An Operator Semigroup Method for Rectangular Plates With 2 Opposite Sides Simply Supported

LIU Jie; HUANG Jun-jie; Alatancang

doi:10.3879/j.issn.1000-0887.2015.07.006

Volume 36 Issue 7

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LIU Jie, HUANG Jun-jie, Alatancang. An Operator Semigroup Method for Rectangular Plates With 2 Opposite Sides Simply Supported[J]. Applied Mathematics and Mechanics, 2015, 36(7): 733-743. doi: 10.3879/j.issn.1000-0887.2015.07.006

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An Operator Semigroup Method for Rectangular Plates With 2 Opposite Sides Simply Supported

doi: 10.3879/j.issn.1000-0887.2015.07.006

¹School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P.R.China;²School of Manzhouli, Inner Mongolia University, Manzhouli, Neimenggu 021400, P.R.China

Funds: The National Natural Science Foundation of China(11305097)

Received Date: 2014-09-30
Rev Recd Date: 2015-05-09
Publish Date: 2015-07-15

Abstract

Abstract

The problem of solving a rectangular thin plate with 2 opposite sides simply supported in elasticity theory by means of the operator semigroup method was addressed. First, the plate equations were transformed into the abstract Cauchy problem. Then, the Hilbert space was defined and it was proved that the corresponding operator matrix generates contraction semigroups. Finally, the uniformly continuous semigroup approximation was applied through the Fourier transform, and the analytical solutions to the equations were given. The method naturally implies the existence and uniqueness of the solution.
- rectangular plate,
- abstract Cauchy problem,
- C₀ semigroup,
- analytical solution

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References(15)

References

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