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Structural Engineering and Mechanics Volume 36, Number 3, October20 2010 , pages 363-380 DOI: https://doi.org/10.12989/sem.2010.36.3.363 |
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An analytical solution of bending thin plates with different moduli in tension and compression |
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Xiao-ting He, Xing-jian Hu, Jun-yi Sun and Zhou-lian Zheng
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| Abstract | ||
| Materials which exhibit different elastic moduli in tension and compression are known as bimodular materials. The bimodular materials model, which is founded on the criterion of positivenegative signs of principal stress, is important for the structural analysis and design. However, due to the inherent complexity of the constitutive relation, it is difficult to obtain an analytical solution of a bimodular bending components except in particular simple problems. Based on the existent simplified model, this paper solves analytically bending thin plates with different moduli in tension and compression. By using the continuity conditions of stress components in unknown neutral layer, we determine the location of the neutral layer, and derive the governing differential equation for deflection, the flexural rigidity, and the internal forces in the thin plate. We also use a circular thin plate with bimodulus to illustrate the application of this solution derived in this paper. The results show that the introduction of different moduli has influences on the flexural stiffness of the bending thin plate. | ||
| Key Words | ||
| bimodulus; tension and compression; thin plate; bending; continuity. | ||
| Address | ||
| Xiao-ting He: College of Civil Engineering, Chongqing University, Chongqing 400045, PR China; Key Laboratory of New Technology for Construction of Cities in Mountain Area, Chongqing University, Ministry of Education, PRC, Chongqing 400045, PR China Xing-jian Hu: College of Civil Engineering, Chongqing University, Chongqing 400045, PR China Jun-yi Sun: College of Civil Engineering, Chongqing University, Chongqing 400045, PR China; Key Laboratory of New Technology for Construction of Cities in Mountain Area, Chongqing University, Ministry of Education, PRC, Chongqing 400045, PR China Zhou-lian Zheng: College of Civil Engineering, Chongqing University, Chongqing 400045, PR China; Key Laboratory of New Technology for Construction of Cities in Mountain Area, Chongqing University, Ministry of Education, PRC, Chongqing 400045, PR China | ||