Mathematical modeling of the contact interaction of the fuel element with creep using the mortar-method

The paper considers the contact problem of the elasticity theory in a static spatial two-dimensional formulation without considering friction. For discretization of the elasticity theory equations, the finite element method was introduced using a triangular unstructured grid and linear and quadratic basis functions. To account for the contact boundary conditions, a modified method of Lagrange multipliers with independent contact boundary is proposed. This method implies the ability to construct a contact boundary with the smoothness degree required for the solution precision and to execute approximation of the Lagrange multiplier function independent of the grids inside the contacting bodies. Various types of the Lagrange multiplier function approximations were studied, including piecewise constant, continuous piecewise linear functions and piecewise linear functions with discontinuities at the difference cells boundaries. Examples of test calculations are provided both for problems with rectilinear and curvilinear contact boundaries. In both cases, the use of discontinuous approximations of the Lagrange multiplier function makes it possible to obtain a numerical solution with fewer artificial oscillations and higher rate of convergence at the grid refinement. It is shown that the numerical solution precision could be improved by more detailed discretization of the contact boundary without changing the grids inside the contacting bodies

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Comparison of the effectiveness of methods for solving systems of linear equations in the problem of modeling the contact interaction of fuel elements in a thermoelastic formulation

Aronov¹,

Rodin²

2022

KIAM Prepr.

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Various algorithms for solving systems of linear algebraic equations that arise when modeling problems of contact interaction of thermoelastic bodies with a changing configuration of the contact surface are considered. The implementations of modified iterative methods, the Uzawa method, as well as algorithms based on the use of the Gauss method and the generalized method of minimal residuals (GMRES) with two iterative refinement options allowing for the exit from contact of individual sections of the contact boundary are presented. The efficiency of the presented algorithms is compared in relation to a problem simulating thermomechanical processes in a section of a fuel element that includes up to 100 fuel pellets.

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Mathematical modeling of the contact interaction of the fuel element with creep using the mortar-method

Cited by 4 publications

References 7 publications

Application of algorithm with variable step in time to solve problem of contact interaction of fuel element with account of creep

Application of algorithm with variable step in time to solve problem of contact interaction of fuel element with account of creep

Comparison of the Lagrange Multipliers Function Approximation Methods in Solving Contact Problems by the Independent Contact Boundary Technique

Comparison of the effectiveness of methods for solving systems of linear equations in the problem of modeling the contact interaction of fuel elements in a thermoelastic formulation

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