• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.2
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• pp.103-111
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• 2005

In this paper, a new meshfree technique which improves the numerical integration accuracy is introduced. This new method called thc Petrov-Galerkin natural clement method(PG-NEM) by authors is based on the Voronoi diagram and the Delaunay triangulation which is based on the same concept used lot conventional natural clement method called the Bubnov-Galerkin natural element method(BG-NEM). But, unlike the BG-NEM, the test basis function is differently chosen, based on the concept of Petrov-Galerkin, such that its support coincides exactly with a regular integration region in background mesh. Therefore, it is expected that the proposed technique ensures the remarkably improved numerical integration accuracy in comparison with the BG-NEM.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.2
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• pp.123-131
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• 2005

According to ow previous study, we confirmed That the Petrov-Galerkin natural element method(PG-NEM) completely resolves the numerical integration inaccuracy in the conventional Bubnov-Galerkin natural element method(BG-NEM). This paper is an extension of PG-NEM to two-dimensional geometrically nonlinear problem. For the analysis, a linearized total Lagrangian formulation is approximated with the PS-NEM. At every load step, the grid points ate updated and the shape functions are reproduced from the relocated nodal distribution. This process enables the PG-NEM to provide more accurate and robust approximations. The representative numerical experiments performed by the test Fortran program, and the numerical results confirmed that the PG-NEM effectively and accurately approximates The large deformation problem.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.2
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• pp.113-121
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• 2005

In order to resolve a common numerical integration inaccuracy of meshfree methods, we introduce an improved natural clement method called Petrov-Galerkin natural element method(PG-NEM). While Laplace basis function is being taken for the trial shape function, the test shape function in the present method is differently defined such that its support becomes a union of Delaunay triangles. This approach eliminates the inconsistency of tile support of integrand function with the regular integration domain, and which preserves both simplicity and accuracy in the numerical integration. In this paper, the validity of the PG-NEM is verified through the representative benchmark problems in 2-d linear elasticity. For the comparison, we also analyze the problems using the conventional Bubnov-Galerkin natural element method(BG-NEM) and constant strain finite clement method(CS-FEM). From the patch test and assessment on convergence rate, we can confirm the superiority of the proposed meshfree method.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.474-479
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• 2004

According to our previous study, it is confirmed that the Petrov-Galerkin natural element method (PGNEM) completely resolves the numerical integration inaccuracy in the conventional Bubnov-Galerkin natural element method (BG-NEM). This paper is an extension of PG-NEM to two-dimensional nonlinear dynamic problem. For the analysis, a constant average acceleration method and a linearized total Lagrangian formulation is introduced with the PG-NEM. At every time step, the grid points are updated and the shape functions are reproduced from the relocated nodal distribution. This process enables the PG-NEM to provide more accurate and robust approximations. The representative numerical experiments performed by the test Fortran program, and the numerical results confirmed that the PG-NEM effectively and accurately approximates the nonlinear dynamic problem.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.1274-1279
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• 2003

In this paper, a new meshfree technique which improves the numerical integration accuracy is introduced. This new method called the Petrov-Galerkin natural element(PG-NE) is based on the Voronoi diagram and the Delaunay triangulation which is based on the same concept used for conventional natural element method called the Bubnov-Galerkin natural element(BG-NE). But, unlike BG-NE method, the test shape function is differently chosen from the trial shape function. The proposed technique ensures that the numerical integration error is remarkably reduced.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.333-340
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• 2004

This paper deals with geometric nonlinear analyses using a new meshfree technique which improves the numerical integration accuracy. The new method called the Petrov-Galerkin natural element method (PGNEM) is based on the Voronoi diagram and the Delaunay triangulation which is based on the same concept used for conventional natural element method called the Bubnov-Galerkin natural element method (BGNEM). But, unlike BGNEM, the test shape function is differently chosen from the trial shape function. In the linear static analysis, it is ensured that the numerical integration error of the PGNEM is remarkably reduced. In this paper, the PGNEM is applied to large deformation problems, and the accuracy of the proposed numerical technique is verified through the several examples.