Kinetic energy of highly elastic membranes

Hilgers, M. G.; Pipkin, A. C.

doi:10.1090/qam/1486549

Authors: M. G. Hilgers and A. C. Pipkin
Journal: Quart. Appl. Math. 55 (1997), 791-800
MSC: Primary 73K10; Secondary 73C50, 73G05
DOI: https://doi.org/10.1090/qam/1486549
MathSciNet review: MR1486549
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Abstract: A theory of elastic sheets with bending stiffness has been proposed in which the strain energy density of the sheet includes a dependence on the second-order derivatives. To study the motion of such sheets, a kinetic energy is required that is accurate to the same order. This is obtained by representing the deformation as a power series in the thickness variable. The lowest-order approximation yields the standard membrane kinetic energy. The next order includes a velocity gradient term. A particularly simple physical interpretation for the additional term is obtained. Furthermore, the matrices involved in this term are shown to possess desirable properties, which can be utilized in future analysis.

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