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RESEARCH PAPERS: Additional Research Papers

Strain Fields on Cell Stressing Devices Employing Clamped Circular Elastic Diaphragms as Substrates

[+] Author and Article Information
J. L. Williams, J. H. Chen, D. M. Belloli

Department of Orthopaedic Surgery and Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104

J Biomech Eng 114(3), 377-384 (Aug 01, 1992) (8 pages) doi:10.1115/1.2891398 History: Received April 30, 1991; Revised September 25, 1991; Online March 17, 2008

Abstract

Solutions are presented for the surface strain fields on inflated elastomeric circular diaphragms used for in vitro cell stressing experiments. It is shown, by using the method developed by Way (1934) to solve the nonlinear von Karman plate equations, that the surface strains due to bending are not negligible and that large negative radial strains arise near the clamped edge for center deflection-to-thickness ratios (w/h)< 10. The method of Hart-Smith and Crisp (1967) was used for w/h>10 to solve the nonlinear equations for symmetrical deformation of axially symmetrical rubber-like membranes. In the membrane solutions the circumferential strains drop parabolically to zero at the clamped edge of the diaphragm, while the radial strains increase slightly with the radius. The solutions for w/h>10 are compared to optical measurements of in-plane displacements used to calculate the circumferential strains on the diaphragm, yielding excellent agreement with the theory.

Copyright © 1992 by The American Society of Mechanical Engineers
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