Saint-Venant's Principle

Toupin, R. A.

doi:10.1007/bf00282253

Cited by 383 publications

(139 citation statements)

References 5 publications

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“…According to Saint-Venant principle, the sphere of influence of a local load is limited [8,9]. Assuming the scope of the influence in z direction is h, then all the stress is zero when z C h, thus,…”

Section: Resultsmentioning

confidence: 99%

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Magneto-optical coupling in bilayer composites of Terfenol-D and Polycarbonate

et al. 2013

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Bilayer composites that can show magnetobirefringence effect were fabricated based on the product effects of magnetostriction and stress-birefringence. Large magneto-optical responses were obtained under a magnetic field lower than 700 Oe at room temperature for the bilayers. The magneto-optical retardation was observed to decrease along the direction vertical to the interface, suggesting a non-uniform stress distribution along the thickness direction in the elasto-optical layer. Local action principle or Saint-Venant's principle was taken into account in analysis of the interlayer elastic coupling and the magneto-birefringence effect. The theory that was consistent with experiments was obtained.

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Section: Resultsmentioning

confidence: 99%

“…Obviously, it is necessary to reconsider the presumption that ''stress distributes uniformly along the thick direction''. In fact, according to the principle of local action, namely, Saint-Venant's principle [8], under a surface force, the stress in an elastic medium distributes nonuniformly in the direction perpendicular to the surface.…”

Section: Introductionmentioning

confidence: 99%

Magneto-optical coupling in bilayer composites of Terfenol-D and Polycarbonate

et al. 2013

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“…Entretanto, uma prova de que o resultado vale dentro da teoria linear só foi conseguida por Toupin [11] em 1965.…”

Section: Qualé De Fato O Enunciado Do "Princípio De Saint-venant"?unclassified

“…Somente em 1965, mais de um século depois da publicação do trabalho de Saint-Venant, e depois de tantas outras tentativas de demosntração do "Princípio de Saint-Venant", R.A. Toupin [11], apresentou a primeira prova rigorosa do "Princípio de Saint-Venant", para um corpo cilíndrico, dentro da teoria da elasticidade linear.…”

Section: O Princípio De Saint-venantunclassified

Notas sobre o Princípio de Saint-Venant

Silva¹

2015

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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“…Dell'Isola and Rosa [7,8] and Davi [9] have investigated the problem for linear piezoelectric materials and dell'Isola and Batra [10] for linear elastic isotropic porous solids. Batra and Yang [11] have proved Toupin's version [12] of the Saint-Venant principle for a linear piezoelectric bar.…”

Section: Introductionmentioning

confidence: 99%

Saint-Venant's problem for a second-order piezoelectric prismatic bar

Vidoli

Batra

Dell’Isola

2000

International Journal of Engineering Science

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For a homogeneous, transversely isotropic, second-order piezoelectric and in®nitesimally prebent, prepolarized and prestretched prismatic bar, we ®nd second-order Saint-Venant solutions. It is found that the electric ®eld alone does not introduce any bending in the second-order piezoelectric bar. However, the electric ®eld induced by the bending of the bar can be used to ascertain the magnitude and direction of the bending vector. The curvature of the centroidal axis of the bar can be changed by the simultaneous application of the electric ®eld and the bending moment. Ó

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Saint-Venant's Principle

Cited by 383 publications

References 5 publications

Magneto-optical coupling in bilayer composites of Terfenol-D and Polycarbonate

Magneto-optical coupling in bilayer composites of Terfenol-D and Polycarbonate

Notas sobre o Princípio de Saint-Venant

Saint-Venant's problem for a second-order piezoelectric prismatic bar

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