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Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya, 2013, Issue 3, Pages 83–96
(Mi vspui138)
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This article is cited in 3 scientific papers (total in 3 papers)
Applied mathematics
Plane problems of concentrated forces for half-linear material
V. M. Mal’kov, Yu. V. Mal'kova St. Petersburg State University, St. Petersburg 199034, Russian Federation
Abstract:
The plane problems of nonlinear elasticity (the plane strains and the plane stresses) are considered for a plane and a half-plane under the action of concentrated forces. Mechanical properties are described by a half-linear material model. Using a harmonious material model has allowed to apply the methods of theory complex functions and receive exact analytical global solutions of problems, including: concentrated force on the interface of materials of a two-componential plane and concentrated force on the border of a half-plane (problems of Flamant and Michel). From global solutions asymptotic stresses and displacements in a vicinity of a force application point are constructed. The comparison of the results obtained with the solutions of Flamant and Michel linear problems has shown that stresses and displacements have identical singularities in a vicinity of a force application point $-1/r$, displacements have logarithmic singularity $-\ln r$. At the same time there are also principal differences: in linear problems only radial stresses are distinct from zero, and in nonlinear and shear stresses they are not equal to zero. Besides, factors at singular members in nonlinear and linear problems are different. Bibliogr. 10.
Keywords:
plane problems, concentrated force, half-linear material, complex functions method, asymptotic series.
Received: March 21, 2013
Citation:
V. M. Mal’kov, Yu. V. Mal'kova, “Plane problems of concentrated forces for half-linear material”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2013, no. 3, 83–96
Linking options:
https://www.mathnet.ru/eng/vspui138 https://www.mathnet.ru/eng/vspui/y2013/i3/p83
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