Analytical Solutions of Rectangular Laminated Plates Under Various Boundary Conditions in the State Space

QING Guang-hui; ZHANG Xiao-huan

doi:10.3879/j.issn.1000-0887.2015.11.005

Volume 36 Issue 11

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QING Guang-hui, ZHANG Xiao-huan. Analytical Solutions of Rectangular Laminated Plates Under Various Boundary Conditions in the State Space[J]. Applied Mathematics and Mechanics, 2015, 36(11): 1167-1177. doi: 10.3879/j.issn.1000-0887.2015.11.005

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Analytical Solutions of Rectangular Laminated Plates Under Various Boundary Conditions in the State Space

doi: 10.3879/j.issn.1000-0887.2015.11.005

College of Aeronautical Engineering, Civil Aviation University of China, Tianjin 300300, P.R.China

Funds: The National Natural Science Foundation of China(60979001)

Received Date: 2015-06-30
Rev Recd Date: 2015-09-30
Publish Date: 2015-11-15

Abstract

Abstract

Based upon the method of boundary displacement functions, the non-homogeneous state equations and the control equations for the solutions of rectangular laminated plates under various boundary conditions were derived. Through dimension expansion, the non-homogeneous equations were converted to homogeneous equations, thus the possible problems of numerical ill-conditions were avoided, and the calculation process was simplified for the homogeneous equations. An introduction of the hypothesis of nonlinear boundary displacement distribution along the thickness direction reasonably decreased the number of sub-layers for the convergence of numerical results. The numerical results in the examples provide standard referential solutions for other numerical or semi-analytical methods. The present method is suitable for the problems under more complex boundary conditions.
- state space,
- rectangular laminated plate,
- boundary displacement function,
- analytical solution

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References(18)

References

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