Kinetic energy of highly elastic membranes

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 | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/qam/1486549

Article copyright:
© Copyright 1997
American Mathematical Society