Xiyong Huang¹, M. H. Aliabadi², Z. Sharif Khodaei³

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.4, pp. 291-330, 2014, DOI:10.3970/cmes.2014.102.291

Abstract In this paper, a stochastic dual boundary element formulation is presented for probabilistic analysis of fatigue crack growth. The method involves a direct differentiation approach for calculating boundary and fracture response derivatives with respect to random parameters. Total derivatives method is used to obtain the derivatives of fatigue parameters with respect to random parameters. First- Order Reliability Method (FORM) is applied to evaluate the most probable point (MPP). Opening mode fatigue crack growth problems are used as benchmarks to demonstrate the performance of the proposed method. More >

Y.C. Shiah¹, Chung-Lei Hsu¹, Chyanbin Hwu^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.4, pp. 257-270, 2014, DOI:10.3970/cmes.2014.102.257

Abstract As has been well documented for the boundary element method (BEM), a volume integral is present in the integral equation for thermoelastic analysis. Any attempt to directly integrate the integral shall inevitably involve internal discretization that will destroy the BEM’s distinctive notion as a true boundary solution technique. Among the schemes to overcome this difficulty, the exact transformation approach is the most elegant since neither further approximation nor internal treatments are involved. Such transformation for 2D anisotropic thermoelasticity has been achieved by Shiah and Tan (1999) with the aid of domain mapping. This paper revisits More >

L. Rodríguez-Tembleque¹, M.H. Aliabadi²

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.3, pp. 183-210, 2014, DOI:10.3970/cmes.2014.102.183

Abstract This work presents new contact constitutive laws for friction and wear modelling in fiber-reinforced plastics (FRP). These laws are incorporated to a numerical methodology which allows us to solve the contact problem taking into account the anisotropic tribological properties on the interfaces. This formulation uses the Boundary Element Method for computing the elastic influence coefficients. Furthermore, the formulation considers micromechanical models for FRP that also makes it possible to take into account the fiber orientation relative to the sliding direction, the fiber volume fraction, the aspect ratio of fibers, or the fiber arrangement. The proposed More >

Peng Weihong^1,2, Gao Feng¹, Cao Guohua³, Xu Yong², Cheng Hongmei¹

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.2, pp. 133-155, 2014, DOI:10.3970/cmes.2014.100.133

Abstract In this paper, the natural boundary element method is used to solve two-dimensional steady-state incompressible Stokes flows in a driven cavity. The analytical functions are expressed for the Stokes problem in an exterior circular domain under single value conditions, which satisfy the Stokes equations’ solutions in the form of complex functions. In order to obtain a uniform integral formula, the velocities on the boundary are expanded into Laurent series, and then compared with the analytical solutions obtained as described above. In this manner, the coefficients of the analytical solutions in the form of complex function… More >

J. Useche¹

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.2, pp. 105-118, 2014, DOI:10.3970/cmes.2014.100.105

Abstract In this work, the harmonic analysis of shallow shells using the Boundary Element Method, is presented. The proposed boundary element formulation is based on a direct time-domain integration using the elastostatic fundamental solutions for both in-plane elasticity and shear deformable plates. Shallow shell was modeled coupling boundary element formulation of shear deformable plate and two-dimensional plane stress elasticity. Effects of shear deformation and rotatory inertia were included in the formulation. Domain integrals related to inertial terms were treated using the Dual Reciprocity Boundary Element Method. Numerical examples are presented to demonstrate the efficiency and accuracy More >

Y.C. Shiah¹, Y.M. Lee², T.C. Huang²

CMC-Computers, Materials & Continua, Vol.39, No.1, pp. 49-71, 2014, DOI:10.3970/cmc.2014.039.049

Abstract A common difficulty arises in characterizing the anisotropic properties of a thin sheet of anisotropic material, especially in the transverse direction. This difficulty is even more phenomenal for measuring its mechanical properties on account of its thickness. As the prelude of such investigation, this paper proposes a novel approach to identify the thermal conductivities of an unknown thin layer of anisotropic material. For this purpose, the unknown layer is sandwiched in isotropic materials with known conductivities. Prescribing proper boundary conditions, one may easily measure temperature data on a few sample boundary points. Therefore, the anisotropic More >

Y.C. Shiah¹, Y.M. Lee², Chi-Chang Wang²

CMC-Computers, Materials & Continua, Vol.33, No.3, pp. 229-255, 2013, DOI:10.3970/cmc.2013.033.229

Abstract In this paper, the boundary integrals for treating 3D field problems are fully regularized for planar elements by the technique of integration by parts (IBP). As has been well documented in open literatures, these integrals appear to be strongly singular and hyper-singular for the associated fundamental solutions. In the past, the IBP approach has only been applied to regularize the integrals for 2D problems. The present work shows that the IBP can also be further extended to treat 3D problems, where two variables of the local coordinates are involved. The presented formulations are fully explicit More >

Ewa Majchrzak^*

Molecular & Cellular Biomechanics, Vol.10, No.3, pp. 201-232, 2013, DOI:10.3970/mcb.2013.010.201

Abstract Heat transfer processes proceeding in the living organisms are described by the different mathematical models. In particular, the typical continuous model of bioheat transfer bases on the most popular Pennes equation, but the Cattaneo-Vernotte equation and the dual phase lag equation are also used. It should be pointed out that in parallel are also examined the vascular models, and then for the large blood vessels and tissue domain the energy equations are formulated separately. In the paper the different variants of the boundary element method as a tool of numerical solution of bioheat transfer problems More >

Marek Jasiński^*

Molecular & Cellular Biomechanics, Vol.10, No.3, pp. 183-199, 2013, DOI:10.3970/mcb.2013.010.183

Abstract In the paper the numerical analysis of thermal processes proceeding in the biological tissue is presented. The tissue is subjected to the external heat flux and 2D problem is taken into account. In order to determine the influence of variations of thermophysical parameters of tissue on the value of Arrhenius injury integral the direct approach of sensitivity analysis is applied. On the basis of tissue damage fraction the thermal injury formation process is analysed. At the stage of numerical realization the boundary element method is used. In the final part of the paper the example More >

R. Q. Rodríguez¹, A.F. Galvis¹, P. Sollero¹, E. L. Albuquerque²

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.4, pp. 259-274, 2013, DOI:10.3970/cmes.2013.096.259

Abstract Over recent years the rapid evolution of the computational power has motivated the development of new numerical techniques to account for engineering solutions. The Boundary Element Method (BEM) has shown to be a powerful numeric tool for the analysis and solution of many physical and engineering problems. However, BEM fully populated and non-symmetric system matrices implies in higher memory requirements and solution times. This work analyze the application of hierarchical matrices and low rank approximations, applying the Adaptive Cross Approximation - ACA, to multiple inclusion potential problems. The use of hierarchical format is aimed at More >