3D mixed boundary elements for elastostatic deformation field analysis

Two-dimensional radial integration displacement discontinuity method with high-order isoparametric elements

On singular integral equations and fundamental solutions of poroelasticity

Applications of the fast multipole fully coupled poroelastic displacement discontinuity method to hydraulic fracturing problems

Revisit of the equivalence of the displacement discontinuity method and boundary element method for solving crack problems

Fatigue failure is probably the most common type of failure in welded construction. It is usually initiates at a stress concentration area within the structure. The fatigue behavior of non-load carrying cruciform fillet welded joint has been studied extensively using boundary element method. The symmetric boundary element method for multiple cracks problem is derived using Betti's reciprocal theorem in auxiliary fictitious state. High order element is proposed to solve the double integrals. The analysis demonstrates that symmetrical Galerkin boundary element method (SGBEM) can be used effectively for analyzing non-load carrying fillet welded cruciform joints containing any number of surface and embedded cracks. The stress intensity factor and the magnification factors Mk are analyzed. General formulation for this kind of fatigue life estimation is derived for engineering design purpose. The fatigue life estimate results are consistent with the code of practice and those of other researchers. This can provide a good method for engineering design under fatigue loading conditions.

Adaptive gridding methods are of fundamental importance both for industry and academia. As one of the computing methods, the Boundary Element Method (BEM) is used to simulate problems whose fundamental solutions are available. The method is usually characterised as constant elements BEM or linear elements BEM depending on the type of interpolation used at the elements. Its popularity is steadily growing because of its advantages over other numerical methods most important of which being that it only involves obtaining data at the boundary and computation of the solution in the domain is merely a case of post processing through the use of an identity. This results in the reduction of the problem dimension by unity. Although there is a reduction in dimension when we use BEM, the method usually results in full matrices which can be expensive to solve. This makes the method costly for problems that require very fine grids like those with hot spots as in the example of impressed current cathodic protection systems (ICCP). The BEM is a global method in nature in that the solution in one node depends on the solutions in all the other nodes of the grid. Hence an error in one node can pollute the solution in all the other nodes. In this thesis, we first focus our attention on defining and studying both the local and global errors for the BEM. This is not a completely new study as the literature suggests, however, our approach is different. We use the basic foundations of the the method to define the errors. Since the method is a global method, first we use the interpolation error on each element to define what we have called a sublocal error. Then using the sublocal error we have defined the local error. Understanding the local errors enabled us study the global error. Theoretical and numerical results show that these errors are second order in grid size for both the constant and linear element cases. Then, having explored errors, we study a method for adaptive grid refinement for the BEM. Rather than using a truly nonuniform grid, we present a method called local defect correction (LDC) that is based on local uniform grid refinement. This method is already developed and documented for other numerical methods such as finite difference and finite volume methods but not for BEM. In the LDC method, the discretization on a composite grid is based on a combination of standard discretizations on several uniform grids with different grid sizes that cover different parts of the domain. At least one grid, the uniform global coarse grid, should cover the entire boundary. The size of the global coarse grid is chosen in agreement with the relatively smooth behaviour of the solution outside the hot spots. Then several uniform local fine grids each of which covers only a (small) part of the boundary are used in the hot spots. The grid sizes of the local grids are chosen in agreement with the behaviour of the continuous solution in that part of the boundary. The LDC method is an iterative process whereby a basic global discretisation is improved by local discretisations defined in subdomains. The update of the coarse grid solution is achieved by adding a defect correction term to the right hand side of the coarse grid problem. At each iteration step, the process yields a discrete approximation of the continuous solution on the corresponding composite grid. We have shown how this discretisation can be achieved for the BEM. We apply the discretisation to an academic example to demonstrate its implementation and later show how to use it for an application as the ICCP system. The results show that it is a cheaper method than solving on a truly composite grid and converges in a single step.

A modular program for Poisson's equation with linear boundary and domain elements

Proposal of numerical models to predict the diffuse field sound absorption of finite sized porous materials – BEM and FEM approaches

Analysis of an interfacial crack in a piezoelectric bi-material via the extended Green’s functions and displacement discontinuity method

In this paper, we propose a two-dimensional (2D) boundary element method (BEM) to explore the coupling properties of two distorted graphene nanoribbons (GNRs) with wrinkles. From the calculation results, it is found that the resonant wavelengths are redshifted compared with a single GNR, and the scattering intensity is greatly increased, due to the coupling between the two GNRs. In the non-degenerate structure, the coupling resonance modes of the two GNRs are the superposition of the resonance modes of every single GNR, and the resonant wavelength and scattering intensity of different modes change differently with the gap between the two GNRs and their heights. When the coupling effect becomes stronger, some modes will split. We explain the results through the charge and current distribution of the GNRs. This work will help to understand the coupling mechanism of surface plasmon resonances of GNRs.

A coupled diffusion-mechanical model with boundary element method to predict concrete cover cracking due to steel corrosion

Extended displacement discontinuity method for analysis of cracks in 2D piezoelectric semiconductors

Boundary element analysis of infinite anisotropic elastic medium containing inclusions and cracks

A direct (potential based) boundary element method (BEM) developed in our company (Romanian Research and Design Institute for Shipbuilding) is briefly presented. It may be applied for the calculation of the potential flow paste the ship hull, also around the lifting bodies like: hydrofoil, nozzle, rudder, propeller. The lifting bodies hydrodynamic calculation has some modelling particularities, e.g.: the wake shape determination, and numerical difficulties, e.g.: the BEM integrals calculation. Therefore the BEM application to such kind of bodies substantially differs from standard BEM application.

A boundary element method (BEM) approach has been developed to solve the time‐dependent 1D advection‐diffusion equation. The 1D solution is part of a 3D numerical scheme for solving advection‐diffusion (AD) problems in fractured porous media. The full 3D scheme includes a 3D solution for the porous matrix, which is coupled with a 2D solution for fractures and a 1D solution for fracture intersections. As the hydraulic conductivity of the fracture intersections is usually higher than the hydraulic conductivity of the fractures and by at least one order of magnitude higher than the hydraulic conductivity of the porous matrix, the fastest flow and solute transport occurs in the fracture intersections. Therefore it is important to have an accurate and stable 1D solution of the transient AD problems. This article presents two different 1D BEM formulations for solution of the AD problems. The particular advantage of these formulations is that they provide one of the most straightforward and simplest ways to couple multiple intersecting 2D Boundary Element problems discretized with linear discontinuous elements. Both formulations are tested and compared for accuracy, stability, and consistency. The analysis helps to select the more suitable formulations according to the properties of the problem under consideration. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004