US-FE-LSPIM TRI3 Element for Free Vibration Analysis

Abstract:

For the purpose of construction an effective element model, the US- FE-LSPIM TRI3 element formulation, which is based on the concept of unsymmetric finite element formulation, is established. Classical linear triangle shape functions and FE-LSPIM TRI3 element shape functions are used as test and trial functions respectively. Classical linear triangle shape functions fulfill the requirements of continuity in displacement field for test functions. The FE-LSPIM TRI3 element shape functions synthesize the individual strengths of meshfree and finite element methods so they are more proper for trial functions. The element is applied in free vibration analysis of two dimension solids. Typical benchmark problems are solved. The results show that this element is more accurate and capable of good performances under both regular and irregular meshes.

• Periodical: Applied Mechanics and Materials (Volumes 246-247)
• Pages: 1278-1282
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.246-247.1278
• Online since: December 2012
• Authors: Hui Hui Chen, Cheng Jia
• Keywords: Free Vibration, MeshFree, Petrov-Galerkin Formulation, Triangle Element, US-FE-LSPIM TRI3 Element

References

[4] Frequency Error % Frequency Error % Frequency Error % 1.

[52] 67.

[18] 03.

[48] 04.

[7] 66.

[44] 93.

69.

[44] 623 2 164. 47.

[26] 49 162. 52.

[24] 99 142. 35.

[9] 47 130. 03 3 178. 46.

[9] 69 163. 93.

76 163. 35.

40 162. 70 4 391. 91.

[59] 28 356. 29.

[44] 80 297. 38.

[20] 86 246. 05 5 411. 07.

[8] 20 408. 31.

[7] 48 399. 16.

[5] 07 379. 90 6 597. 72.

[52] 70 576. 20.

[47] 20 545. 75.

[39] 42 391. 44 It also can be concluded that US-FE-LSPIM TRI3 Element gives better answers compared with the T3 and Q4 element. Conclusions The analysis of structural dynamics problems is of great importance in the field of computational mechanics. To find a more efficient approach to this problem, the US- FE-LSPIM TRI3 element is derived based on the concept of unsymmetric finite element formulation. Typical numerical examples of free vibration are solved by using US- FE-LSPIM TRI3 element. It is shown that this element is of high precisions and capable of excellent performances under both regular and irregular meshes. Acknowledgements This study is supported by Scientific Research Project for Introduced Talents of Yancheng Institute of Technology (project no. XKR2011016). References.

DOI: 10.4028/www.scientific.net/amm.246-247.1278

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