Decomposition method for solving systems of differential equations for the problems of modelling corrosion deformation processe
Journal Title: Комп’ютерне моделювання: аналіз, управління, оптимізація - Year 2017, Vol 2, Issue 2
Abstract
The article offers and justifies a method for solving systems of differential equations (SDE) that simulate time changes of stress and strain state due to the influence of corrosive environment (the process of corrosion deformation). The objective of modelling is the determination of the construction durability that is the time of its flawless operation. The finite element model of the object under study determines dimension of SDE modelling the process of corrosion deformation. The right-hand sides of the differential equations contain functions of mechanical stresses. The finite element method is used to calculate stresses. The proposed decomposition method is based on the transformation of the initial differential equations by introducing functions describing the influence of the remaining equations and the subsequent solution of one of these equations. Based on the analysis of the factors influencing the stress change in the area of the given finite element, we propose to introduce into the corresponding differential equation a function approximating the change of internal forces over time. In this case, the discrepancy between the results of the initial SDE solution and an individual equation is determined only by the error in approximating the dependence of the internal force on time. The article shows that this allows a multi-rate reduction of computational costs. In addition, for a numerical solution of SDE, we propose to use a modified algorithm of the Euler method with a variable integration step by argument. The result of the solution is determination of corrosive construction durability, i.e. operating time before exhaustion of bearing capacity. To illustrate the proposed method, we solved the problem of calculating the durability of a flat-plate subjected to corrosive wear. The article provides the results of numerical experiments confirming the accuracy of the proposed numerical solution with minimal computational costs. The decomposition method for solving SDE, modelling the process of corrosion deformation of plane-stressed plates, can be generalized to other classes of constructions.
Authors and Affiliations
D. G. Zelentsov, O. A. Liashenko
Keywords
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