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## Applicationes Mathematicae

1996-1997 | 24 | 3 | 251-265
Tytuł artykułu

### Stress equations of motion of Ignaczak type for the second axisymmetric problem of micropolar elastodynamics

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A second axially-symmetric initial-boundary value problem of linear homogeneous isotropic micropolar elastodynamics in which the displacement and rotation take the forms $\underline{u}=(0,u_θ,0)$, $\underline{φ}=(φ_r,0,φ_z)$ ((r,θ,z) are cylindrical coordinates; cf. [17]) is formulated in a pure stress language similar to that of [12]. In particular, it is shown how $\underline{u}$ and $\underline{φ}$ can be recovered from a solution of the associated pure stress initial-boundary value problem, and how a singular solution corresponding to harmonic vibrations of a concentrated body couple in an infinite space can be obtained from the solution of a pure stress problem.
Słowa kluczowe
EN
Czasopismo
Rocznik
Tom
Numer
Strony
251-265
Opis fizyczny
Daty
wydano
1997
otrzymano
1995-08-08
Twórcy
autor
• Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
Bibliografia
• [1] S. Drobot, On Cosserat continua, Zastos. Mat. 12 (1971), 323-346.
• [2] J. Dyszlewicz, Stress formulation of the second axially-symmetric problem of micropolar theory of elasticity, Bull. Acad. Polon. Sci. Sér. Sci. Tech. 21 (1973), 45-56.
• [3] J. Dyszlewicz, The stress and displacement functions for the second axisymmetric problem of micropolar elastostatics, Arch. Mech. 27 (1975), 393-404.
• [4] J. Dyszlewicz, The problem of stress equations of motion of Ignaczak type. The axisymmetric and plane problems of micropolar elastodynamics, manuscript, IPPT PAN, Warszawa, 1987 (in Polish).
• [5] J. Dyszlewicz, Boundary and Initial-Boundary Value Problems for Micropolar Elastostatic and Elastodynamic Equations, WPW, Wrocław, 1990 (in Polish).
• [6] A. C. Eringen, Linear theory of micropolar elasticity, J. Math. Mech. 15 (1966), 909-930.
• [7] M. E. Gurtin, The Linear Theory of Elasticity, in: Encyclopedia of Physics, vol. 6a/2, Springer, Berlin, 1972.
• [8] I. S. Gradshteĭn and I. M. Ryzhik, Tables of Integrals, Sums, Series and Products, Nauka, Moscow, 1971 (in Russian).
• [9] D. Iesan, On the plane coupled micropolar thermoelasticity, Bull. Acad. Polon. Sci. Sér. Sci. Tech. 16 (1968), 379-384.
• [10] D. Iesan, On the linear theory of micropolar elasticity, Internat. J. Engrg. Sci. 7 (1969), 1213-1220.
• [11] J. Ignaczak, A completeness problem for stress equations of motion in the linear elasticity, Arch. Mech. 15 (1963), 225-234.
• [12] J. Ignaczak, Tensorial equations of motion for elastic materials with microstructure, in: Trends in Elasticity and Thermoelasticity, Witold Nowacki Ann. Volume, Wolters-Noordhoff, Groningen, 1971, 90-111.
• [13] W. Kasprzak and B. Lysik, Dimensional Analysis, WNT, Warszawa, 1988 (in Polish).
• [14] V. D. Kupradze, T. G. Gegelya, M. O. Baskhelishvili and T. V. Burkhuladze, Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity, Nauka, Moscow, 1976 (in Russian).
• [15] J. Mikusiński, Operational Calculus, Pergamon, New York, 1959.
• [16] W. Nowacki, Theory of Elasticity, PWN, Warszawa, 1970 (in Polish).
• [17] W. Nowacki, Theory of Asymmetric Elasticity, PWN, Warszawa, 1981 (in Polish).
• [18] Z. Olesiak, Stress differential equations of the micropolar elasticity, Bull. Acad. Pol. Sci. Sér. Sci. Tech. 18 (1970), 177-184.
• [19] I. N. Sneddon, The Use of Integral Transforms, McGraw-Hill, New York, 1972.
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Bibliografia
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