H.B. Chen

The International Conference on Computational & Experimental Engineering and Sciences, Vol.20, No.4, pp. 105-106, 2011, DOI:10.3970/icces.2011.020.105

Abstract The calculation of field values and their derivatives near the domain boundary through the boundary element method (BEM) will meet the nearly singularity problem, i.e. the boundary layer effect problem. The tangential derivatives of field values on the boundary often meet an obvious deduction of calculation accuracy. An effective algorithm was proposed by Chen et al. [1,2] to treat these two problems in the same time in elastic BEM and it was recently extended to calculate the second derivative values in potential problem [3]. This algorithm is based on the regularized formulations and is now called the regularized indirect algorithm.… More >

Dehao Yu

The International Conference on Computational & Experimental Engineering and Sciences, Vol.20, No.2, pp. 63-64, 2011, DOI:10.3970/icces.2011.020.063

Abstract In many fields of scientific and engineering computing the Artificial Boundary Method has been widely applied to solve boundary value problems of partial differential equations, especially it is a very important method for solving problems on unbounded domains. This method is first suggested by K. Feng and D. Yu, called the natural boundary element method, and then also called DtN method by J.B. Keller and D. Givoli. The exact artificial boundary condition is the natural boundary integral equation on the artificial boundary, that is just the Dirichlet to Neumann mapping.

The natural boundary integral equation is hypersingular integral equation.… More >

H. T. Wang, L. Shi

The International Conference on Computational & Experimental Engineering and Sciences, Vol.19, No.1, pp. 11-12, 2011, DOI:10.3970/icces.2011.019.011

Abstract A three-dimensional fast boundary element solver is developed for the shape optimization of nozzles of nuclear reactor pressure vessels (RPVs). In a RPV, pressure and mechanical loads may lead to high stress concentration due to the discontinuity of the structure, especially at the inner surface of the cold/hot legs. This work aims to minimize these stress concentrations by optimizing the geometry of the openings using modern shape optimization techniques and fast boundary element method. Shape optimization methods based on the principle of biological adaptive growth are incorporated into a boundary element method program and used to optimize the design of… More >

Shuncai Li, Zhengzhu Dong, Dan Ma.

The International Conference on Computational & Experimental Engineering and Sciences, Vol.16, No.3, pp. 93-94, 2011, DOI:10.3970/icces.2011.016.093

Abstract Roadway with local short supporting is not only a common phenomenon in engineering, but also short of in-depth theoretical study. Existing literature on underground stress field theory of surrounding rock, generally gives the analytical solution of stress for the surrounding rock of roadway with uniform supporting or no supporting, but doesn't give a corresponding stress solution for local supporting or local short supporting. Based on the circular roadway local short supporting mechanical model, according to the boundary element method of bi-harmonic boundary value problem of exterior circular domain, the boundary integral formula of Airy stress function is deduced for the… More >

Y.C. Shiah, C.L. Tan

The International Conference on Computational & Experimental Engineering and Sciences, Vol.16, No.1, pp. 31-32, 2011, DOI:10.3970/icces.2011.016.031

Abstract In the boundary element method (BEM), interior point solutions for the displacements and the stresses at an interior point of an elastic body are obtained through the numerical evaluation of the Somigliana's identities. It is carried out as a secondary exercise in the BEM analysis, after the boundary integral equation (BIE) has been solved for all the unknown displacements and tractions on the surface of the domain. In the integrals of these identities, the integrands contain terms with up to second order derivatives of the Green's function for the displacements of the elastic problem.

The Green's function, or fundamental… More >

Ney Augusto Dumont

The International Conference on Computational & Experimental Engineering and Sciences, Vol.22, No.4, pp. 192-192, 2019, DOI:10.32604/icces.2019.05284

Abstract The use of boundary integral equations as an attempt to solve general problems of elasticity and potential has largely preceded the use of domain-related developments, which only became feasible (and conceivable) with the advent of powerful computational devices. On the other hand, the present-day matrix, computational-ready outline of the boundary element method (including its nowadays prevalent name) has borrowed – in part correctly and in part wrongly – much from the finite element concepts and formulation. We propose a revisit of the method, including, as for elasticity problems: a) conceptual reformulation in terms of weighted residuals with a consistent derivation… More >

L. Palermo Jr., L.P.C.P.F. Almeida¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.7, No.2, pp. 83-88, 2008, DOI:10.3970/icces.2008.007.083

Abstract The differentiation of the kernels of integrals in the displacement BIE to obtain one for stresses increases the order of the kernel singularity and additional care are necessary to treat the improper integrals. The application of the tangential differential operator (TDO) can reduce the order of the kernel singularity when the stress BIE employs Kelvin type fundamental solutions. This paper presents the numerical formulation for the TDO to three-dimensional problems. The TDO uses the derivatives of the shape function for displacements instead of introducing another interpolation function. Furthermore, the paper shows the additional integrals for the TDO to be applied… More >

J. Useche¹, P. Sollero², E.L. Albuquerque², L. Palermo³

The International Conference on Computational & Experimental Engineering and Sciences, Vol.6, No.3, pp. 175-182, 2008, DOI:10.3970/icces.2008.006.175

Abstract The computational fracture analysis of cracked thick plates repaired with adhesively bonded composite patches using a boundary element formulation is presented. The shear deformable cracked isotropic plate was modeled using the Reissner's plate theory. In order to model the repair, a three parameter boundary element formulation, based on Kirchhoff's theory for symmetric layered composite plates was established. Interaction forces and moments between the cracked plate and the composite repair were modeled as distributed loads. Coupling equations, based on kinematic compatibility and equilibrium considerations for the adhesive layer, were established. In-plane shear-deformable model with transversal stiffness was considered in order to… More >

Hong-ying Huang^2,1, De-hao Yu ²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.2, No.3, pp. 67-74, 2007, DOI:10.3970/icces.2007.002.067

Abstract In this paper, we apply the coupling of natural boundary element method and finite element method to solve a three-dimensional nonlinear interface problem. Two equations are coupled by interface conditions on the interface boundary. A spherical surface as the artificial boundary is introduced. The equivalent coupled variational problem is described. The existence and uniqueness of the solution of concerned problem as well as the estimates of its approximate solution are obtained. Some numerical examples are presented to demonstrate the effectiveness of this method. More >

Godwin Kakuba^1,∗, John M. Mango¹, Martijn J.H. Anthonissen²

CMES-Computer Modeling in Engineering & Sciences, Vol.119, No.1, pp. 207-225, 2019, DOI:10.32604/cmes.2019.04269

Abstract Sometimes boundary value problems have isolated regions where the solution changes rapidly. Therefore, when solving numerically, one needs a fine grid to capture the high activity. The fine grid can be implemented as a composite coarse-fine grid or as a global fine grid. One cheaper way of obtaining the composite grid solution is the use of the local defect correction technique. The technique is an algorithm that combines a global coarse grid solution and a local fine grid solution in an iterative way to estimate the solution on the corresponding composite grid. The algorithm is relatively new and its convergence… More >