Origin Intensity Factor Research Articles

Improved singular boundary method for elasticity problems

This paper presents a simple approach to evaluate origin intensity factors of the singular boundary method (SBM), a recent strong-form boundary discretization numerical technique. The SBM overcomes the perplexing ‘fictitious boundary issue’ associated with the method of fundamental solutions (MFS) and in it the source points and collocation points coincide on the real physical boundary. By analogy with the boundary element method (BEM), we develop a desingularization strategy for the direct computation of singular kernels in the SBM, without losing the merits of being truly meshless, integration-free, and easy-to-implement. In addition, an efficient non-linear co-ordinate transformation is employed to tackle the near singularities of the kernel functions, when the calculation point is close to, but not on, the boundary. It is shown that the proposed SBM fully inherits the merits of the BEM and MFS. The advantages, disadvantages and potential applications of the proposed method, as compared with the MFS and the BEM, are also examined and discussed in detail.

Solving Inhomogeneous Problems by Singular Boundary Method

This study makes the first attempt to extend the singular boundary method (SBM) to inhomogeneous problems in conjunction with the dual reciprocity method (DRM). The SBM is a new boundary-type meshless method and utilizes the fundamental solution to calculate the homogeneous solution of the governing equation of interest, where the inverse interpolation technique is designed to evaluate the origin intensity factor while overcoming the singularity of the fundamental solution at the origin. In this study, the DRM is employed to evaluate the particular solution of Poisson equation with multiquadratic functions. The efficiency and accuracy of the proposed SBM-DRM scheme are tested to the three benchmark inhomogeneous Poisson problems. We also demonstrate the stability of the SBM-DRM scheme in dealing with noisy boundary data.

An Improved Formulation of Singular Boundary Method

AbstractThis study proposes a new formulation of singular boundary method (SBM) to solve the 2D potential problems, while retaining its original merits being free of integration and mesh, easy-to-program, accurate and mathematically simple without the requirement of a fictitious boundary as in the method of fundamental solutions (MFS). The key idea of the SBM is to introduce the concept of the origin intensity factor to isolate the singularity of fundamental solution so that the source points can be placed directly on the physical boundary. This paper presents a new approach to derive the analytical solution of the origin intensity factor based on the proposed subtracting and adding-back techniques. And the troublesome sample nodes in the ordinary SBM are avoided and the sample solution is also not necessary for the Neumann boundary condition. Three benchmark problems are tested to demonstrate the feasibility and accuracy of the new formulation through detailed comparisons with the boundary element method (BEM), MFS, regularized meshless method (RMM) and boundary distributed source (BDS) method.

Singular boundary method for steady-state heat conduction in three dimensional general anisotropic media

The singular boundary method (SBM) is a recent strong-form meshless boundary collocation method. Like the method of fundamental solutions (MFS), the SBM uses the fundamental solution of the governing differential equation of interest as the basis function and is mathematically simple, truly meshless, accurate, and easy-to-program. Unlike the MFS, the SBM, however, uses the concept of the origin intensity factor to isolate the singularity of the fundamental solutions and overcomes the fictitious boundary issue which has long perplexed the MFS. This study makes the first attempt to apply the SBM to steady-state heat conduction in three-dimensional (3D) anisotropic materials. Five benchmark numerical examples demonstrate that the SBM is accurate, convergent, stable, and computationally efficient in solving this kind of problems.

Infinite domain potential problems by a new formulation of singular boundary method

This study proposes a new formulation of singular boundary method (SBM) and documents the first attempt to apply this new method to infinite domain potential problems. The essential issue in the SBM-based methods is to evaluate the origin intensity factor. This paper derives a new regularization technique to evaluate the origin intensity factor on the Neumann boundary condition without the need of sample solution and nodes as in the traditional SBM. We also modify the inverse interpolation technique in the traditional SBM to get rid of the perplexing sample nodes in the calculation of the origin intensity factor on the Dirichlet boundary condition. It is noted that this new SBM retains all merits of the traditional SBM being truly meshless, free of integration, mathematically simple, and easy-to-program without the requirement of a fictitious boundary as in the method of fundamental solutions (MFS). We examine the new SBM by the four benchmark infinite domain problems to verify its applicability, stability, and accuracy.