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.

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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

Abstract

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.

2010 MSC Number:

O343.5

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

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References

[1] Medri G. A nonlinear elastic model for isotropic materials with different behavior in tension and compression[J]. Transactions of the ASME, 1982,26(104): 26-28.
[2] Ambartsumyan S A. Elasticity Theory of Different Modulus[M]. WU Rui-feng, ZHANG Yun-zhen transl. Beijing: China Railway Publishing House, 1986. (Chinese version)
[3] Srinivasan R S, Ramachandra L S. Large deflection analysis of bimodulus annular and circular plates using finite elements[J]. Computers & Structures, 1989,31(5): 681-691.
[4] Srinivasan R S, Ramachandra L S. Axisymmetric buckling and post-bucking of bimodulus annular plates[J]. Eng Struct, 1989,11(7):195-198.
[5] ZHANG Yun-zhen, WANG Zhi-feng. The finite element method for elasticity with different moduli in tension and compression[J]. Journal of Computed Structural Mechanics and Applications, 1989,6(1): 236-246. (in Chinese)
[6] Papazoglou J L, Tsouvalis N G, Mechanical behaviour of bimodulus laminated plates[J]. Composite Structures, 1991,17(1): 1-22.
[7] YANG Hai-tian, WU Rui-feng, YANG Ke-jian, et al. Solution to problem of dual extension compression elastic modulus with initial stress method[J]. Journal of Dalian University of Technology, 1992, 32(1):35-39. (in Chinese)
[8] TSENG Yi-ping, LEE Cheng-tao. Bending analysis of bimodular laminates using a higher-order finite strip method[J]. Composite Structures, 1995,30(4): 341-350.
[9] YE Zhi-ming. A new fmite element formulation for planar elastic deformation[J]. Internat J for Numerical Methods in Engineering, 1997,14(40): 2579-2592.
[10] TSENGYi-ping,JIANGYu-ching. Stress analysis of bimodular laminates using hybrid stress plate elements[J]. International Journal of Solids Structures, 1998,35 (17): 2025-2028.
[11] YE Zhi-ming, YU Huang-ran, YAO Wen-juan. A finite element formulation for different Young' s modulus when tension and compression loading[A]. In:Jin Ho Kwak Ed. Com2Mac Conference on Computational Mathematics[C]. South Korea: Pohang University of Science and Technology, 2001,2-5.
[12] Raffaele Zinno, Fabrizio Greco. Damage evolution in bimodular laminated composites[J]. Composite Structures, 2001,53(4): 381-402.
[13] Gao X-L, Li K, Mall S. A mechanics-of-materials model for predicting Young' s modulus of damaged woven fabric composites involving three damage modes[J]. International Journal of Solids and Structures, 2003,40(4): 981-999.
[14] YAO Wen-juan, YE Zhi-ming. Analytical solution of bending compression colume using different tension compression modulus[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(9):983-993.

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

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[1]	YAO Wen-juan;YE Zhi-ming. ANALYTICAL SOLUTION OF BENDING-COMPRESSION COLUMN USING DIFFERENT TENSION-COMPRESSION MODULUS [J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(9): 983-993.
[2]	Han Qiang;Zhang Nianmei;Yang Guitong. CHAOTIC MOTION OF A NONLINEAR THERMO-ELASTIC ELLIPTIC PLATE [J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(9): 960-966.