Numerical Solution to the Contact Interaction Problem of Nuclear Fuel Element Components Using the Mortar Method and the Domain Decomposition Method

The paper presents algorithms for solving axisymmetric contact interaction problems for several thermoelastic bodies using unmatched meshes. We employed the finite element method to obtain numerical solutions to problems of thermal conductivity and the theory of elasticity. We took contact interaction into account by applying the mortar method and the method of domain decomposition. The mortar method requires solving an ill-conditioned system of linear algebraic equations with a zero block at the main diagonal. To solve it numerically, we used a modified method of successive over-relaxation (MSSOR), which makes it possible to reduce solving the system of equations for all contacting bodies to sequentially solving systems of equations for each body separately. We showcase our algorithm results by solving an example problem simulating thermomechanical processes in a nuclear fuel element. We analyse the features of the stress-strain state in the structure and compare the results obtained using the mortar method and the domain decomposition method. The computational domain in the problem considered consisted of 10 nuclear fuel pellets and a cladding section. The analysis results showed that the quantitative stress-strain state properties in a system of bodies obtained by the two methods are quite close to each other. This confirms the fact that these algorithms may be correctly applied to solving similar problems