FASTER UPLIFT ANALYSIS USING INVERSE OF PARTIAL TANGENT STIFFNESS MATRIX

Abstract

 In the seismic design of nuclear power plant (NPP) buildings, the evaluation of basement uplift is an important factor. However, a lot of calculation time is required for these analyses with large finite element (FE) models, which then becomes a problem.

 This study proposes a novel method to accelerate the uplift analysis for NPP buildings. The proposed method does not require an inverse matrix operation of the whole tangent stiffness matrix, which requires considerable computation time when using the tangent stiffness method. Instead, by using the inverse of the partial tangent stiffness matrix, the calculation time can be reduced

 First, the outline and details of the method are described. Then, the results of the experiments that were performed to evaluate the proposed method are presented.

 

 The findings of this study are as follows:

 

 (1) The proposed method uses two inverse matrices to correct the displacement vector. One of them is the inverse of a partial matrix of only the degrees of freedom connected to nonlinear elements in a tangential stiffness matrix. The other method is the inverse matrix of the initial stiffness matrix. The proposed method can thus save on computational cost of the inverse matrix operation for the large total tangent stiffness matrix, which is required in the conventional tangential stiffness method, and reduces the overall computation time.

 

 (2) The proposed method is applied to sample problems to validate the effectiveness. The results indicate that the proposed method can reduce calculation time to less than half of that required for the tangential stiffness method, while ensuring accuracy of the analysis regardless of the magnitude of uplift. In addition, it is important to make the squire partial matrix in which the size corresponds to the degree of freedom connecting the nonlinear elements. Furthermore, it is confirmed that the speedup effect of the proposed method increases as the model size increases.