• Journal of Mechanical Science and Technology
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• v.20 no.1
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• pp.94-109
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• 2006

An improved meshfree method called the Petrov-Galerkin natural element (PG-NE) method is introduced in order to secure the numerical integration accuracy. As in the Bubnov-Galerkin natural element (BG-NE) method, we use Laplace interpolation function for the trial basis function and Delaunay triangles to define a regular integration background mesh. But, unlike the BG-NE method, the test basis function is differently chosen, based on the Petrov-Galerkin concept, such that its support coincides exactly with a regular integration region in background mesh. Illustrative numerical experiments verify that the present method successfully prevents the numerical accuracy deterioration stemming from the numerical integration error.

• 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.

• Interaction and multiscale mechanics
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• v.1 no.3
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• pp.339-355
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• 2008

A Galerkin meshfree method is presented for analyzing shear deformable cylindrical panels. Based upon the analogy between the cylindrical panel and the curved beam a pure bending mode for cylindrical panel is rationally constructed. The meshfree approximation employed herein is characterized by an enhanced moving least square or reproducing kernel basis function that can exactly represent the pure bending mode and thus meets the requirement of Kirchhoff mode reproducing condition. The variational form is discretized using the efficient stabilized conforming nodal integration with a smoothed nodal gradient based curvature. The resulting meshfree formulation satisfies the integration constraint for bending exactness. Moreover, it is shown here that the smoothed gradient preserves several desired properties which are valid for the standard gradient obtained by direct differentiation, such as partition of nullity and reproduction of a constant strain field. The efficacy of the proposed approach is demonstrated by two benchmark cylindrical panel examples.