On the completeness of Hu Haichang’s solution. (English) Zbl 0622.73021
The completeness of Hu Haichang’s solution is proved in the case of convex regions in z-direction under a supplementary condition. On the other hand, for non-convex region in z-direction, Hu Haichang’s solution is proved to be incomplete.
MSC:
| 74B99 | Elastic materials |
| 31B20 | Boundary value and inverse problems for harmonic functions in higher dimensions |
| 74E10 | Anisotropy in solid mechanics |
References:
| [1] | Mindlin, R., Note on the Galerkin and Papkovitch stress functions.Bull. Amer. Math. Soc. 42 (1936) 373–376. · JFM 62.0939.02 · doi:10.1090/S0002-9904-1936-06304-4 |
| [2] | Hu Hai-chang, On the three-dimensional problems of the theory of elasticity of a transversely isotropic body,Journal of Academia Sinica (Beijing), 2 (1953). · Zbl 0052.20502 |
| [3] | Muki, Asymmetric problems of the theory of elasticity for a semi-infinite solid and a thick plane,Progress in Solid Mechanics, I (ed. by Sneddon and Hill) (1960). · Zbl 0093.10903 |
| [4] | Eubanks, R. A., and Sternberg, E., On the completeness of the Papkovitch stress function.J. Rational Mech. Anal., 5 (1956), 735–746. · Zbl 0072.19002 |
| [5] | Kellogg, O. D., Foundations of Potential Theory, Berling, Springer, (1929), 260. · JFM 55.0282.01 |
| [6] | Slobodyansky, M. G., On the general and complete form of solutions of the equations of elasticity (in Russian).Prac. Math. Mech. 23 (1959), 468–482. |
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