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
Related Articles
- EP ID EP642512
- DOI -
- Views 124
- Downloads 0
Застосування функціонально-модульного підходу до проектування підсистеми визначення збалансованого раціону харчування
Запропоновано проектування інформаційної підсистеми визначення збалансованого раціону харчування. У зв’язку з необхідністю здорового харчування серед населення було поставлено задачу провести проектування підсистеми, яка...
Развитие и становление трансдисциплинарных и междисциплинарных исследований и роль информатики
Рассмотреные методологии трансдисциплинарных и междисциплинарных научных исследований, информационные технологии их поддержки непосредственно или косвенно апеллируют к научной картине мира, которая позволит повысить эффе...
Free vibrations modeling of the rectangular plate with an arbitrary from hole
The Reissner variations principle is used to study influence of an arbitrary hole on the frequencies of rectangular plate. Deflection and moments are approximated independently through the R-functions with a few (not def...
Research of the trajectory of pollution diffusion from a point source depending on the nature of the landscape
The behavior of the flow of pollutants during process of diffusion from a chimney is investigated in this paper. It will help to understand the process of air pollution better. By means of the Solid Edge program three th...
Применение генетических алгоритмов в задачах дискретной оптимизации корродирующих конструкций
В работе предлагается новый эффективный алгоритм решения задач оптимального проектирования корродирующих шарнирно-стержневых конструкций, предполагающий получение решения с заданной точностью. При решении оптимизационной...