.e. limits on the stress values) are then imposed on the problem and eventually, the topology optimization of trusses ends up in a Linear Programming (LP) problem. The solution to the LP problem is straightforward and results in a global optimum. Accordingly, the outcome of our formulation is a global optimum.When the displacement constraints are included among the constraints, the truss topology optimization turns into a nonlinear optimization problem. To convert the problem to a linear programming problem, we used discrete design variables and converted the problem to a binary (zero-one) integer programming. Several examples were solved and compared to the published examples in the literature. It was observed that our method of truss topology optimization ends up with the same results as the previous research works, but with much less calculations. Nevertheless, our results are proved to be the global optimum, whereas the methods used in the literature cannot prove their global optimality

In this paper, a semi-analytical solution is presented for the free vibration analysis of a three-phase polymer-based truncated conical shell reinforced with Graphene NanoPlatelets (GNPs) and glass fibers, embedded in an elastic foundation. The conical shell is modeled based on the First-order Shear Deformation Theory (FSDT), and the elastic foundation is modeled using the Pasternak model. The effective mechanical properties of the three-phase polymer/GNP/fiber composite are estimated utilizing the rule of mixture, Halpin-Tsai model, and the micromechanical relations. The set of the governing equations and associated boundary conditions are derived using Hamilton’s principle, and are solved analytically in the circumferential direction using trigonometric functions and numerically in the meridional direction via the Differential Quadrature Method (DQM). The natural frequencies and corresponding mode shapes are derived for various boundary conditions, including different combinations of clamped, simply supported, and free edges at both ends of the shell. Convergence of the presented numerical solution is examined, the accuracy of the presented results is confirmed, and the effects of various parameters on the natural frequencies of the shell are investigated including the circumferential wave number, semi-vertex angle of the cone, weight fraction of the fibers, weight fraction of the GNPs, and the boundary conditions.

The stochastic meshless local Petrov–Galerkin method is employed for dynamic analysis of multilayer cylinders made of fully saturated porous materials considering uncertainties in the constitutive mechanical properties. The multilayer porous cylinder is assumed to be under shock loading. To approximate the trial functions in the radial point interpolation method  (RPIM), the radial basis functions (RBFs) are utilized. The Monte Carlo simulation is used to generate the random fields for mechanical properties. The results are obtained for various random variables, which are simulated by uniform, normal and lognormal probability density functions with various coefficients of variation (COV), changing from 0 to 20%. The obtained results from the presented stochastic analysis are compared to those obtained from the analysis considering deterministic mechanical properties. The results show that the uncertainty in mechanical properties has a significant effect on the structural responses, especially for big values of COVs.

In the present research, the effect of altering the rotational speed of the Rushton impeller inside the bioreactor was simulated and investigated for proper air distribution and changes in the shear stress rate. The simulation was performed using the multiphase approach of the zero-equation scattered phase model, via the K-Epsilon Standard perturbation model, in stable three-dimensional manner using ANSYS Products 2019 R3 and Ansys CFX software packages. The governing equations of the system were solved by the finite volume method for the entire system. To properly inject air into the bioreactor, a sparger ring was used under the impeller. The results revealed that increasing the impeller rotation speed could help better disperse the air inside the bioreactor. However, it also increases the shear stress rate inside the bioreactor. It was also shown that increasing the speed and getting more energy from it creates turbulence in the liquid. Additionally, its effect on the gas phase is reduced for the rotation speeds more than 150 rpm. Considering the rotation speed of the impeller and its effect on the mixing of gas-liquid phase, the intra-liquid stress and the average mass transfer rate, the speed of 350 to 450 rpm may be considered as the optimal speed. Finally, it was found that by increasing the rotation speed of the impeller, better mixing in the bioreactor could not be achieved and the optimal speed had to be determined.

Rotary friction welding is one of the most important techniques for joining different parts in advanced industries. Measuring the history of thermomechanical and microstructural parameters can be challenging and costly. To address these challenges, the finite element method was used to simulate thermomechanical and microstructural aspects of the welding of identical superalloy Inconel718 tubes. Therefore, in this research, thermomechanical and microstructural simulations were developed to calculate essential mechanical and metallurgical parameters such as temperature, strain, strain rate, volume fraction of dynamic recrystallization, and grain size distribution. Some of these parameters were then used to be verified with experimental test results. In the microstructural simulation, the Johnson-Avrami model was applied to convert thermomechanical parameters to metallurgical factors by using a FORTRAN subroutine. By employing the dynamic recrystallization kinetics model, the thickness of the recrystallization zone in the wall thickness was calculated to be 480 and 850 micrometers at the center and edge of the tube wall, respectively. These values were reported in the experimental measurements as 500 and 800 micrometers, respectively. Additionally, the grain size change from the center to the edge of the wall thickness, close to the weld interface, were predicted from 2.07 to 2.15 micrometers by simulations, which was comparable with the experimental measurements of 1.9 to 2.2 micrometers. Also, different types of curves were represented to investigate the correlation between thermomechanical and microstructural parameters. Predictable results were concluded from microstructure evolutions with changes by thermomechanical results.

A strong magnetic field provides a new method of heat transfer with high heat flux. A numerical simulation for a heat sink with high heat flux under an external uniform magnetic field in three different directions is used to investigate the flow field and displacement heat transfer between liquid metal and hot surfaces. Due to its high density and large thermal and electrical conductivity coefficients, gallinsten liquid metal has been used as a working fluid. Discretization of the Navier-Stokes equations is performed by the upstream second-order finite volume method. The results show that the effect of applying a magnetic field in the Y and Z directions (perpendicular to the flow axis) on the heat sink with a Hartmann number of 88, improves the displacement heat transfer coefficient by 15% and 8%, respectively. The best efficiency in increasing the heat transfer was obtained by applying the magnetic field in the Y direction. By applying the magnetic field in the Y direction to the heat sink, the displacement heat transfer coefficient was increased by 11.9% for Hartman number of 44, 15% for Hartman number of 88, and 17.7% for Hartman number of 132, compared to zero Hartman number. By applying the magnetic field in Z direction to the heat sink, the displacement heat transfer coefficient was increased by 4.3% for Hartmann number of 44, 8% for Hartmann number of 88, 11.4% for Hartmann number of 132 and 22.1% for Hartmann number of 330, compared to Hartmann number of zero. Also, the results show that the effect of applying a magnetic field perpendicular to the flow axis has increased the velocity gradient. As a result, the pressure drop and friction coefficient of the heat sink have increased.