Antiplane strain (shear) of orthotropic non-homogeneous prismatic shell-like bodies

• Autorzy: Chinchaladze N. , Jaiani G.
• Języki publikacji: EN

Abstrakty

EN

Antiplane strain (shear) of orthotropic non-homogeneous prismatic shell-like bodies are considered when the shear modulus depending on the body projection (i.e., on a domain lying in the plane of interest) variables may vanish either on a part or on the entire boundary of the projection. We study the dependence of the well-posedness of the boundary conditions (BCs) on the character of the vanishing of the shear modulus. The case of vibration is considered as well.

Słowa kluczowe

EN

antiplane strain; degenerate elliptic equations; weighted spaces; Hardy’s inequality

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2017
• Tom: Vol. 69, nr 4-5
• Strony: 305--316
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Chinchaladze N.

• Iv. Javakhishvili Tbilisi State University Faculty of Exact and Natural Sciences I. Vekua Institute of Applied Mathematics 2 University st. 0186 Tbilisi, Georgia

autor

Jaiani G.

• Iv. Javakhishvili Tbilisi State University Faculty of Exact and Natural Sciences I. Vekua Institute of Applied Mathematics 2 University st. 0186 Tbilisi, Georgia

Bibliografia

• 1. I. Vekua, Shell Theory: General Methods of Construction, Pitman Advanced Publishing Program, Boston-London-Melbourne, p. 491, 1985.
• 2. G. Jaiani, Cusped Shell-like Structures, Springer Briefs in Applied Science and Technology, Springer-Heidelberg-Dordrecht-London-New York, p. 84, 2011.
• 3. G. Jaiani, Antiplane strain (shear) of isotropic non-homogeneous prismatic shell-like bodies, Bull. TICMI, 19, 2, 40–54, 2015.
• 4. N. Chinchaladze, On some dynamical problems of the antiplane strain (shear) of isotropic non-homogeneous prismatic shell-like bodies, Bull. TICMI, 19, 2, 55–65, 2015.
• 5. G. Jaiani, Initial and boundary value problems for singular differential equations and applications to the theory of cusped bars and plates, Complex methods for partial differential equations (ISAAC Serials, 6), H. Begehr, O. Celebi, W. Tutschke [Eds.], Kluwer, Dordrecht, 113–149, 1999.
• 6. G. Jaiani, On a physical interpretation of Fichera’s function, Acad. Naz. dei Lincei, Rend. della Sc. Fis. Mat. e Nat., S. VIII, Vol. LXVIII, fasc. 5, 426–435, 1980.
• 7. G. Jaiani, The first boundary value problem of cusped prismatic shell theory in zero approximation of Vekua theory (in Russian, Georgian and English summaries), Proceedings of I. Vekua Institute of Applied Mathematics, 29, 5–38, 1988.
• 8. G. Jaiani, Application of Vekua’s dimension reduction method to cusped plates and bars, Bull. TICMI, 5, 27–34, 2001.
• 9. G. Fichera, On a unified theory of boundary value problems for elliptic-parabolic equations of second order, Boundary Problems in Differ. Equat. (edited by Langer), Madison, Univ. of Wisconsin Press, 97–120, 1960.
• 10. O.A. Oleynik, E.V. Radkevich, The Second Order Equations with Non-Negativ Charachteristic Form (in Russian), Itogi Nauki, Mathematica, Moscow, p. 252, 1971.
• 11. G. Jaiani, On a generalization of the Keldysh theorem, Georgian Mathematical Journal, 2, 3, 291–297, 1995.
• 12. A.V. Bitsadze, Equations of Mixed Type (in Russian), Izdat. Acad. Nauk SSSR, Moscow, 1959.
• 13. J.L. Lions, E. Magenes, Non-homogeneous Boundary Value Problems and Applications, Springer, Berlin, 1972.
• 14. W. McLean, Strongly Elliptic Systems and Boundary Integral Equations, Cambridge Univ. Press, Cambridge, 2000.
• 15. B. Opic, A. Kufner, Hardy-type Inequalities, Longman Sci. Tech., Harlow, 1990.
• 16. G. Jaiani, A. Kufner, Oscillation of cusped Euler–Bernoulli beams and Kirchhoff–Love plates, Hacettepe Journal of Mathematics and Statistics, 35, 1, 7–53, 2006.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).