In a previous work, it was shown how the linearized strain tensor field can be considered as the sole unknown in the Neumann problem of linearized elasticity posed over a domain , instead of the displacement vector field in the usual approach. The purpose of this Note is to show that the same approach applies as well to the Dirichlet–Neumann problem. To this end, we show how the boundary condition on a portion of the boundary of Ω can be recast, again as boundary conditions on , but this time expressed only in terms of the new unknown .
Dans un travail antérieur, on a montré comment le champ des tenseurs linéarisés des déformations peut être considéré comme la seule inconnue dans le problème de Neumann pour lʼélasticité linéarisée posé sur un domaine , au lieu du champ des déplacements dans lʼapproche habituelle. Lʼobjet de cette Note est de montrer que la même approche sʼapplique aussi bien au problème de Dirichlet–Neumann. À cette fin, nous montrons comment la condition aux limites sur une portion de la frontière de Ω peut être ré-écrite, à nouveau sous forme de conditions aux limites sur , mais exprimées cette fois uniquement en fonction de la nouvelle inconnue .
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Philippe Ciarlet 1; Cristinel Mardare 2
@article{CRMATH_2013__351_7-8_329_0, author = {Philippe Ciarlet and Cristinel Mardare}, title = {Expression of {Dirichlet} boundary conditions in terms of the strain tensor in linearized elasticity}, journal = {Comptes Rendus. Math\'ematique}, pages = {329--334}, publisher = {Elsevier}, volume = {351}, number = {7-8}, year = {2013}, doi = {10.1016/j.crma.2013.04.015}, language = {en}, }
TY - JOUR AU - Philippe Ciarlet AU - Cristinel Mardare TI - Expression of Dirichlet boundary conditions in terms of the strain tensor in linearized elasticity JO - Comptes Rendus. Mathématique PY - 2013 SP - 329 EP - 334 VL - 351 IS - 7-8 PB - Elsevier DO - 10.1016/j.crma.2013.04.015 LA - en ID - CRMATH_2013__351_7-8_329_0 ER -
%0 Journal Article %A Philippe Ciarlet %A Cristinel Mardare %T Expression of Dirichlet boundary conditions in terms of the strain tensor in linearized elasticity %J Comptes Rendus. Mathématique %D 2013 %P 329-334 %V 351 %N 7-8 %I Elsevier %R 10.1016/j.crma.2013.04.015 %G en %F CRMATH_2013__351_7-8_329_0
Philippe Ciarlet; Cristinel Mardare. Expression of Dirichlet boundary conditions in terms of the strain tensor in linearized elasticity. Comptes Rendus. Mathématique, Volume 351 (2013) no. 7-8, pp. 329-334. doi : 10.1016/j.crma.2013.04.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.04.015/
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