ANALYTICAL SOLUTION FOR BENDING BEAM SUBJECT TO LATERAL FORCE WITH DIFFERENT MODULUS

Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (10): 1107-1117.

ANALYTICAL SOLUTION FOR BENDING BEAM SUBJECT TO LATERAL FORCE WITH DIFFERENT MODULUS

姚文娟, 叶志明

Department of Civil Engineering, Shanghai University; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P.R.China

收稿日期:2003-03-06 修回日期:2004-05-31 出版日期:2004-10-18 发布日期:2004-10-18
通讯作者: YE Zhi-ming

ANALYTICAL SOLUTION FOR BENDING BEAM SUBJECT TO LATERAL FORCE WITH DIFFERENT MODULUS

YAO Wen-juan, YE Zhi-ming

Department of Civil Engineering, Shanghai University; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P.R.China

Received:2003-03-06 Revised:2004-05-31 Online:2004-10-18 Published:2004-10-18

摘要/Abstract

摘要： A bending beam,subjected to state of plane stress,was chosen to investigate.The determination of the neutral surface of the structure was made,and the calculating formulas of neutral axis,normal stress,shear stress and displacement were derived.It is concluded that, for the elastic bending beam with different tension-compression modulus in the condition of complex stress, the position of the neutral axis is not related with the shear stress, and the analytical solution can be derived by normal stress used as a criterion, improving the multiple cyclic method which determines the position of neutral point by the principal stress. Meanwhile, a comparison is made between the results of the analytical solution and those calculated from the classic mechanics theory, assuming the tension modulus is equal to the compression modulus, and those from the finite element method (FEM) numerical solution. The comparison shows that the analytical solution considers well the effects caused by the condition of different tension and compression modulus. Finally, a calculation correction of the structure with different modulus is proposed to optimize the structure.

Abstract: A bending beam,subjected to state of plane stress,was chosen to investigate.The determination of the neutral surface of the structure was made,and the calculating formulas of neutral axis,normal stress,shear stress and displacement were derived.It is concluded that, for the elastic bending beam with different tension-compression modulus in the condition of complex stress, the position of the neutral axis is not related with the shear stress, and the analytical solution can be derived by normal stress used as a criterion, improving the multiple cyclic method which determines the position of neutral point by the principal stress. Meanwhile, a comparison is made between the results of the analytical solution and those calculated from the classic mechanics theory, assuming the tension modulus is equal to the compression modulus, and those from the finite element method (FEM) numerical solution. The comparison shows that the analytical solution considers well the effects caused by the condition of different tension and compression modulus. Finally, a calculation correction of the structure with different modulus is proposed to optimize the structure.

中图分类号:

O343.5

姚文娟;叶志明. ANALYTICAL SOLUTION FOR BENDING BEAM SUBJECT TO LATERAL FORCE WITH DIFFERENT MODULUS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(10): 1107-1117.

YAO Wen-juan;YE Zhi-ming . ANALYTICAL SOLUTION FOR BENDING BEAM SUBJECT TO LATERAL FORCE WITH DIFFERENT MODULUS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(10): 1107-1117.

参考文献

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ANALYTICAL SOLUTION FOR BENDING BEAM SUBJECT TO LATERAL FORCE WITH DIFFERENT MODULUS

ANALYTICAL SOLUTION FOR BENDING BEAM SUBJECT TO LATERAL FORCE WITH DIFFERENT MODULUS

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