This paper is concerned with a method for the analysis of two-dimensional crack problems using the boundary element method. In this method, a domain to be analyzed is divided into two regions: the near-tip region, which is a circular in shape and centered at the crack tip, and the outer region. The displacements and stresses in the near-tip region are expressed by the truncated infinite series of the eigenfunction with unknown coefficients. The outer region is formulated by the boundary element method. The system of linear algebraic equations with respect to nodal displacements, nodal tractions and the coefficients of the series are constructed by discretized boundary integration in the outer region and the continuity conditions. The two parallel edge cracked rectangular plate without symmetry under a uniform tension is treated and the dimensionless stress intensity factors are calculated.

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In this paper, the three boundary value problems on Poisson's problem are analyzed by using a new meshless method that is called the over-range collocation method (ORCM). By introducing some collocation points, which are located at outside of domain of the analyzed body, unsatisfactory issue of the positivity conditions of boundary points can be avoided. Convergence studies in the numerical examples show that the ORCM possesses good convergence for both the unknown variables and their derivatives. Quite accurate numerical results calculated by both regular nodal models and irregular nodal models have been obtained.

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The linear elastic cantilever beam problem is analyzed by using the over-range collocation method (ORCM). Because the over-range points are used only in interpolating calculation, no over-constrained condition is imposed into the solved problems. While the over-range points can be used in interpolating calculation of boundary points, so that the unsatisfactory issue of the positivity conditions of boundary points in collocation methods can be avoided. Convergence studies show that the ORCM possesses good convergence for both the displacement and deformation energy, and quite accurate numerical results have been obtained.

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Characteristics of void coalescence process due to hydrogen load effects in the multiple void array are simulated using the finite element method. The goals of this paper are to characterize the effects of hydrogen on the void coalescence process within the multiple void array, and to determine the void array and void volume fraction configuration in which hydrogen has the strongest effect on the occurrence of void coalescence. We use the couple analyses between the large deformation elastic-plastic analysis in the presence of hydrogen for structural analysis and hydrogen diffusion analysis using the hydrogen enhanced localized plasticity (HELP) theory. These coupled analyses are applied to the five different models with the different void volume fraction and void array. The numerical results show that both hydrogen and the void characteristics - void array and void volume fraction - affect metallic material failure. The internal necking void coalescence occurs in the square void array while the void sheet mode of coalescence occurs in the diagonal void array. Hydrogen has the strongest effect on the occurrence of void coalescence when the void volume fraction is large and the void array is square, induces a pronounced localized plastic deformation at the ligament between voids, and is present in high concentrations in regions with high values of the equivalent plastic strain.

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An anisotropy-resolving subgrid-scale (SGS) model for large eddy simulation was investigated. This SGS model is constructed by combining an isotropic linear eddyviscosity model with an extra anisotropic term. Although the basic performance of this model was validated by application to fundamental test cases, there still remain several points to be further investigated. In particular, it had not been made clear how the extra anisotropic term worked for improving the predictive performance under a coarse gridresolution condition. For this purpose, we investigated in detail the predicted turbulent structures in the near-wall region. In this study, primary attention was given to the role of the extra anisotropic term in the model. By comparison of the results obtained with and without this extra anisotropic term, it was found that this term was generally effective to enhance unsteady motions of vortex structures generated in the near-wall region. These motions are thought to increase the Reynolds shear stress, resulting in the improvement of the prediction accuracy.

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The direct method developed in the first paper (J. Comp. Sci. Tech. 6 (2012), 147-156) to solve the finite-difference systems for Poisson's equation is extended to the cases with more complex boundary conditions. The first case is the plasma reactor of the international standard and the second is the three-dimensional plasma reactor. In the first case the computer execution time for the present method is 1 to 3% of the time for SOR with Chebyshev acceleration. In the second case the computer time for the present method is nearly the same as that for FFT method.

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