Skip to main content Accessibility help
×
Home
Hostname: page-component-59b7f5684b-j5sqr Total loading time: 0.486 Render date: 2022-09-28T23:07:07.360Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "displayNetworkTab": true, "displayNetworkMapGraph": false, "useSa": true } hasContentIssue true

Exact analysis of simply supported rhombic plates under uniform pressure

Published online by Cambridge University Press:  24 October 2008

K. Rajaiah
Affiliation:
Indian Institute of Science, Bangalore 12, India
Akella Kameswara Rao
Affiliation:
Indian Institute of Science, Bangalore 12, India

Abstract

The simply supported rhombic plate under transverse load has received extensive attention from elasticians, applied mathematicians and engineers. All known solutions are based on approximate procedures. Now, an exact solution in a fast converging explicit series form is derived for this problem, by applying Stevenson's tentative approach with complex variables. Numerical values for the central deflexion and moments are obtained for various corner angles. The present solution provides a basis for assessing the accuracy of approximate methods for analysing problems of skew plates or domains.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1974

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Aggarwala, B. D.Bending of rhombic plates. Quart. J. Mech. Appl. Math. 19 (1966), 7982.CrossRefGoogle Scholar
(2)Bassali, W. A. and Hanna, N. O. M.Bending of curvilinear and rectilinear polygonal plates symmetrically loaded over a concentric circle. Proc. Cambridge Philos. Soc. 57 (1961), 166179.CrossRefGoogle Scholar
(3)Bassali, W. A. and Barsoum, F. R.The transverse flexure of uniformly loaded curvilinear and rectilinear polygonal plates. Proc. Cambridge Philos. Soc. 62 (1966), 523540.CrossRefGoogle Scholar
(4)Favre, H.Contribution à l'étude des plaques obliques. Schweiz. Bauzeitung 60 (1942).Google Scholar
(5)Hanuska, A.Über die Möglichkeit die Eigenfunktionen zur Berechnung nicht-rechteckiger Viereckplatten anzuwenden. Rev. Mec. Appl. 5 (1960), 779.Google Scholar
(6)Iyengar, K. T. S., Srinivasan, R. S. and Sunderarajan, C.Some studies on skew plates. The Aeronautical Journal of the Royal Aero. Soc. 75 (1971), 130132.Google Scholar
(7)Jensen, V. P.Analysis of skew slabs. Univ. of Illinois, Engineering Experiment Station Bulletin 332 (1941).Google Scholar
(8)Lardy, P.Die strenge Lösung des Problems der schiefen Platte. Schweiz. Bauzeitung 67 (1949), 207.Google Scholar
(9)Morray, L. S. D.Bending of simply supported rhombic plate under uniform normal loading. Quart. J. Mech. Appl. Math. 15 (1962), 413426.Google Scholar
(10)Murray, N. W.The polygon-circle paradox and convergence in thin plate theory. Proc. Cambridge Philos. Soc. 73 (1973), 279282.CrossRefGoogle Scholar
(11)Muskhelishvili, N. I.Some Basic Problems of the Mathematical Theory of Elasticity (translated by Radok, J. R. M.P. Noordhoff Ltd.) (1953).Google Scholar
(12)Rajaiah, K. and Rao, A. K.Effect of boundary condition description on convergence of solution in a boundary value problem. J. Computational Phys. 3 (1968), 190201.CrossRefGoogle Scholar
(13)Rajaiah, K. and Rao, A. K.On limiting cases in the flexure of simply supported regular polygonal plates. Proc. Cambridge Philos. Soc. 65 (1969), 831834.CrossRefGoogle Scholar
(14)Rushton, K. R.Electrical analogue solutions for the deformation of skew plates. Aero. Quart. 15 (1964), 169180.CrossRefGoogle Scholar
(15)Sampath, S. G. and Rao, A. K. Some problems in the flexure of thin rectilinear plates. Indian Institute of Science, Bangalore, Dept. of Aeronautical Engineering, Rept. 112S (1966).Google Scholar
(16)Stevenson, A. C.The boundary couples in thin plates. Philos. May. 34 (1943), 105114.CrossRefGoogle Scholar
(17)Warren, W. E.Bending of rhombic plates. AIAA J. 2 (1964), 166167.CrossRefGoogle Scholar
(18)Williams, M. L. Surface stress singularities resulting from various boundary conditions in angular corners of plates under bending. Proc. of First U.S. National Congress of Appl. Mech., Illinois Institute of Technology, Chicago, Illinois (1951), pp. 325329.Google Scholar
3
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Exact analysis of simply supported rhombic plates under uniform pressure
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Exact analysis of simply supported rhombic plates under uniform pressure
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Exact analysis of simply supported rhombic plates under uniform pressure
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *