Kinetic Energy of Highly Elastic Membranes
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.
Recommended Citation
Hilgers, M. G., & Pipkin, A. C. (1997). Kinetic Energy of Highly Elastic Membranes. Quarterly of Applied Mathematics, 55(4), pp. 791-800. American Mathematical Society; Brown University.
The definitive version is available at https://doi.org/10.1090/qam/1486549
Department(s)
Business and Information Technology
International Standard Serial Number (ISSN)
0033-569X
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 American Mathematical Society; Brown University, All rights reserved.
Publication Date
01 Jan 1997
