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Evolution Equations and Control Theory (EECT)
 

Modeling of a nonlinear plate

Pages: 155 - 169, Volume 1, Issue 1, June 2012      doi:10.3934/eect.2012.1.155

 
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Shun Li - Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China (email)
Peng-Fei Yao - Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China (email)

Abstract: We consider modeling of a nonlinear thin plate under the following assumptions: (a) the materials are nonlinear; (b) the deflections are small (linear strain displacement relations). When the middle surface is planar, we consider the bending of a plate to establish the strain energy, the equilibrium equations, and the motion equations. For a shell with a curved middle surface in $\mathbb{R}^3$, we derive a nonlinear model where a deformation in three-dimensions is concerned.

Keywords:  Material nonlinearity, strain energy function, Riemannian geometry.
Mathematics Subject Classification:  74B20, 35L77, 35L75, 35L35 and 35L25.

Received: October 2011;      Revised: January 2012;      Available Online: March 2012.

 References