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
 Citation: 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.

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

##### doi: 10.3879/j.issn.1000-0887.2015.07.006
Funds:  The National Natural Science Foundation of China(11305097)
• Rev Recd Date: 2015-05-09
• Publish Date: 2015-07-15
• 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.
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