Wael Elleithy

Iterative Coupling of BE and FE Methods in Elastostatics

Iterative domain decomposition coupling is one of the recent approaches for combining the boundary element method (BEM) and the finite element method (FEM). The domain of the original problem is subdivided into two sub-domains, which are separately modeled by the FEM and BEM. Successive renewal of the variables on the interface of the two sub-domains is performed through an iterative procedure to reach the final convergence. In this paper, we investigate the iterative method. We also establish the convergence conditions. A simple numerical example is given to elaborate on the effect of different factors such as initial guess, boundary conditions, and geometrical and material properties of the sub-domains on solution convergence.

Interface relaxation algorithms for BEM-BEM coupling and FEM-BEM coupling

This paper presents several interface relaxation algorithms for boundary element–boundary element coupling (BEM–BEM) and for finite element–boundary element coupling (FEM–BEM). The domain of the original problem is sub-divided into sub-domains, which are modeled by the finite element or boundary element methods. The multi-domain system is coupled using smoothing operators on the inter-domain boundaries. Separate computations for the BEM and FEM sub-domains and successive update of the boundary conditions at the interfaces are performed until convergence is achieved. The interface relaxation coupling algorithms preserve the nature of the FEM and BEM. Further, they do not require any access to the matrices generated by the FEM or BEM and make it easier to utilize different software in different sub-domains.

An overlapping domain decomposition approach for coupling the finite and boundary element methods

Abstract An overlapping iterative domain decomposition approach for the coupling of the finite element method (FEM) and the boundary element method (BEM) is presented in this paper. In this proposed method, the domain of the original problem is subdivided into a FEM sub-domain and a BEM sub-domain, such that the two sub-domains partially overlap over a common region. The common region is modeled by both methods. A brief discussion on the existing iterative coupling methods and their limitations are given in the first part of this paper. In the second part, the proposed overlapping method is described and the convergence conditions are presented. Two numerical examples are given to demonstrate the capability of the proposed method for handling cases where the Neumann boundary conditions are specified on the entire external boundary of the FEM or BEM sub-domains.

Convergence of the domain decomposition finite element-boundary element coupling methods

In this work, we analyze three available domain decomposition methods. We also establish the convergence conditions. The theoretical analysis provides an interval in which a relaxation parameter has to be chosen in order to achieve convergence. Moreover, it allows the selection of the relaxation parameter so that convergence is achieved with the minimum number of iterations. Several example problems are given for elaboration.

Interface Relaxation Algorithms For Coupling The FEM And BEM

In this paper, we present two interface relaxation algorithms, namely the geometric construction based algorithm and the Robin relaxation algorithm, for coupling the finite element and boundary element methods. Coupling consists of partitioning the domain onto finite element and boundary element sub-domains and imposes some boundary conditions on the interface. The computations are carried out separately for both sub-domains. The obtained solutions do not satisfy the interface boundary conditions and interface relaxation is applied to obtain new interface boundary values, which satisfies them better. The procedures are iterated until convergence is achieved. A high level description of the two algorithms is presented. We also present a description of various existing domain decomposition coupling algorithms, which may be viewed as interface relaxation coupling ones. A simple numerical example is given for illustration. The interface relaxation algorithms presented in this paper are extendable to multi-domain coupling and to solve nonlinear problems.

EFFECT OF HOLIDAYS AND SURFACE DAMAGE TO FBEC ON REINFORCEMENT CORROSION

Abstract This study was conducted to evaluate the effect of holidays and damage to fusion bonded epoxy coating (FBEC) on reinforcement corrosion in chloride-contaminated concrete. The effect of these parameters on the corrosion of FBEC bars was compared with corrosion of mild steel by measuring the corrosion potentials and corrosion current density at regular intervals. The corrosion current density measurements indicated that the defect-free FBEC bars were in a passive condition in the concrete specimens with up to 2% chloride by weight of cement. The long-term maintenance-free performance was not assured in the concrete specimens with chloride concentration of 1% and above and made with FBEC bars having >1% surface damage or with 3 holidays per linear foot. The long-term performance of FBEC bars with up to two pinholes (ASTM A 775 limit) was satisfactory in the concrete specimens with up to 2% chlorides, by weight of cement. Furthermore, surface damage to FBE coating is more critical compared to holidays, from the point of view of corrosion of FBEC bars, in chloride-bearing concrete.

Multi-region adaptive finite element-boundary element method for elasto-plastic analysis

In this paper, a multi-region adaptive finite element–boundary element (FEM-BEM) method for elasto-plastic analysis is presented. The method is suitable for several plasticity models, i.e. von-Mises, Tresca, Mohr–Coulomb, Drucker–Prager, Hill, and Hoffman yield criteria. The domain of the original problem is divided into the finite element and the boundary element sub-domains: the FEM is utilized in regions where plastic material behaviour is expected to develop, whereas the complementary linear elastic region is approximated using the symmetric Galerkin BEM. The adaptive method estimates the finite element and boundary element sub-domains, automatically generates the corresponding meshes and adapts the sub-domains, according to the state of computation.

The use of Past Projects as Means to Enhance the Education Experience of Civil Engineering Students

In view of the importance of undergraduate students cognitive learning experience in higher education, this study was conducted in order to investigate the effectiveness of the use of past civil engineering projects as case studies. The outcomes indicate that the use of case studies enhances the students educational experiences that conduce to cognitive learning and motivate for future ethical practice. In general, the use of case studies reassures the students aspiration in becoming practicing civil engineers upon graduation.

Effect of thermal variations on bond strength of fusion-bonded epoxy-coated bars

Fusion-bonded epoxy coating is extensively used to enhance the corrosion resistance of reinforcing steel. The bond strength between these bars and the concrete is expected to be less than that of the uncoated bars and it may be further impaired due to prolonged exposure to thermal variations. This investigation was conducted to evaluate the effect of thermal variations, simulating the changes in the night to day temperature, on the bond strength of fusion-bonded epoxy-coated steel reinforcement. The pull-out specimens, prepared using bars of two different sizes and two coating thickness, were exposed to thermal cycling. The critical and ultimate bond strength of the fusion-bonded epoxy-coated bars were compared with that of the uncoated bars. The results indicated a reduction in the critical bond strength between concrete and the fusion-bonded coated bars. Furthermore, the difference between the critical bond strength in the coated and uncoated bars decreased with increasing thermal cycles, indicating that thermal variation has a greater effect on bond strength than the coating thickness.

Some Recent Developments in Coupling of Finite Element and Boundary Element Methods - Part I: An Overview

Conventional and a class of domain decomposition finite element–boundary element coupling (FEM–BEM) methods are reviewed. This is Part I of two papers. In Part II, a review of the mixed Dirichlet-Neumann domain decomposition FEM-BEM coupling method is presented and optimal dynamic values of the relaxation parameters for the mixed Dirichlet-Neumann FEM-BEM coupling method are, furthermore, derived.