M. R. Hematiyan^1,*, B. Jamshidi¹, M. Mohammadi²

CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.3, pp. 1349-1369, 2022, DOI:10.32604/cmes.2022.018235 - 30 December 2021

Abstract The method of fundamental solutions (MFS) is a boundary-type and truly meshfree method, which is recognized as an efficient numerical tool for solving boundary value problems. The geometrical shape, boundary conditions, and applied loads can be easily modeled in the MFS. This capability makes the MFS particularly suitable for shape optimization, moving load, and inverse problems. However, it is observed that the standard MFS lead to inaccurate solutions for some elastostatic problems with stress concentration and/or highly anisotropic materials. In this work, by a numerical study, the important parameters, which have significant influence on the… More >

Yui-Chuin Shiah^{1, *}, Sheng-Chi Huang¹, M. R. Hematiyan²

CMC-Computers, Materials & Continua, Vol.64, No.2, pp. 701-727, 2020, DOI:10.32604/cmc.2020.010417 - 10 June 2020

Abstract In engineering practice, analysis of interfacial thermal stresses in composites is a crucial task for assuring structural integrity when sever environmental temperature changes under operations. In this article, the directly transformed boundary integrals presented previously for treating generally anisotropic thermoelasticity in two-dimension are fully regularized by a semi-analytical approach for modeling thin multi-layers of anisotropic/isotropic composites, subjected to general thermal loads with boundary conditions prescribed. In this process, an additional difficulty, not reported in the literature, arises due to rapid fluctuation of an integrand in the directly transformed boundary integral equation. In conventional analysis, thin… More >

Y.C. Shiah¹, C.L. Tan², Y.H. Chen³

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.4, pp. 243-257, 2013, DOI:10.3970/cmes.2013.096.243

Abstract The present authors have recently proposed an efficient, alternative approach to numerically evaluate the fundamental solution and its derivatives for 3D general anisotropic elasticity. It is based on a double Fourier series representation of the exact, explicit form of the Green’s function derived by Ting and Lee (1997). This paper reports on the successful implementation of the fundamental solution and its derivatives based on this Fourier series scheme in the boundary element method (BEM) for 3D general anisotropic elastostatics. Some numerical examples of stress concentration problems and a crack problem are presented to demonstrate the More >

Tao Zhang^1,2, Leiting Dong^2,3, Abdullah Alotaibi⁴, Satya N. Atluri^2,5

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.1, pp. 1-28, 2013, DOI:10.3970/cmes.2013.094.001

Abstract In this paper, a novel Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method is developed for solving the inverse Cauchy problem of linear elasticity, wherein both the tractions as well as displacements are prescribed/measured at a small portion of the boundary of an elastic body. The elastic body may be isotropic/anisotropic and simply connected or multiply-connected. In the MLPG mixed collocation method, the same meshless basis function is used to interpolate both the displacement as well as the stress fields. The nodal stresses are expressed in terms of nodal displacements by enforcing the constitutive relation between… More >

Y.C. Shiah¹, C. L. Tan², C.Y. Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.1, pp. 1-22, 2012, DOI:10.3970/cmes.2012.087.001

Abstract The fundamental solution, or Green's function, for 3D anisotropic elastostatics as derived by Ting and Lee (1997) [Q.J. Mech. Appl. Math.; 50: 407-426] is one that is fully explicit and algebraic in form. It has, however, only been utilized in boundary element method (BEM) formulations quite recently even though it is relatively straightforward and direct to implement. This Green's function and its derivatives are necessary items in this numerical analysis technique. By virtue of the periodic nature of the angles when it is expressed in the spherical coordinate system, the present authors have very recently… More >

Y.C. Shiah¹, C. L. Tan²

CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.2, pp. 95-108, 2011, DOI:10.3970/cmes.2011.078.095

Abstract By differentiating the Green function of Ting and Lee (1997) for 3D general anisotropic elastotatics in a spherical coordinate system as an intermediate step, and then using the chain rule, derivatives of up to the second order of this fundamental solution are obtained in exact, explicit, algebraic forms. No tensors of order higher than two are present in these derivatives, thereby allowing these quantities to be numerically evaluated quite expeditiously. These derivatives are required for the computation of the internal point displacements and stresses via Somigliana's identity in BEM analysis. Some examples are presented to More >

Y.C. Shiah¹, C. L. Tan², R.F. Lee¹

CMES-Computer Modeling in Engineering & Sciences, Vol.69, No.2, pp. 167-198, 2010, DOI:10.3970/cmes.2010.069.167

Abstract In this paper, fully explicit, algebraic expressions are derived for the first and second derivatives of the Green's function for the displacements in a three dimensional anisotropic, linear elastic body. These quantities are required in the direct formulation of the boundary element method (BEM) for determining the stresses at internal points in the body. To the authors' knowledge, similar quantities have never previously been presented in the literature because of their mathematical complexity. Although the BEM is a boundary solution numerical technique, solutions for the displacements and stresses at internal points are sometimes required for More >

K.P. Baxevanakis¹, A.E. Giannakopoulos²

CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.2, pp. 181-198, 2010, DOI:10.3970/cmes.2010.060.181

Abstract The present work gives a systematic and rigorous implementation of (edge type) circular Volterra dislocation loops in ordinary axisymmetric finite elements using the thermal analogue and the integral representation of dislocations through stresses. The accuracy of the proposed method is studied in problems where analytical solutions exist. The full fields are given for loop dislocations in isotropic and anisotropic crystals and the Peach-Koehler forces are calculated for loops approaching free surfaces and bimaterial interfaces. The results are expected to be very important in the analysis of plastic yield strength, giving quantitative results regarding the influence More >

C. L. Tan¹, Y.C. Shiah², C.W. Lin²

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.3, pp. 195-214, 2009, DOI:10.3970/cmes.2009.041.195

Abstract The explicit, closed-form expressions of the Green's functions for generally anisotropic elastic solids in three-dimensions that have been derived using Stroh's formalism are employed in a formulation of the boundary element method (BEM). Unlike several other existing schemes, the evaluation of these fundamental solutions does not require further numerical integration in the BEM algorithm; they have surprisingly not been implemented previously. Three numerical examples are presented to demonstrate the veracity of the implementation and the general applicability of the BEM for the 3D elastic stress analysis of generally anisotropic solids. The results are compared with More >

Y. C. Shiah¹, C. L. Tan², V.G. Lee³

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.3, pp. 205-226, 2008, DOI:10.3970/cmes.2008.034.205

Abstract The main impediment to the development of efficient algorithms for the stress analysis of 3D generally anisotropic elastic solids using the boundary element method (BEM) and the local boundary integral equation (LBIE) meshless method over the years is the complexity of the fundamental solutions and the computational burden to evaluate them. The ability to analytically simplify and reduce them into as explicit a form as possible so that they can be directly computed will offer significant cost savings. In addition, they facilitate easy implementation using existing numerical algorithms with the above-mentioned methods that have been More >