有限元素樑結構接觸分析

Contact Analysis of Beam Structure by Using Finite Element Method

林佑星(You-Hsing Lin)

指導教授 ： 康淵 ； 張永鵬

中原大學/工學院/機械工程學系/碩士(2007年)

https://doi.org/10.6840/cycu200700892

摘要

本文使用有限元素法的共用節點(joint nodes)、耦合(couple)及接觸(contact)作為結構的連結方式，根據樑元素及薄殼元素之物理意義，探討連結方式的限制性，在前處理建模作連結時間的便易性，以及分析結果差異性的比較。本文以兩平行懸臂樑結構，圓柱垂直於板結構，以及樑平行於板結構作為分析的模型，使用實體元素的分析結果為基準，與樑元素及薄殼元素的模型分析結果相比較；樑元素根據Timoshenko樑理論建模，薄殼元素根據Mindlin-Reissner薄殼理論建模。

關鍵字

Timoshenko樑元素 ； 組合結構 ； 耦合 ； Mindlin-Reissner薄殼元素 ； 共用節點 ； 接觸

並列摘要

This thesis presents a FEM method which use joint nodes, couple and contact to connect the models of a structure, also discusses limitations of these approaches, the conveniences of pre-process modeling, and the differences of analysis results on the basis of beam element and shell element. The FEM models, which are two parallel cantilerel beams, a cylinder vertical to a thin plate and a beam paralleled a plate, compared to the analysis results of using beam element and shell element according to solid element; beam elements are based on Timoshenko beam theory, shell elements are based on Mindlin-Reissner shell theory.

並列關鍵字

contact ； assembled structure ； joint nodes ； Timoshenko beam elements ； couple ； Mindlin-Reissner shell elements

參考文獻

1. Courant, R., “Variation Methods for the Solution of Problems of Equilibrium and Vibrations,” Bulletin of the American Mathematical Society, vol. 49, Providence, RI, pp. 1-23, 1943.

2. Zienkiewicz, O. C. and Cheung, Y. K. K., The Finite Element Method in Structural and Continuum Mechanics, McGraw-Hill, London, 1967.

3. Thomas, D. L., Wilson, J. M., and Wilson, R. R., “Timoshenko Beam Finite Element”, journal of Sound and Vibration, pp. 315-330, 1973.

4. Necib, B., Sun, C. T., “Analysis of Truss Beams Using A High Order Timoshenko Beam Finite Element”, journal of Sound and Vibration, Vol.130, No. 1 , pp. 149-159, 1989.

5. Nelson, H. D., “A Finite Rotating Shaft Element Using Timoshenko Beam Theroy”, ASME J. Mechanical Design, Vol. 102, pp. 793-803, 1980.