L.S. Miers¹, J.C.F. Telles²

Structural Durability & Health Monitoring, Vol.1, No.3, pp. 225-232, 2005, DOI:10.3970/sdhm.2005.001.225

Abstract The present paper aims at introducing the concept of Green's function type fundamental solutions (i.e., unit source fundamental solutions satisfying particular boundary conditions) into the context of meshless approaches, particularly dealing with the local boundary integral equation method (LBIE) derived from the classic boundary integral equation procedure. The Green's functions discussed here are mainly the so-called half-plane solution, corresponding to a unit source within a semi-plane bounded by a flux-free straight line and an infinite plane containing internal lines of potential discontinuity. The latter is here introduced in numerical fashion, as an extension of the authors' previous numerical Green's function… More >

Donghong He¹, Hang Ma^{2, *}

CMES-Computer Modeling in Engineering & Sciences, Vol.118, No.1, pp. 15-40, 2019, DOI:10.31614/cmes.2019.04327

Abstract To deal with the problems encountered in the large scale numerical simulation of three dimensional (3D) elastic solids with fluid-filled pores, a novel computational model with the corresponding iterative solution procedure is developed, by introducing Eshelby’s idea of eigenstrain and equivalent inclusion into the boundary integral equations (BIE). Moreover, by partitioning all the fluid-filled pores in the computing domain into the near- and the far-field groups according to the distances to the current pore and constructing the local Eshelby matrix over the near-field group, the convergence of iterative procedure is guaranteed so that the problem can be solved effectively and… More >

Z.Y. Qian¹, Z.D. Han¹, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.6, pp. 541-562, 2004, DOI:10.3970/cmes.2004.005.541

Abstract Novel non-hyper-singular [i.e., only strongly-singular] boundary-integral-equations for the gradients of the acoustic velocity potential, involving only O(r⁻²) singularities at the surface of a 3-D body, are derived, for solving problems of acoustics governed by the Helmholtz differential equation. The gradients of the fundamental solution to the Helmholtz differential equation for the velocity potential, are used in this derivation. Several basic identities governing the fundamental solution to the Helmholtz differential equation for velocity potential, are also derived. Using these basic identities, the strongly singular integral equations for the potential and its gradients [denoted here as φ-BIE, and q-BIE, respectively], are rendered… More >

J. Sladek¹, V. Sladek¹, P. Stanak¹, E. Pan²

CMES-Computer Modeling in Engineering & Sciences, Vol.64, No.3, pp. 267-298, 2010, DOI:10.3970/cmes.2010.064.267

Abstract The plate equations are obtained by means of an appropriate expansion of the mechanical displacement and electric potential in powers of the thickness coordinate in the variational equation of electroelasticity and integration through the thickness. The appropriate assumptions are made to derive the uncoupled equations for the extensional and flexural motion. The present approach reduces the original 3-D plate problem to a 2-D problem, with all the unknown quantities being localized in the mid-plane of the plate. A meshless local Petrov-Galerkin (MLPG) method is then applied to solve the problem. Nodal points are randomly spread in the mid-plane of the… More >

A. Aimi¹, M. Diligenti¹, S. Panizzi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.2, pp. 185-220, 2010, DOI:10.3970/cmes.2010.058.185

Abstract In this paper we consider 2D wave propagation Neumann exterior problems reformulated in terms of a hypersingular boundary integral equation with retarded potential. Starting from a natural energy identity satisfied by the solution of the differential problem, the related integral equation is set in a suitable space-time weak form. Then, a theoretical analysis of the introduced formulation is proposed, pointing out the novelties with respect to existing literature results. At last, various numerical simulations will be presented and discussed, showing accuracy and stability of the space-time Galerkin boundary element method applied to the energetic weak problem. More >

Z. D. Han¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 665-678, 2003, DOI:10.3970/cmes.2003.004.665

Abstract The numerical implementation of the truly Meshless Local Petrov-Galerkin (MLPG) type weak-forms of the displacement and traction boundary integral equations is presented, for solids undergoing small deformations. In the accompanying part I of this paper, the general MLPG/BIE weak-forms were presented [Atluri, Han and Shen (2003)]. The MLPG weak forms provide the most general basis for the numerical solution of the non-hyper-singular displacement and traction BIEs [given in Han, and Atluri (2003)], which are simply derived by using the gradients of the displacements of the fundamental solutions [Okada, Rajiyah, and Atluri (1989a,b)]. By employing the various types of test functions,… More >

Shenghu Ding^1,*, Qingnan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.114, No.3, pp. 335-349, 2018, DOI:10.3970/cmes.2018.114.335

Abstract A multi-layered model for heat conduction analysis of a thermoelectric material strip (TEMs) with a Griffith crack under the electric flux and energy flux load has been developed. The materials parameters of the TEMs vary continuously in an arbitrary manner. To derive the solution, the TEMs is divided into several sub-layers with different material properties. The mixed boundary problem is reduced to a system of singular integral equations, which are solved numerically. The effect of strip width on the electric flux intensity factor and thermal flux intensity factor are studied. More >

Xiaoping Zhang

The International Conference on Computational & Experimental Engineering and Sciences, Vol.18, No.2, pp. 35-36, 2011, DOI:10.3970/icces.2011.018.035

Abstract In this paper, we first discuss the midpoint rule for evaluating hypersingular integrals with the kernel \qopname \relax osin-2(x-s)/2 defined on a circle, and the key point is placed on its pointwise superconvergence phenomenon. We show that this phenomenon occurs when the singular point s is located at the midpoint of each subinterval and obtain the corresponding supercovergence analysis. Then we apply the rule to construct a collocation scheme for solving the relevant hypersingular integral equation, by choosing the midpoints as the collocation points. It's interesting that the inverse of coefficient matrix for the resulting linear system has an explicit… More >

The International Conference on Computational & Experimental Engineering and Sciences, Vol.7, No.2, pp. 101-106, 2008, DOI:10.3970/icces.2008.007.101

Abstract A nonliear meshless local Petrov-Galerkin (NMLPG) method for solving nonlinear boundary value problems, based on the nonlinear regular local boundary integral equation (NRLBIE) and the moving least squares approximation, is proposed in the present paper. No special integration scheme is needed to evaluate the volume and boundary integrals. The integrals in the present method are evaluated only over regularly-shaped sub-domains and their boundaries. This flexibility in choosing the size and the shape of the local sub-domain will lead to a more convenient formulation in dealing with the nonlinear problems. Compared to the original meshless local Petrov-Galerkin (MLPG) method that has… 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 >