CMES-Vol. 14, No. 3, 2006

Open Access

ARTICLE

Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method For Elasticity Problems
S. N. Atluri¹, H. T. Liu², Z. D. Han²
CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.3, pp. 141-152, 2006, DOI:10.3970/cmes.2006.014.141
Abstract The Meshless Local Petrov-Galerkin (MLPG) mixed collocation method is proposed in this paper, for solving elasticity problems. In the present MLPG approach, the mixed scheme is applied to interpolate the displacements and stresses independently, as in the MLPG finite volume method. To improve the efficiency, the local weak form is established at the nodal points, for the stresses, by using the collocation method. The traction boundary conditions are also imposed into the stress equations directly. It becomes very simple and straightforward to impose various boundary conditions, especially for the high-order PDEs. Numerical examples show that More >

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A Dual BEM Genetic Algorithm Scheme for the Identification of Polarization Curves of Buried Slender Structures
L.A. de Lacerda¹, J. M. da Silva¹
CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.3, pp. 153-160, 2006, DOI:10.3970/cmes.2006.014.153
Abstract A two-dimensional boundary element formulation is presented and coupled to a genetic algorithm to identify polarization curves of buried slender structures. The dual boundary element method is implemented to model the cathodic protection of the metallic body and the genetic algorithm is employed to deal with the inverse problem of determining the non-linear polarization curve, which describes the relation between current density and electrochemical potential at the soil metal interface. In this work, this non-linear relation resulting from anodic and cathodic reactions is represented by a classical seven parameters expression. Stratified soil resistivity is modeled More >

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On the NGF Procedure for LBIE Elastostatic Fracture Mechanics
L.S. Miers¹, J.C.F. Telles²
CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.3, pp. 161-170, 2006, DOI:10.3970/cmes.2006.014.161
Abstract This work aims at extending the concept of the Numerical Green's Function (NGF), well known from boundary element applications to fracture mechanics, to the Local Boundary Integral Equation (LBIE) context. As a "companion" solution, the NGF is used to remove the integrals over the crack boundary and is introduced only for source points whose support touches or contains the crack. The results obtained with the coupling of NGF-LBIE in previous potential discontinuity Laplace's equation problems and the authors' experience in NGF-BEM fracture mechanics were the motivation for this development. More >

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The Application of a Hybrid Inverse Boundary Element Problem Engine for the Solution of Potential Problems
S. Noroozi¹, P. Sewell¹, J. Vinney¹
CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.3, pp. 171-180, 2006, DOI:10.3970/cmes.2006.014.171
Abstract A method that combines a modified back propagation Artificial Neural Network (ANN) and Boundary Element Analysis (BEA) was introduced and discussed in the author's previous papers. This paper discusses the development of an automated inverse boundary element problem engine. This inverse problem engine can be applied to both potential and elastostatic problems.
In this study, BEA solutions of a two-dimensional potential problem is utilised to test the system and to train a back propagation Artificial Neural Network (ANN). Once training is completed and the transfer function is created, the solution to any subsequent or new… More >

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ARTICLE

SPH in a Total Lagrangian Formalism
Rade Vignjevic¹, Juan R. Reveles¹, James Campbell¹
CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.3, pp. 181-198, 2006, DOI:10.3970/cmes.2006.014.181
Abstract To correct some of the main shortcomings of conventional SPH, a version of this method based on the Total Lagrangian formalism, T. Rabczuk, T. Belytschko and S. Xiao (2004), is developed. The resulting scheme removes the spatial discretisation instability inherent in conventional SPH, J. Monaghan (1992).
The Total Lagrangian framework is combined with the mixed correction which ensures linear completeness and compliance with the patch test, R. Vignjevic, J. Campbell, L. Libersky (2000). The mixed correction utilizes Shepard Functions in combination with a correction to derivative approximations.
Incompleteness of the kernel support combined with… More >

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