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Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (4): 427-438.doi: https://doi.org/10.1007/s10483-015-1922-9

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Analytic elasticity solution of bi-modulus beams under combined loads

Huiling ZHAO1, Zhiming YE1,2   

  1. 1. Department of Civil Engineering, Shanghai University, Shanghai 200072, China;
    2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • 收稿日期:2014-07-07 修回日期:2014-09-29 出版日期:2015-04-01 发布日期:2015-04-01
  • 通讯作者: Huiling ZHAO E-mail:hlzhao@shu.edu.cn
  • 基金资助:
    Project supported by the Doctoral Fund of Ministry of Education of China (No. 20103108110019), the National Natural Science Foundation of China (No. 51208292), and the National Key Technology R&D Programs (Nos. 2011BAG07B01 and 2012BAK24B04)

Analytic elasticity solution of bi-modulus beams under combined loads

Huiling ZHAO1, Zhiming YE1,2   

  1. 1. Department of Civil Engineering, Shanghai University, Shanghai 200072, China;
    2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • Received:2014-07-07 Revised:2014-09-29 Online:2015-04-01 Published:2015-04-01
  • Contact: Huiling ZHAO E-mail:hlzhao@shu.edu.cn
  • Supported by:
    Project supported by the Doctoral Fund of Ministry of Education of China (No. 20103108110019), the National Natural Science Foundation of China (No. 51208292), and the National Key Technology R&D Programs (Nos. 2011BAG07B01 and 2012BAK24B04)

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被引次数

3

摘要： A unified stress function for bi-modulus beams is proposed based on its mechanic sense on the boundary of beams. Elasticity solutions of stress and displacement for bi-modulus beams under combined loads are derived. The example analysis shows that the maximum tensile stress using the same elastic modulus theory is underestimated if the tensile elastic modulus is larger than the compressive elastic modulus. Otherwise, the maximum compressive stress is underestimated. The maximum tensile stress using the material mechanics solution is underestimated when the tensile elastic modulus is larger than the compressive elastic modulus to a certain extent. The error of stress using the material mechanics theory decreases as the span-to-height ratio of beams increases, which is apparent when L/h ≤5. The error also varies with the distributed load patterns.

关键词: elasticity theory, analytic solution, bi-modulus, combined loads

Abstract: A unified stress function for bi-modulus beams is proposed based on its mechanic sense on the boundary of beams. Elasticity solutions of stress and displacement for bi-modulus beams under combined loads are derived. The example analysis shows that the maximum tensile stress using the same elastic modulus theory is underestimated if the tensile elastic modulus is larger than the compressive elastic modulus. Otherwise, the maximum compressive stress is underestimated. The maximum tensile stress using the material mechanics solution is underestimated when the tensile elastic modulus is larger than the compressive elastic modulus to a certain extent. The error of stress using the material mechanics theory decreases as the span-to-height ratio of beams increases, which is apparent when L/h ≤5. The error also varies with the distributed load patterns.

Key words: elasticity theory, analytic solution, bi-modulus, combined loads

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