نشریه روش های عددی در مهندسی
سال چهل و سوم شماره 2 (تابستان 1403)

Unlike triangular/tetrahedral elements used in the finite element method for two/three-dimensional problems, local refinement of meshes composed of quadrilateral/hexahedral elements while maintaining the compatibility is challenging, and often results in severe distortion of the elements. A well-known and widely used approach to address this issue is the local mesh refinement based on transitional elements with hanging nodes. The key point in this method is enforcing the displacement continuity at the transitional element boundaries in the presence of hanging nodes. Transitional elements introduced in the literature employ various formulations depending on their placement within the mesh, and are also constrained by a maximum number of hanging nodes. along the element boundary. Therefore, their implementation for a general case is quite complicated. This paper presents a novel transitional element based on alternative shape functions, which offers a unified formulation for different placements of transitional elements in the mesh, applicable to any number of hanging nodes. Additionally, an analytical proof is provided to demonstrate the continuity and partition of unity properties in the proposed method, used in local mesh refinement. Finally, numerical examples in two and three dimensions are simulated to compare the accuracy and convergence of the proposed method against the existing methods in the literature.

Orthotropic plates used in composite structures are subject to local buckling, including compressive buckling. In the process of designing and building most large structures or instruments with complex geometry, joints in the structure are unavoidable. Today, adhesive joints are widely used in connecting composite structures due to some advantages over mechanical joints. In this article, the buckling phenomenon of orthotropic rectangular multilayer plates connected with glue has been investigated, and the force effects of the glue layer under buckling loading conditions have been studied. In order to obtain the critical buckling loads under different boundary conditions, the generalized differential quadrature method (GDQM) has been used. Buckling analysis is presented based on first-order shear deformation theory (FSDT) for carbon/epoxy, glass/epoxy and Kevlar/epoxy composite materials with different porcelain layers. The effect of thickness and type of the adhesive as a bonding layer has been investigated. In plates made of a type of porcelain layer, two-way carbon epoxy plates show higher buckling strength, and in general, the higher the ratio of length to width of the plates is, the higher the buckling strength will be. In the connections, the obtained results have been compared with the results from the finite element analysis in ABAQUS commercial software.

In recent years, many studies have been conducted on the field of microchannels' sinks. The microchannel sink absorbs heat from other equipments and transfers it to the fluid by maximizing the contact area. In the present research, three-dimensional water flow, nanofluid and hybrid nanofluid in heat sink with constant heat flux, have been studied. The simulation process have been done in the commercial software ANSYS fluent. In the simulation process, the constant and uniform heat flux boundary condition has been applied to the bottom of the heat sink's wall. The influence of variables such as the nanoparticles volume fraction, nanoparticles types and Reynolds values on the hydrodynamic performance and heat sink will be investigated. After this stage, two types of nanofluid and one type of hybrid nanofluid in 0.04, 0.02 and 0.01 volume fractions will be considered as well. In this paper, first the pressure drops and heat transfer will be examined, and then the best nanofluid will be defined by considering the coefficient of thermal performance. The simulations show that the heat transfer decreases with increasing the volume fraction in the water-aluminium oxide nanofluid. On the other hand, the heat transfer increases with raising the volume fraction in the water-copper nanofluid. Also in the water-aluminium oxide-copper hybrid nanofluid, the heat transfer rises up in the 0.04 volume fraction in the range of 400 and above values for the Reynolds number.

In this paper, a two-dimensional half-space model is presented in the presence of a subsurface circular cavity under a uniform surface scalar pulse. In this regard, a dual reciprocity boundary element method (DR-BEM) was successfully developed, in which the discretizing process was only applied to the boundary of the model as well as a few internal points. The simple formulation and step-by-step transient analysis in the absence of time-domain fundamental solutions were some of the characteristics of the implemented approach. First, by introducing the method and briefly presenting the formulation, a time-domain algorithm was prepared based on the mentioned approach, then it was validated by comparing with the existing analytical solutions. Moreover, by modeling a half-space domain including a subsurface circular cavity, the transient displacement was obtained at different points of the ground surface and the cavity wall, subjected to the surface pulse of the Ricker wavelet type function. The results showed that the presence of the cavity was effective not only in changing the distribution pattern, but also in the formation of safe areas behind the wave front. The efficient approach is recommended to all researchers in the field of geotechnical earthquake engineering, especially in the analysis of surface explosions.

The supply chain of a product encompasses all organizations and companies involved in the processes of procurement, supply, production, distribution, and delivery of that product to the customer. One of the most critical aspects of supply chain management is the coordination among these elements. Perishable products, which are recognized as widely used items, hold a significant position in inventory control research because these items may deteriorate, evaporate, or degrade over time, leading to a loss of value or quantity. Therefore, determining the order quantity and timing for such products is crucial. Additionally, supply chain members often face budget constraints, and the manufacturer secures part of the required liquidity at the beginning of production by receiving a portion of the total order amount upfront. Determining this portion is also of great importance. In this study, a two-level supply chain, consisting of a wholesaler and a manufacturer producing a perishable product, has been examined. To foster long-term coordination and collaboration among members and to maximize supply chain profit, a discount mechanism has been utilized. This mechanism includes one discount based on order timing and another based on the prepayment ratio. Finally, a numerical example has been analyzed, and sensitivity analysis has been conducted on the problem's parameters. The results demonstrate that by implementing the coordination mechanism and determining the optimal values for order quantity, order timing, and prepayment ratio, the profit of both the members and the entire supply chain increases in the coordinated state compared to the uncoordinated state.

The isogeometric method was introduced to bridge the gap between computer-aided design (CAD) and analysis. This method offers advantages such as precise geometric modeling, suitable refinement methods, easy access to higher-order functions, and higher computational accuracy. The aim of this research is to provide an efficient method for applying the distributed loads on curved surfaces in isogeometric analysis. One of the main challenges in this method is how to apply boundary conditions on complex geometries. In curved models, some control points may not lie on the geometry, leading to ambiguity in the distribution of loads on these points. This study uses NURBS functions, which are standard non-interpolatory functions in CAD systems, to approximate the solution space and describe the geometry. Additionally, to leverage the capabilities of CAD tools, the process of importing geometries created in Rhino into isogeometric analysis using Bézier extraction is explained. The results confirm the accuracy and efficiency of the proposed method.

Aluminum wires, due to their extensive use in various industries, particularly in the electrical industry, have been of significant importance. One of the most effective methods for investigating microstructure is the utilization of crystal plasticity theory. In this study, the microstructural changes of a 1000 aluminum wire (grade 1350) with a diameter of 4 mm under torsional loading are examined using a spectral solver (Fast Fourier Transform) in DAMASK software. For this purpose, Crystal Plasticity Fast Fourier Transform (CPFFT) is applied to a Representative Volume Element (RVE) containing 100 grains. The initial non-random texture is assigned to the Representative Volume Element (RVE) as quaternion numbers, and then, using a crystal plasticity spectral solver, the deformed quaternion numbers due to shear deformation are extracted. Using the MTEX toolbox available in Matlab, these numbers are transformed into pole figures (PF), inverse pole figures (IPF), and orientation distribution functions (ODF) of grains were converted and plotted. The accuracy of CPFFT results is validated against experimental results from Electron Backscatter Diffraction (EBSD) tests. Comparison of the results for a π-radian rotation sample shows that components A، A^*1 ، A^*2، B and B are created at the pole figure results, but did not indicate any component from the orientation distribution function in both EBSD and CPFFT test samples.

Bone has a hierarchical structure which features a complex arrangement at different length scales, endowing it with unique mechanical, chemical, and biological capabilities. To understand the mechanical properties of bone, one must consider its hierarchical structure as well as its composition. In the current research, two-dimensional numerical models of the cortical tissue microstructure of bone were created as three-phase and four-phase composites by scripting in Python, and were imported into the Abaqus software. Subsequently, fracture analysis in the transverse section of dense tissue under tensile loading was conducted using the phase-field method formulation. Initially, as a benchmark problem, data related to bovine pelvic bone was attributed to a three-phase composite, and after validating the implemented phase-field method, the primary simulation was performed for three-phase and four-phase models, with data related to human cortical bone tissue. Then, for each of the simulated three-phase and four phase models with human data, a stress-strain diagram in the tensile loading state was extracted. The outputs, obtained from the simulation performed on the two numerical models, differed from each other. The difference indicates the significant role of the bone tissue microstructure in fracture. The results showed that the ultimate strength of the three-phase model is greater than that of the four-phase model. The presence of cement lines as a weaker material phase compared to other material phases caused this difference. Conversely, the flexibility of the four-phase model was greater than that of the three-phase model. This study demonstrated the role of cement lines in increasing flexibility and reducing ultimate strength. This feature could be a mechanism for deviation or even stopping a crack in the structural model. Additionally, at the end of the work, the effect of increased porosity on the reduction of the final strength of the bone was examined, and it was shown that with increased porosity, the final strength will significantly decrease.