S. Beyer¹, Ch. Zhang², S. Hirose³, J. Sladek, V. Sladek⁴

Structural Durability & Health Monitoring, Vol.3, No.3, pp. 177-190, 2007, DOI:10.3970/sdhm.2007.003.177

Abstract This paper presents a hypersingular time-domain boundary element method (BEM) for transient dynamic crack analysis in two-dimensional (2-D), homogeneous, anisotropic and linear elastic solids. A finite crack in an infinite or a finite solid subjected to impact loading conditions is investigated. A combination of the classical displacement boundary integral equations (BIEs) on the external boundary and the hypersingular traction BIEs on the crack-faces is applied. The present BEM uses the time-domain dynamic fundamental solutions for anisotropic solids derived by Wang and Achenbach (1994). An explicit time-stepping scheme based on collocation method is developed. Numerical examples More >

Jean-Jacques Sinou¹

Structural Durability & Health Monitoring, Vol.3, No.3, pp. 133-164, 2007, DOI:10.3970/sdhm.2007.003.133

Abstract This paper aims to establish a damage identification methodology, called the Frequencies' Ratio Surfaces Intersection method (FRSI-method), for predicting not only the location and depth of the crack but also the crack orientation in a circular cross section beam. Two new criterions %Δ_i^cracked and %ψ_i,j^cracked that consider only the ratio of the natural frequencies of the cracked beam are introduced and discussed in order to detect the crack parameters. In order to avoid worse diagnostic, it is demonstrated that a robust identification of crack location is possible by investigating the emergence of extra antiresonance peaks… More >

N. Ohno¹, D. Okumura¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.4, No.4, pp. 207-214, 2007, DOI:10.3970/icces.2007.004.207

Abstract The self energy of geometrically necessary dislocations (GNDs) is considered to inevitably introduce the higher-order stress work-conjugate to slip gradient in single crystals. It is pointed out that this higher-order stress stepwise changes in response to in-plane slip gradient and thus directly influences the onset of initial yielding in polycrystals. The self energy of GNDs is then incorporated into the strain gradient theory of Gurtin (2002). The resulting theory is applied to model crystal grains of size D, leading to a D-1-dependent term with a coefficient determined by grain shape and orientation. It is thus More >

A.H.W. Ngan¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.4, No.3, pp. 137-144, 2007, DOI:10.3970/icces.2007.004.137

Abstract When a random structure is loaded by far-field stresses, the elements inside will not be subject to the same forces because of structural inhomogeneities. Such a system represents an interesting analog to a thermal system at equilibrium -- the structural irregularities qualify for a description by a Shannon-like entropy, and there is also the usual (e.g. elastic) strain energy. When an entropy is related to energy, one immediately steps into the familiar field of statistical mechanics, but for a strained random structure, the real (Kelvin) temperature plays no role. Instead, an effective temperature exists but More >

N. Mai-Duy¹, T. Tran-Cong¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.3, pp. 127-132, 2007, DOI:10.3970/icces.2007.003.127

Abstract This lecture presents an overview of the Integral Collocation formulation for numerically solving partial differential equations (PDEs). However, due to space limitation, the paper only describes the latest development, namely schemes based only on one-dimensional (1D) integrated interpolation even in multi-dimensional problems. The proposed technique is examined with Chebyshev polynomials and radial basis functions (RBFs). The latter can be used in both regular and irregular domains. For both basis functions, the accuracy and convergence rates of the new technique are better than those of the differential formulation. More >

Chein-Shan Liu¹, Yung-Wei Chen², Jiang-Ren Chang²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.2, pp. 93-100, 2007, DOI:10.3970/icces.2007.003.093

Abstract A new collocation method is developed here to solve the elliptic boundary value problems with singularities. Specifically, we consider the Motz problem as a test of the performance of the new method, which is found accurate and effective. More >

WU XueHong¹, SHEN ShengPing², TAO WenQuan^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.22, No.1, pp. 65-76, 2007, DOI:10.3970/cmes.2007.022.065

Abstract Meshless local Petrov-Galerkin collocation method is applied to compute two-dimensional heat conduction problems in irregular domain. By taking the Dirac's Delta function as the test function, the local domain integration is avoided. The essential boundary conditions can be implemented easily in this method. A case that has analytical solution shows the present method can obtain desired accuracy and efficient. Two cases in engineering are computed to validate the approach by comparing the present method with the finite volume method (FVM) solutions obtained from a commercial CFD package FLUENT 6.3. The results show that the present More >

P. H. Wen¹, Y. C. Hon²

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.3, pp. 177-192, 2007, DOI:10.3970/cmes.2007.021.177

Abstract In this paper, we perform a geometrically nonlinear analysis of Reissner-Mindlin plate by using a meshless collocation method. The use of the smooth radial basis functions (RBFs) gives an advantage to evaluate higher order derivatives of the solution at no cost on extra-interpolation. The computational cost is low and requires neither the connectivity of mesh in the domain/boundary nor integrations of fundamental/particular solutions. The coupled nonlinear terms in the equilibrium equations for both the plane stress and plate bending problems are treated as body forces. Two load increment schemes are developed to solve the nonlinear More >

L.N. Gergidis, D. Kourounis, S. Mavratzas, A. Charalambopoulos¹

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.2, pp. 157-176, 2007, DOI:10.3970/cmes.2007.021.157

Abstract A new complete set of scattering eigensolutions of Helmholtz equation in spheroidal geometry is constructed in this paper. It is based on the extension to exterior boundary value problems of the well known Vekua transformation pair, which connects the kernels of Laplace and Helmholtz operators. The derivation of this set is purely analytic. It avoids the implication of the spheroidal wave functions along with their accompanying numerical deficiencies. Using this novel set of eigensolutions, we solve the acoustic scattering problem from a soft acoustic spheroidal scatterer, by expanding the scattered field in terms of it. More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.1, pp. 53-66, 2007, DOI:10.3970/cmes.2007.021.053

Abstract A newly modified Trefftz method is developed to solve the exterior and interior Dirichlet problems for two-dimensional Laplace equation, which takes the characteristic length of problem domain into account. After introducing a circular artificial boundary which is uniquely determined by the physical problem domain, we can derive a Dirichlet to Dirichlet mapping equation, which is an exact boundary condition. By truncating the Fourier series expansion one can match the physical boundary condition as accurate as one desired. Then, we use the collocation method and the Galerkin method to derive linear equations system to determine the More >