On Constanda’s matrix of nonuniqueness in a theory of plates in asymmetric elasticity
Authors:
Chong-Qing Ru and Peter Schiavone
Journal:
Quart. Appl. Math. 56 (1998), 137-145
MSC:
Primary 73K10; Secondary 73B25
DOI:
https://doi.org/10.1090/qam/1604817
MathSciNet review:
MR1604817
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Abstract: We apply the direct method to the solution of the Dirichlet problem in the bending of micropolar plates and show that a necessary and sufficient condition for solubility is the nonsingularity of a special constant matrix constructed for any smooth closed boundary curve.
- George C. Hsiao and Ralph E. Kleinman, On a unified characterization of capacity, Potential theory (Prague, 1987) Plenum, New York, 1988, pp. 103–119. MR 986284, DOI https://doi.org/10.1007/978-1-4613-0981-9_14
- Einar Hille, Analytic function theory. Vol. II, Introductions to Higher Mathematics, Ginn and Co., Boston, Mass.-New York-Toronto, Ont., 1962. MR 0201608
- Christian Constanda, On integral solutions of the equations of thin plates, Proc. Roy. Soc. London Ser. A 444 (1994), no. 1921, 317–323. MR 1290086, DOI https://doi.org/10.1098/rspa.1994.0021
- Peter Schiavone and Christian Constanda, Existence theorems in the theory of bending of micropolar plates, Internat. J. Engrg. Sci. 27 (1989), no. 4, 463–468. MR 998293, DOI https://doi.org/10.1016/0020-7225%2889%2990136-5
- P. Schiavone and C. Constanda, Uniqueness in the elastostatic problem of bending of micropolar plates, Arch. Mech. (Arch. Mech. Stos.) 41 (1989), no. 5, 785–791 (1990). MR 1097054
P. Schiavone, The application of the boundary integral equation method to boundary value problems in the bending of thin micropolar plates, Ph.D. Thesis, University of Strathclyde, Glasgow, Scotland, 1988
G. C. Hsiao and R. E. Kleinman, On a unified characterization of capacity, Potential Theory, Plenum, Prague, 1988, pp. 5–119
E. Hille, Analytic Function Theory, Vol. II, Ginn and Company, Boston, New York, 1962
C. Constanda, On integral solutions of the equations of thin plates, Proc. Royal Soc. London A 444, 317–323 (1994)
P. Schiavone and C. Constanda, Existence theorems in the theory of bending of micropolar plates, Internat. J. Engrg. Sci. 27, 463–468 (1989)
P. Schiavone and C. Constanda, Uniqueness in the elastostatic problem of bending of micropolar plates, Arch. Mech. 41, 5, 785–791 (1989)
P. Schiavone, The application of the boundary integral equation method to boundary value problems in the bending of thin micropolar plates, Ph.D. Thesis, University of Strathclyde, Glasgow, Scotland, 1988
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Article copyright:
© Copyright 1998
American Mathematical Society
