Modification of the iterative method for solving linear viscoelasticity boundary value problems and its implementation by the finite element method
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The problem of structural design of polymeric and composite viscoelastic materials is currently of great interest. The development of new methods of calculation of the stress–strain state of viscoelastic solids is also a current mathematical problem, because when solving boundary value problems one needs to consider the full history of exposure to loads and temperature on the structure. The article seeks to build an iterative algorithm for calculating the stress–strain state of viscoelastic structures, enabling a complete separation of time and space variables, thereby making it possible to determine the stresses and displacements at any time without regard to the loading history. It presents a modified theoretical basis of the iterative algorithm and provides analytical solutions of variational problems based on which the measure of the rate of convergence of the iterative process is determined. It also presents the conditions for the separation of space and time variables. The formulation of the iterative algorithm, convergence rate estimates, numerical computation results, and comparisons with exact solutions are provided in the tension plate problem example.
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- 4.Chazal, C., Pitti, R.M.: Integral approach for time dependent materials finite element method. J. Theor. Appl. Mech. 49(4), 1029–1048 (2011)Google Scholar
- 6.Christensen, R.M.: Theory of Viscoelasticity, 2nd edn. Academic Press, New York (1982)Google Scholar
- 17.Rabotnov, Y.N.: Elementy nasledstvennoy mekhaniki tverdykh tel. Nauka, Moscow (1977). [in Russian]Google Scholar
- 18.Reddy, J.N.: An Introduction to Continuum Mechanics. CUP, New York (2008)Google Scholar
- 21.Svetashkov, A.A.: Iteracionnye metody reshenija zadach linejnoj i nelinejnoj vjazkouprugosti, termovjazkouprugosti, termouprugosti. Thesis (DSci in Physics and Mathematics). Scientific Research Institute of Applied Mathematics and Mechanics, Tomsk State University, Tomsk (2000b). [in Russian]Google Scholar