Axisymmetric Deformation of a Pressurized Thin Elastic Membrane with Nonuniform Thickness
Publication: Journal of Engineering Mechanics
Volume 133, Issue 10
Abstract
Many circular elastic membranes used in practice involve nonuniform thickness, which is a main source of error that affects the functionality of the membrane. An analytical framework is developed in this paper to solve the deflection profile of a pressurized circular membrane with nonuniform thickness. The nonlinear solution is established within the deformed configuration. The results are compared with finite-element simulation with good agreement.
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Acknowledgments
The work was supported in part by the Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY, and in part by NSF CMMI-0407743 and CMMI-0643726. The writer is benefited from discussion with Professor John Hutchinson at Harvard University.
References
ABAQUS. (2004). ABAQUS 6.4 user’s manual, ABAQUS Inc., Pawtucket, R.I.
Alaca, B. E., Selby, J. C., Saif, M. T. A., and Sehitoglu, H. (2002). ”Biaxial testing of nanoscale films on compliant substrates: Fatigue and fracture.” Rev. Sci. Instrum., 73, 2963–2970.
Chen, L. Y., and Shield, R. T. (1974). “On the vibration and stability of finitely inflated spherical and cylindrical elastic membranes.” Rep. No. 397, Dept. of TAM, Univ. of Illinois, Ill.
Haque, M. A., and Saif, M. T. A. (2004). “Deformation mechanisms in free-standing nanoscale thin films: A quantitative in situ transmission electron microscope study.” Proc. Natl. Acad. Sci. U.S.A., 101, 6335–6340.
Huang, H. B., and Spaepen, F. (2000). “Tensile testing of free-standing Cu, Ag, and Al thin films and multilayers.” Acta Mater., 48, 3261–3269.
Kydoniefs, A. D. (1967). “The finite inflation of an elastic toroidal membrane.” Int. J. Eng. Sci., 5, 477–494.
Kydoniefs, A. D., and Spencer, A. J. M. (1967). “The finite inflation of an elastic toroidal membrane of circular cross section.” Int. J. Eng. Sci., 5, 367–391.
Libai, A., and Simmons, J. G. (1998). The nonlinear theory of elastic shells, Cambridge University Press, Cambridge.
Mitchell, D., Guo, Y., and Sarihan, V. (2001). “Methodology for studying the impact of intrinsic stress on the reliability of the electroless Ni UBM structure.” IEEE Trans. Compon. Packag. Technol., 24, 667–671.
Moreau, W. M. (1988). Semiconductor lithography: Principles and materials, Plenum, N.Y.
Nix, W. D. (1989). “Mechanical properties of thin films.” Metall. Trans. A, 20, 2217–2245.
Oliver, W. C., and Pharr, G. M. (2004). “Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology.” J. Mater. Res., 19, 3–20.
Pakula, L. S., Yang, H., Pham, H. T. M., Frenc, P. J., and Sarro, P. M. (2004). “Fabrication of a CMOS compatible pressure sensor for harsh environments.” J. Micromech. Microeng., 14, 1478–1483.
Palisoc, A., Veal, G., Cassapakis, C., Greschik, G., and Mikulas, M. (1998). “Geometry attained by pressurized membranes.” Proc. SPIE, 3356, 747–757.
Pugno, N., Peng, B., and Espinosa, H. D. (2005). “Predictions of strength in MEMS components with defects—A novel experimental–theoretical approach.” Int. J. Solids Struct., 42, 647–661.
Read, D. T., Cheng, Y. W., Keller, R. R., and McColskey, J. D. (2001). “Tensile properties of free-standing aluminum thin films.” Scr. Mater., 45, 583–589.
Reissner, E. (1959). “On finite bending of pressurized tubes.” J. Appl. Mech., 26, 386–392.
Vlassak, J. J., and Nix, W. D. (1992). “A new bulge test technique for the determination of Young’s modulus and Poisson’s ratio of thin films.” J. Mater. Res., 7, 3242–3249.
Weber, W. J., Cesarone, R. J., Miller, R. B., and Doms, P. E. (2002). “A view of the future of NASA’s deep space network and associated systems.” NASA Space Ops Report No. 02-T01-033.
Xiang, Y., Chen, X., and Vlassak, J. J. (2005). “The plane-strain bulge test for thin films.” J. Mater. Res., 20, 2360–2370.
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© 2007 ASCE.
History
Received: Dec 29, 2005
Accepted: Apr 19, 2007
Published online: Oct 1, 2007
Published in print: Oct 2007
Notes
Note. Associate Editor: Bojan B. Guzina
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