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The Quarterly Journal of Mechanics and Applied Mathematics 1961 14(3):257-270; doi:10.1093/qjmam/14.3.257
© 1961 by Oxford University Press
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THE LARGE DEFLEXION OF THIN CANTILEVERED PLATES

PART I. GENERAL THEORY

J. J. MAHONY {dagger}

( Department of Aeronautics, University of Sydney, N.S.W. )

A scheme of solution, especially suited for digital computers, is presented for the case of the bending of a cantilevered plate of small constant thickness, under the action of prescribed normal loads which produce moderately large deflexions. It takes the form of an asymptotic expansion of the solution of the von Kármán equations in terms of a large non-dimensional loading parameter. The leading term of the expansion is a combination of the solution obtained using the inextensional theory of bending and a suitable boundary layer solution. The form of the higher order terms is deduced and it is shown how they may be obtained in terms of quadratures and solutions of ordinary linear differential equations.


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