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A Meshless Local Natural Neighbour Interpolation Method Applied to Structural Dynamic Analysis

Y. H. Liu1,2, S. S. Chen1, J. Li1, Z. Z. Cen1

Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing 100084, P. R.China
Corresponding author. Tel: +86-10-62773751; fax: +86-10-62781824; Email:

Computer Modeling in Engineering & Sciences 2008, 31(3), 145-156.


A novel meshless method for structural dynamic analysis is presented and discussed in this paper. It is called meshless local natural neighbour interpolation (MLNNI) method, which uses a meshless spatial approximation based only on nodes. The MLNNI is derived from the generalized meshless local Petrov-Galerkin (MLPG) method as a special case. Local weak forms are developed using weighted residual method locally from the dynamic partial differential equation. In the construction of trial functions, the natural neighbour interpolation (NNI) is employed to simplify the treatment of the essential boundary conditions. The domain integration is evaluated over included Delaunay triangles in each polygonal subdomain. The validity and strength of the proposed method for free and forced vibration analyses are demonstrated throughout different numerical applications. It is proven from the results that the proposed method is quite easy to implement, very accurate and highly efficient for both free vibration analysis and forced vibration analysis.


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Liu, Y. H., Chen, S. S., Li, J., Cen, Z. Z. (2008). A Meshless Local Natural Neighbour Interpolation Method Applied to Structural Dynamic Analysis. CMES-Computer Modeling in Engineering & Sciences, 31(3), 145–156.

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