Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

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.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/qam/1486549
Article copyright: © Copyright 1997 American Mathematical Society

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