| 高兴军,马海涛,陈太聪.弹性地基上Timoshenko梁的精确数值解[J].计算力学学报,2011,28(6):904~908 |
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| 弹性地基上Timoshenko梁的精确数值解 |
| Exact numerical solutions of Timoshenko beams on elastic foundations |
| 投稿时间：2010-05-13 修订日期：2010-09-06 |
| DOI：10.7511/jslx20116015 |
| 中文关键词: 弹性地基 Timoshenko梁 Trefftz单元 精确数值解 |
| 英文关键词:elastic foundations Timoshenko beams Trefftz element exact numerical solutions |
| 基金项目:华南理工大学亚热带建筑科学国家重点实验室自主研究课题2008ZA08,2008ZC21资助项目. |
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| 中文摘要: |
| 研究了弹性地基上Timoshenko梁的高精度有限元分析方法,利用控制微分方程的基本解建立了单元形函数,提出了弹性地基上Timoshenko梁分析的Trefftz单元。通过对引入的非节点自由度进行静力凝聚,得到的精确单元与常规单元具有相同的节点自由度。文中还讨论了有效降低计算过程中舍入误差的方法。算例结果表明,采用提出的新单元,只需使用极少的单元即可获得数值精确解。 |
| 英文摘要: |
| This paper presents a study on the exact finite element solution of Timoshenko beams on elastic foundation.New shape functions are constructed using the general solution of governing differential equations of equilibrium and a Trefftz element is developed.The proposed exact element has the same nodal degrees of freedom as the conventional element after the nodeless degree of freedom introduced in the derivation is condensed at the element level.Methods for avoiding possible numerical errors due to roundoff errors are also discussed.Numerical examples are presented to demonstrate the efficiency of the new element. |
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