Sommario
Si fa notare che esistono almeno due soluzioni diverse del problema dei carichi concentrati nella teoria lineare, a due dimensioni, delle coppie di volume quando la formulazione è basata sul teorema di unicità.
Si dimostra una estensione di questo teorema di unicità. Si trova un gruppo di condizioni sufficienti per l'unicità; queste condizioni vengono usate nella formulazione del problema del carico concentrato che dà luogo ad un'unica soluzione.
La nuova condizione significativa è che l'ordine della singolarità dello sforzo è limitato a O(r−1), dove r è la distanza dal carico concentrato.
Summary
It is pointed out that there exist at least two different solutions of the problem of concentrated loads in the two-dimensional, linear couple-stress theory when the formulation is based on the usual uniqueness theorem. An extension of this uniqueness theorem is proved. A set of conditions sufficient for uniqueness is found and is used in a formulation of the concentrated load problem which results in a unique solution. The significant new condition is that the order of the stress singularity is limited to O(r−1), where r is the distance from the concentrated load.
References
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This work is a result of research sponsored by the Office of Naval Research, U.S. Navy, under Contract Nonr-610(06).
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Hartranft, R.J., Sih, G.C. Uniqueness of the concentrated-load problem in the linear theory of couple-stress elasticity. Meccanica 3, 195–198 (1968). https://doi.org/10.1007/BF02129253
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DOI: https://doi.org/10.1007/BF02129253