The Sanders-Koiter shell equations can be reduced to two coupled equations for all minimal midsurfaces
Authors:
G. E. Latta and J. G. Simmonds
Journal:
Quart. Appl. Math. 33 (1975), 170-174
DOI:
https://doi.org/10.1090/qam/99668
MathSciNet review:
QAM99668
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Abstract: For an elastically isotropic shell of constant thickness with an analytic midsurface of zero mean curvature, it is shown that the linear Sanders—Koiter equations can be reduced exactly to two coupled fourth-order partial differential equations, involving as unknowns a stress function and the rotation of the midsurface about the normal.
J. L. Sanders, Jr., On the shell equations in complex form, in Proc. Second Sympos. Thin Elastic Shells, Springer-Verlag, Berlin and New York, 1969, pp. 135–156
F. Y. M. Wan, The exact reduction of equations of elastic shells of revolution, Studies in Appl. Math. 48, 361–375 (1969)
- James G. Simmonds, Simplifications and reduction of the Sanders-Koiter linear shell equations for various midsurface geometries, Quart. Appl. Math. 28 (1970), 259–275. MR 267821, DOI https://doi.org/10.1090/S0033-569X-1970-0267821-7
- James G. Simmonds, Extension of Koiter’s $L_{2}$-error estimate to approximate shell solutions with no strain energy functional, Z. Angew. Math. Phys. 22 (1971), 339–345 (English, with German summary). MR 287772, DOI https://doi.org/10.1007/BF01591417
D. J. Struik, Differential geometry, 2nd edition, Addison-Wesley, Reading, Mass., 1961
J. L. Sanders, Jr., On the shell equations in complex form, in Proc. Second Sympos. Thin Elastic Shells, Springer-Verlag, Berlin and New York, 1969, pp. 135–156
F. Y. M. Wan, The exact reduction of equations of elastic shells of revolution, Studies in Appl. Math. 48, 361–375 (1969)
J. G. Simmonds, Simplification and reduction of the Sanders-Koiter linear shell equations for various midsurface geometries, Quart. Appl. Math. 28, 259–275 (1970)
J. G. Simmonds, Extension of Koiter’s L$_{2}$-error estimate to approximate shell solutions with no strain energy functional, Z. A. M. P. 22, 339–345 (1971)
D. J. Struik, Differential geometry, 2nd edition, Addison-Wesley, Reading, Mass., 1961
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Article copyright:
© Copyright 1975
American Mathematical Society
