Skip to main content
SpringerLink
Log in

Analytical solution for bending beam subject to lateral force with different modulus

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

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.

    Google Scholar 

  2. Ambartsumyan S A.Elasticity Theory of Different Modulus[M]. WU Rui-feng, ZHANG Yun-zhen trans. Beijing: China Railway Publishing House, 1986. (Chinese version)

    Google Scholar 

  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.

    Article  MATH  Google Scholar 

  4. Srinivasan R S, Ramachandra L S. Axisymmetric buckling and post-bucking of bimodulus annular plates[J].Eng Struct, 1989,11(7):195–198.

    Article  Google Scholar 

  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)

    Google Scholar 

  6. Papazoglou J L, Tsouvalis N G, Mechanical behaviour of bimodulus laminated plates[J].Composite Structures, 1991,17(1):1–22.

    Article  Google Scholar 

  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)

    Google Scholar 

  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.

    Google Scholar 

  9. YE Zhi-ming. A new finite element formulation for planar elastic deformation[J].Internat J for Numerical Methods in Engineering, 1997,14(40):2579–2592.

    Google Scholar 

  10. TSENG Yi-ping, JIANG Yu-ching. Stress analysis of bimodular laminates using hybrid stress plate elements[J].International Journal of Solids Structures, 1998,35(17):2025–2028.

    Article  Google Scholar 

  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.Com2 Mac Conference on Computational Mathematics[C]. South Korea: Pohang University of Science and Technology, 2001, 2–5.

    Google Scholar 

  12. Raffaele Zinno, Fabrizio Greco. Damage evolution in bimodular laminated composites[J].Composite Structures, 2001,53(4):381–402.

    Article  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Yao Wen-juan associate, Doctor & Ye Zhi-ming

Authors
  1. Yao Wen-juan associate, Doctor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ye Zhi-ming
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Contributed by Y Zhi-ming

Biography: Yao Wen-juan (1957≈)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wen-juan, Y., Zhi-ming, Y. Analytical solution for bending beam subject to lateral force with different modulus. Appl Math Mech 25, 1107–1117 (2004). https://doi.org/10.1007/BF02439863

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02439863

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation