On the convergence of domain decomposition algorithm for the body with thin inclusion

• Autorzy: Styahar A. , Savula Y.
• Języki publikacji: EN

Abstrakty

EN

We consider a coupled 3D model that involves computation of the stress-strain state for the body with thin inclusion. For the description of the stress-strain state of the main part, the linear elasticity theory is used. The inclusion is modelled using Timoshenko theory for shells. Therefore, the dimension of the problem inside the inclusion is decreased by one. For the numerical solution of this problem we propose an iterative domain decomposition algorithm (Dirichlet-Neumann scheme). This approach allows us to decouple problems in both parts and preserve the structure of the corresponding matrices. We investigate the convergence of the aforementioned algorithm and prove that the problem is well-posed.

Słowa kluczowe

EN

elasticity theory; Timoshenko shell theory; Steklov-Poincare operator; domain decomposition

PL

teoria sprężystości; teoria Tymoszenki; operator Steklova-Poincare'a

• Wydawca: Oficyna Wydawnicza Politechniki Białostockiej
• Czasopismo: Acta Mechanica et Automatica
• Rocznik: 2015
• Tom: Vol. 9, no. 1
• Strony: 27--32
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Styahar A.

• Faculty of Applied Mathematics and Informatics, Department of Applied Mathematics, Ivan Franko Lviv National University, Universytetska,1, 79000, Lviv, Ukraine

autor

Savula Y.

• Faculty of Applied Mathematics and Informatics, Department of Applied Mathematics, Ivan Franko Lviv National University, Universytetska,1, 79000, Lviv, Ukraine

Bibliografia

• 1. Dyyak I., Savula Ya., Styahar A. (2012), Numerical investigation of a plain strain state for a body with thin cover using domain decomposition, Journal of Numerical and Applied Mathematics, 3 (109), 23–33.
• 2. Dyyak I., Savula Ya. (1997), D-Adaptive mathematical model of solid body with thin coating, Mathematical Studies, 7 (1), 103–109.
• 3. Hsiao G.C., Wendland W.L. (2008), Boundary integral equations, Springer.
• 4. Nazarov S. (2005), Asymptotic analysis and modeling of a jointing of a massive body with thin rods, Journal of Mathematical Sciences, 127 (5), 2192-2262.
• 5. Niemi A.H., Babuska I., Pitkaranta J., Demkowicz L. (2010), Finite element analysis of the Girkmann problem using the modern hpversion and the classical h-version, ICES Report, 10-47.
• 6. Pelekh B. (1978), Generalized shell theory, Lviv (in Russian).
• 7. Quarteroni A., Valli. A. (1999), Domain decomposition methods for partial differential equations, Oxford.
• 8. Savula Ya., Mang H., Dyyak I., Pauk N. (2000), Coupled boundary and finite element analysis of a special class of two-dimensional problems of the theory of elasticity, Computers and Structures, 75 (2), 157-165.
• 9. Sulym H. (2007), Bases of mathematical theory of thermoelastic eqiulibrium of deformable solids with thin inclusions, Research and Publishing Center of Shevchenko Scientific Society, Lviv (in Ukrainian).
• 10. Vynnytska L., Savula Ya. (2008), The stress-strain state of elastic body with thin inclusion, Ph.-Math. Modeling and Information Techonogies, 7, 21-29 (in Ukrainian).
• 11. Vynnytska L., Savula Ya. (2012), Mathematical modeling and numerical analysis of elastic body with thin inclusion, Computational Mechanics, 50 (5), 533-542.