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| Element stiffness matrix for Timoshenko beam with variable cross-section |
| Received:October 09, 2012 Revised:December 19, 2012 |
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| DOI：10.7511/jslx201402021 |
| KeyWord:beam element with variable cross-section stiffness matrix the principle of potential energy geometric nonlinearity error |
| Author | Institution |
| 传光红 |
同济大学 土木工程学院, 上海 |
| 陈以一 |
同济大学 土木工程防灾国家重点实验室, 上海 |
| 童根树 |
浙江大学 建筑工程学院, 杭州 |
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| Abstract: |
| The variable cross-section members have been widely used in engineering practice for many years,thus it is necessary to investigate their element stiffness matrixes.In this paper,based on the principle of potential energy,the element stiffness matrix with approximation to second order are obtained,where the change rates of both the flexural and shear stiffness are treated as infinitesimal quantities (or Infinitesimal).It is noted that the effects of geometric nonlinearity due to axial force as well as shear deformation is considered in the matrix.In addition,based on the differential equilibrium equations of the members,the flexural and shear displacements modes with approximation to second order,expressed as cubic and quintic polynomial respectively,are also obtained.Moreover,the singularity of the element stiffness matrix and the expression of axial stiffness are discussed in detail.By comparing the obtained matrix results with some exact solutions,it is indicated that the accuracy of the obtained element stiffness matrix can be guaranteed.Finally,the convergence of this method is discussed by comparing with other methods in a case study. |
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