Geodesic
Effective properties of a composite beam subjected to torsion
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2010), pp. 30-35 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of finding the effective characteristics of a rectilinear beam under pure torsion is considered. The problem is reduced to finding the torsional stress function determined from the solution of a boundary-value problem in the cross section of the beam for a partial differential equation with variable coefficients. Two special boundary-value problems are formulated to find the effective characteristics. It is shown that the effective coefficients are reciprocal in the case of torsion of a layer with nonuniform thickness. In the two-dimensional case, the problem is solved by a finite element method. The cases of a square beam with single and multiple inclusions are discussed. The dependence of the effective characteristics on the inclusion's volume fraction is analyzed. 
@article{VMUMM_2010_2_a4,
     author = {L. V. Olekhova},
     title = {Effective properties of a composite beam subjected to torsion},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {30--35},
     year = {2010},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2010_2_a4/}
}
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L. V. Olekhova. Effective properties of a composite beam subjected to torsion. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2010), pp. 30-35. http://geodesic.mathdoc.fr/item/VMUMM_2010_2_a4/