Keywords: coupled problems, creep of concrete, orthotropic damage, prestressed concrete, finite elements method, parallel computations, Schur complements method.

decreasing coal resources caused a renaissance of nuclear power plants, a relatively stable and clean source of energy. Other sources of energy such as solar and wind power plants were greatly supported by European Union funds but their nonuniform power, which depends on climatic conditions, causes problems with overloading of supply networks. Thus these power plants have to be supplemented from other stable sources. From this reason, many european countries consider construction of new nuclear power plants or the possibility of lifetime prolongation of existing ones.

Our department was involved in preparation of the analysis for lifetime prolongation of nuclear power plant in Temelín. The main objective of the analysis was prediction of security of the concrete containment. The analysis should capture a period of about thirty years with an eventual extension of up to fifty years.

The containment is represented by post-tensioned concrete cylindrical structure which contains steel bar reinforcement in vertical, radial and horizontal directions. The interior of the cylinder wall also contains a hoop of tendons placed in a system of channels. In those conditions, the three-dimensional geometrical model has to be used in order to capture strains in the radial steel reinforcement. Three-dimensional geometry together with the use of advanced material models led to reduction in the model to the representative segment of the containment wall.

In the analyses performed, the creep, ageing and damage effects were taken into account in the concrete. From the above assumptions, the nonlinear thermo-mechanical analysis was performed and its results are presented and discussed. The problem was solved using the SIFEL program which is developed on our department [1]. High demands on computation speed and memory of the sequential version of SIFEL led to the parallelisation of the code based on domain decomposition method. The Schur complement method was implemented for the solution of the system of linear algebraic equations. The paper also describes the system of numbering of the unknowns which had to be parallelised as a result of coupled degrees of freedom (DOFs) on the boundary nodes among particular subdomains.

In this case, the parallel version used an elimination method for system of equations instead of the conjugate gradient method which had to be used in sequential calculations as a result of the large memory demands of the problem. The resulting speed-up on eight processors was over 10 in this case. It should be noted that this was the result of not only by the parallel Schur complement method but also by initial stiffness matrix approach which was enabled by the reduction of memory demands in the domain decomposition.

1

J. Kruis, T. Koudelka, T. Krejcí, "Efficient computer implementation of coupled hydro-thermo-mechanical analysis", Mathematics and Computers in Simulation, 80, 1578-1588, 2010. doi:10.1016/j.matcom.2008.11.010

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