Interior Boundary Research Articles

Boundary integral equation method for periodic dissimilar elastic inclusions in an infinite plate

This paper provides a theoretical derivation and a numerical solution for an infinite plate with periodic dissimilar inclusions. The matrix and periodic inclusions have different elastic properties, and a remote loading is applied for the infinite matrix. The original problem is decomposed into two problems, one is the interior boundary value problem (BVP) and the other is the exterior BVP. Both BVPs are formulated in the form of complex variable boundary integral equation (CVBIE). In addition, both BIEs are solved numerically after discretization of the integral equations. For the exterior BVP with periodic notches, the remainder estimation technique (RET) is suggested to evaluate the influence to the central notch from many (from Nth to infinity) neighboring notches. This will significantly improve the efficiency of solution. Two numerical examples are provided. In the examples, the ratio of the two shear moduli of elasticity changes from near 0 (1.d–6), 0.1, 0.5, 1, 2 to 10.

Study of Circular Tapping Plates, with a Circumferential Vertical Load at the Interior Boundary by Transfer-Matrix Method

The work presents a calculus of the circular tapping plates, embedded at the exterior circumference, charged with a concentrated circumferential vertical load at the interior circumference, using the Transfer-Matrix Method. The approach is based of the theory of Dirac’s and Heaviside’s functions and operators. The circular plate’s calculus is important for a lot of industry domains, including the robotics too. We can obtain the two state vectors: for the first ring-the exterior circumferential element and for the latest ring-the interior circumferential element. We can calculate after, for the values r0<r<R, all the state vectors for all the rings of the circular tapping plate. With the Transfer-Matrix Method is very easy to program this calculus algorithm.

The Stochastic Reflection Problem in Hilbert Spaces

We construct a Markov process X associated with the stochastic reflection problem on a closed convex subset with non empty interior and smooth boundary in a Hilbert space, as a solution to a random convex control problem. The transition semigroup corresponding to X is exactly that defined by the Kolmogorov equation with Neumann homogeneous boundary conditions (see [3]).

A constitutive model for modeling of the deformation behavior in microforming with a consideration of grain boundary strengthening

Micro-manufacturing technology is now getting more and more important in industries due to product miniaturization. Microforming, as one of the micro-manufacturing processes, has attracted much attention in the past decade. In microforming, the traditional metal-forming theories are often crippled or rendered totally inefficient in analysis of micro-deformation behavior due to the size effect arising from the part geometry scaling down from macro- to micro-scale. To reveal its deformation behavior, the size effect needs to be considered and appropriate constitutive models to be developed. In this research, by employing the surface layer and composite models, each grain in the microforming workpiece is divided into two portions, viz., grain interior and grain boundary. The flow stress of grain is determined by the ‘law of mixtures’ based on the flow stresses of grain interior and boundary, and in such a way that a new constitutive model is developed with a consideration of grain boundary strengthening. This new constitutive model considers both the grain and geometry size effects simultaneously. Using this newly developed model, the micro-bulk upsetting and the micro-tensile test of sheet metal are numerically simulated by Finite Element Method (FEM). The grain and geometry size effect on the flow stress of workpiece is thus investigated. The model is further applied to the micro-extrusion of CuZn30 alloy with three different grain sizes. The validity of the model is thus verified through physical experiments and FEM simulations of three different micro-plastic deformation processes.

Studies of the interactive effect of specimen and grain sizes on the plastic deformation behavior in microforming

Microforming process provides an efficient approach to fabricating microparts via microscaled plastic deformation. However, the material properties change and the size effect occur when the workpiece size is scaled down from macro- to microlevel, which makes the development of microforming system difficult. It is thus necessary to study the size effect phenomena and microscaled deformation behaviors. In this research, the upsetting of annealed pure copper cylinders with different sizes from macro- to microscale is conducted to investigate the interactive effect of specimen and grain sizes on material deformation behavior. It is found that flow stress decreases and surface roughening and inhomogeneous flow take place with the increase of grain size and the decrease of specimen size. Furthermore, the properties of grain interior and grain boundary change, and the properties of surface grains become significant in the overall deformation behavior. It leads to the deviation between the Hall–Petch relation and the experimental results. It is further revealed that the flow stress has a linear relationship with the ratio of specimen size to grain size (D/d) at a given strain, and the change rate of the flow stress with D/d could be independent of strain. By examining the changes of working hardening and slip distance, it is found that there could be a delay in the formation of dislocation cell, and the slip distance and the size of dislocation cell could increase with the decrease of D/d. The presented size effect phenomena and the discussed physics thus provide a basis for the further exploration of the microscale plastic deformation behavior.

Coupling of Discontinuous Galerkin Finite Element and Boundary Element Methods

This paper presents three new coupling methods for interior penalty discontinuous Galerkin finite element methods and boundary element methods. The new methods allow one to use discontinuous basis functions on the interface between the subdomains represented by the finite element and boundary element methods. This feature is particularly important when discontinuous Galerkin finite element methods are used. Error and stability analysis is presented for one of the methods. Numerical examples suggest that all three methods exhibit very similar convergence properties, consistent with available theoretical results.

Effect of mold temperature on the microstructure and corrosion properties of a 14-karat gold alloy

The objective of this research was to investigate the effect of mold temperature on grain interior and grain boundary reactions in a14-karat gold alloy. The alloy (Au-15%Ag-3%Pd-24 mass%Cu) was cast into an investment with different mold temperatures (22, 250,400, and 700°C) and then analyzed using SEM, X-ray diffraction, and potentiodynamic polarization tests. Lower mold temperatures(22 and 250°C) retarded a grain boundary reaction evidently present when using higher mold temperatures (400 and 700°C). Phase separation, which was manifested as a dual phase grain boundary nodular formation, was observed at a higher degree at 400°C mold temperature than at 700°C. The corrosion potentials of alloys cast at lower mold temperatures were more noble than those cast at higher mold temperatures, suggesting improved corrosion properties. Results of this study showed that the microstructure, crystalline phases present, and corrosion properties of 14-karat gold alloy were keenly influenced by the mold temperature, which controls and influences the cooling rate.

On some structures of soft topology

In this paper, we define soft exterior and study its basic properties. We establish several important results relating soft interior, soft exterior, soft closure, and soft boundary in soft topological spaces. Moreover, we characterize soft open sets, soft closed sets, and soft clopen sets via soft boundary. All these findings will provide a base to researchers who want to work in the field of soft topology and will help to establish a general framework for applications in practical fields.

A Fourth-Order Accurate Embedded Boundary Method for the Wave Equation

A fourth-order accurate embedded boundary method for the scalar wave equation with Dirichlet or Neumann boundary conditions is described. The method is based on a compact Pade-type discretization of spatial derivatives together with a Taylor series method (modified equation) in time. A novel approach for enforcing boundary conditions is introduced which uses interior boundary points instead of exterior ghost points. This technique removes the small-cell stiffness problem for both Dirichlet and Neumann boundary conditions, is more accurate and robust than previous methods based on exterior ghost points, and guarantees that the solution is single-valued when slender bodies are treated. Numerical experiments are presented to illustrate the stability and accuracy of the method as well as its application to problems with complex geometries.

J011025 VOFモデルと非反復時間進行アルゴリズムを用いたタンクスロッシング非定常問題の数値的研究

It is desirable that fuel is continuously supplied to the gasoline tank intake, even when we have got on vehicle with nearly empty fuel. As a means which reduces surface agitation by sloshing, giving baffles to a tank is often considered. In this study, we simulate sloshing phenomena based on the Navier-Stokes equation by using of volume of fluid (VOF) model and non iterative time advancement (NITA) scheme. We examine the accuracy and efficiency of calculation by using of NITA scheme, which varies depending on two kinds of algorithms and under-relaxation factors. In the simulation of flow visualization, the tank with baffles is analyzed first. Then, the baffles are switched from wall boundaries to interior boundaries and the tank without baffles is analyzed under the same conditions as the tank with baffles. Finally, liquid interface and velocity magnitude are indicated by a contour.

Numerical solution of elastic inclusion problem using complex variable boundary integral equation

Based on a complex variable boundary integral equation (CVBIE) suggested previously, this paper provides a numerical solution for the elastic inclusion problem using CVBIE. A dissimilar elastic inclusion is embedded in the infinite matrix. The original problem is decomposed into two problems. One is an interior boundary value problem (BVP) for the elastic inclusion, while the other is an exterior BVP for the matrix with notch. Both problems are connected by conventional boundary integral equations (BIEs) in complex variables. After performing discretization for the coupled BIEs, the inverse matrix technique is suggested to solve the relevant algebraic equations. Based on the properties of some integral operators, three ways for the inverse matrix technique are suggested. Several numerical examples are carried out to prove the efficiency of the suggested method.

Evaluation of Sub-Zonal Airflow Models for the Prediction of Local Interior Boundary Conditions – Natural and Forced Convection Cases

Currently, researchers are striving to advance the possibilities to calculate the integrated phenomena of heat, air and moisture flows in buildings, with specific focus on the interactions between the building zones and building components. This paper presents an investigation of the capability and applicability of the sub-zonal airflow model to predict the local indoor environmental conditions, as well as the local surface transfer coefficients near building components. Two test cases were analyzed for, respectively, natural and forced convection in a room. The simulation results predicted from the sub-zonal airflow models are compared to experimental data and numerical computational fluid dynamics (CFD) results. The study shows that sub-zonal models combined with an appropriate surface transfer coefficient model are able to give reliable predictions of the local indoor environmental conditions and surface transfer coefficients near the building component for the analyzed cases. The relatively short computation time and flexibility of the sub-zonal model makes the application attractive for transient simulation of heat, air and moisture transport in buildings. However, the availability of appropriate reference conditions, for example experimental or numerical results, is a prerequisite for the development of a reliable sub-zonal model.

Homogenization of the diffusion equation with nonlinear flux condition on the interior boundary of a perforated domain — the influence of the scaling on the nonlinearity in the effective sink-source term

In this paper, we study the asymptotic behavior of solutions ue of the initial boundary value problem for parabolic equations in domains \( {\Omega_\varepsilon } \subset {\mathbb{R}^n} \), n ≥ 3, perforated periodically by balls with radius of critical size eα, α = n/(n − 2), and distributed with period e. On the boundary of the balls a nonlinear third boundary condition is imposed. The weak convergence of the solutions ue to the solution of an effective equation is given. Furthermore, an improved approximation for the gradient of the microscopic solutions is constructed, and a corrector result with respect to the energy norm is proved.

A Dynamically Consistent Closure for Zonally Averaged Ocean Models

Abstract Simple idealized layered models and primitive equation models show that the meridional gradient of the zonally averaged pressure has no direct relation with the meridional flow. This demonstrates a contradiction in an often-used parameterization in zonally averaged models. The failure of this parameterization reflects the inconsistency between the model of Stommel and Arons and the box model of Stommel, as previously pointed out by Straub. A new closure is proposed. The ocean is divided in two dynamically different regimes: a narrow western boundary layer and an interior ocean; zonally averaged quantities over these regions are considered. In the averaged equations three unknowns appear: the interior zonal pressure difference Δpi, the zonal pressure difference Δpb of the boundary layer, and the zonal velocity uδ at the interface between the two regions. Here Δpi is parameterized using a frictionless vorticity balance, Δpb by the difference of the mean pressure in the interior and western boundary, and uδ by the mean zonal velocity of the western boundary layer. Zonally resolved models, a layer model, and a primitive equation model validate the new parameterization by comparing with the respective zonally averaged counterparts. It turns out that the zonally averaged models reproduce well the buoyancy distribution and the meridional flow in the zonally resolved model versions with respect to the mean and time changes.

Some properties of soft topological spaces

For dealing with uncertainty researchers introduced the concept of soft sets. Shabir and Naz (2011) [28], defined several basic notions on soft topology and studied many properties. In this paper, we continue investigating the properties of soft open (closed), soft nbd and soft closure. We also define and discuss the properties of soft interior, soft exterior and soft boundary which are fundamental for further research on soft topology and will strengthen the foundations of the theory of soft topological spaces.

Boundary integral equation method for two dissimilar elastic inclusions in an infinite plate

This paper provides a numerical solution for an infinite plate containing two dissimilar elastic inclusions, which is based on complex variable boundary integral equation (CVBIE). The original problem is decomposed into two problems. One is an interior boundary value problem (BVP) for two elastic inclusions, while other is an exterior BVP for the matrix with notches. After performing discretization for the coupled boundary integral equations (BIEs), a system of algebraic equations is formulated. The inverse matrix technique is suggested to solve the relevant algebraic equations, which can avoid using the assembling of some matrices. Several numerical examples are carried out to prove the efficiency of suggested method and the hoop stress along the interface boundary is evaluated.

Wood Board Defects Sorting Based on Method of Possibilistic C-Means Improved Support Vector Data Description

This paper exposes automatic classification for wooden board according to its knot defects. A four-parameter-classification vector, which includes the knot size and red component pixels of interior and exterior and boundary part of the knot, is formed to recognize the knot type. A possibilistic c-means (PCM) improved support vector data description (SVDD) method was proposed to construct a multi-classifier to classify four types of wood knots. The results obtained with our method show a real improvement of the recognition rate, which is 94%, compared to the original SVDD classifier, which recognition rate is just 86%, and experiments also testify PCM can help SVDD overcome the shortage of being sensitive to the noises and outliers.

Numerical solution of Stokes flow generated by vortices: part 1: around an elliptical cylinder

In this second part paper, the two-dimensional flow inside an elliptical cylinder is studied in the presence of no-slip boundary conditions. For simplicity, line vortices are assumed to be parallel to the elliptical cylinder axis, all axes in the same plane. The interior boundary value problem is solved in terms of a stream function. Numerical solutions for the flow field are obtained by application of the boundary element method. The streamline patterns are sketched for a number of special cases where the elliptical cylinder is either stationary or rotating about its own axis. In particular, some interesting flow patterns are observed in the parameter space which may have potential significance in studies of various flows. We also investigate the change in streamline topologies as the parameters are varied. Eddies of various sizes and shapes appear depending on the primary vortices and their locations. The results presented may be relevant for a variety of applications including vortex mixing. The analytical closed-form expressions for the single vortex inside an elliptical cylinder and double vortices inside circular a cylinder are found.

Interior Boundaries for Degenerate Elliptic Equations and Viscosity Solutions

Linear elliptic equations which are degenerate elliptic on a closed interior surface Γ which divides in two separate parts the original domain are considered. Existence and uniqueness of a viscosity solution in the whole domain and in every of the subdomains is proved under some conditions on the geometry of Γ.

Two dimensional shallow-water flow model with immersed boundary method

This study demonstrates an immersed boundary (IB) method which integrates a depth-averaged two dimensional flow model is proposed to tackle a typical fluid–solid phase problem in fluid dynamics field. The finite-difference scheme with curvilinear coordinate system is employed to discretize the shallow-water flow equations. Lagrangian markers and Eulerian grid are applied to portray the geometric contour of interior boundary and discretize the flow domain, respectively. The Dirac delta function is accordingly conducted to link both Lagrangian and Eulerian coordinate systems. The numerical simulations of single pier are performed and compared to examine the effect of marker’s mesh width, grid size, and the various Dirac delta functions. Experimental data from literatures are compared with numerical results to justify the validity of the proposed IB model. To further demonstrate the model capability, the model is applied to the hypothetical cases of piers in parallel, and compared with theoretical results.