The finite element method is applied to the calculation of the deflection under a uniformly distributed load and the natural frequencies of the rhombic cantilever plate. This has required the derivation of stiffness and inertia matrices for a plate element of parallelogrammic planform.
Although, in common with the work of past investigators, the accuracy of the results decreases with increase in skew angle it is shown that the method is adequate for angles up to about 45°.
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References
1.
WilliamsM. L.‘Surface stress singularities resulting from various boundary conditions in angular corners of plates under bending’, U.S. Nat. Congr. appl. Mech.1951, 325 (Illinois Institute of Technology, Chicago, Illinois).
2.
CoullA.‘The direct stress analysis of swept cantilever plates of low aspect ratio’, Aircraft Engng196537 (No. 6, June), 182.
3.
ReissnerE.SteinM.‘Torsion and transverse bending of cantilever plates’, N.A.C.A. tech. Note2369, 1951.
4.
PlassH. J.GainesJ. H.NewsomC. D.‘Application of Reissner's variational principle to cantilever plate deflection and vibration problems’, J. appl. Mech.196229, 127.
5.
BartonM. V.‘Vibrations of rectangular and skew cantilever plates’, J. appl. Mech.195118, 129.
6.
ClaassenR. W.‘Vibrations of skew cantilever plate’, Tech. Rept No. PMR-TR-62–1. Pacific Missile Range, Point Mugu, California, May 1963.
7.
DaweD. J.‘A finite element approach to plate vibration problems’, J. mech. Engng Sci.19657 (No. 1), 28.
8.
ZienkiewiczO. C.CheungY. K.‘The finite element method for analysis of elastic isotropic and orthotropic slabs’, Proc. Instn civ. Engrs196428 (Aug.), 471.
9.
MeloshR. J.‘Basis for derivation of matrices for the direct stiffness method’, Am. Inst. Aero. Astro. J.19631 (No. 7), 1631.
10.
ArgyrisJ. H.KelseyS.KamelH.‘Matrix methods of structural analysis-a precis of recent developments’, Matrix methods of structural analysis (Ed. de VeubekeF.) 1964 (Pergamon Press, Oxford).
11.
DaweD. J.‘Vibration of rectangular plates of variable thickness’, J. mech. Engng Sci.19668 (No. 1), 42.
12.
SlyperH. A.DaweD. J.Communication on ‘The finite element method for analysis of elastic isotropic and orthotropic slabs’, by O. C. Zienkiewicz and Y. K. Cheung (to be published inProc. Instn civ. Engrs).
13.
WilliamsM. L.‘Theoretical and experimental effect of sweep upon stress and deflection distribution in aircraft wings of high solidity-Part 5. Some experimental deflection data for uniformly thin swept rectangular cantilever plates of low aspect ratio’, California Institute of Technology AF-TR-5761, 1950.
14.
WilliamsM. L.‘A review of certain analysis methods for swept-wing structures’, J. Aero. Sci.195219, 615.
15.
MorleyL. S. D.Skew plates and structures1964, 66 (Pergamon Press, Oxford).