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The Quarterly Journal of Mechanics and Applied Mathematics 1992 45(1):57-75; doi:10.1093/qjmam/45.1.57
© 1992 by Oxford University Press
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ELASTIC SHEETS WITH BENDING STIFFNESS

M. G. HILGERS and A. C. PIPKIN

( Division of Applied Mathematics, Brown University Providence, Rhode Island 02912, USA )

A theory of large deformations of elastic membranes with bending stiffness is formulated, by applying the minimum-energy principle to a strain-energy density that depends on the second derivatives of the deformation as well as the first derivatives. Controllable deformations are determined. The theory is illustrated by applying it to the strain-energy function for small stretches of an isotropic material, and to a modification of this function that appears to be more useful for analytical purposes.


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