Elastic–plastic analysis of nuclear structures with millions of DOFs using the hierarchical domain decomposition method Original Research Article

The hierarchical domain decomposition method (HDDM) proposed by Comp. Sys. Eng. 4 (1993) 495 is applied to the large scale elastic–plastic finite element (FE) analysis of nuclear structures. The HDDM is a method to implement the finite element method (FEM) on various kinds of parallel environments. The substructure-based iterative methods can effectively be used with the HDDM to solve the large scale linear algebraic equations derived from the implicit FEM. In this paper, some key techniques to parallelize the static elastic–plastic FE analysis by the HDDM are described. As illustrative examples, a support structure of the high temperature engineering test reactor (HTTR), a pressure vessel, and an internal pump of a pressure vessel are analyzed. The structure of HTTR and the pressure vessel are modeled by hexahedral solid elements whose total degrees of freedom (DOFs) are about 1.3 millions (M) and 3 M, respectively. The internal pump is modeled by quadratic tetrahedral elements whose total DOFs are about 2 M. The elastic–plastic analysis of a simple cube with 10 M DOFs is also carried out. Both the conjugate gradient method for solving the linear equations and the Newton–Raphson method for solving nonlinear problems successfully converge.