Article

Received 28.12.2023

Revised 23.05.2024

Accepted 30.06.2024

Retrieved from Iss. 115, P. 2, 2024

Pages 96 -106

Kuzminets, M., Maksymyuk, Yu., & Martynyuk, I. (2024). EFFICIENCY OF THE ALGORITHM FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS BASED ON EXTRAPOLATION OF DISPLACEMENTS. Automobile Roads and Road Construction, (115.2), 96-106. https://doi.org/10.33744/0365-8171-2024-115.2-096-106

EFFICIENCY OF THE ALGORITHM FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS BASED ON EXTRAPOLATION OF DISPLACEMENTS

Mykola Kuzminets Yuriy Maksymyuk Ivan Martynyuk

Simulation of long-term processes of physically and geometrically nonlinear deformation requires the use of step algorithms. Such algorithms can be constructed on the basis of the iterative procedure. When it is implemented, the efficiency can be increased by changing the stiffness matrix by recalculating the coordinates of the components of the instantaneous stiffness tensor of the elastoplastic material or by extrapolating the displacements in the next step solution of the problem. In this regard, this article conducts a study of the reliability and efficiency of the results of solving physically and geometrically nonlinear problems using the above-mentioned approaches. This was done by solving a number of test cases, and by analyzing the errors relative to the reference and experimental data, and the computational costs required to solve the problems

physically nonlinear deformation, geometrically nonlinear deformation, numerical methods, creep deformations taking into account material damage, finite element method (MSE), plane-deformed and axisymmetric solids, form change, viscoelasticity, step-by-step algorithm
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https://doi.org/10.33744/0365-8171-2024-115.2-096-106