A piping system is composed of pipes with various thickness, diameter and length. Accurate analysis of a piping system requires a complicated three-dimensional finite element model and a computer system with large memory size, while a simplified beam model may result in response prediction with deteriorated accuracy. An efficient model for seismic analysis of piping systems is proposed. The proposed model is developed by introducing the pipe joint element which accounts for the local deformations of a pipe joint. Pipes are represented by beam elements and the effect of local deformations of pipe joints is modelled by the pipe joint element deformations. The proposed model which is as simple and efficient as a beam model can be used to obtain the seismic response of piping systems with an accuracy very close to that obtained by a complicated finite element model.
For the analysis of structures, specifically if it is large-scaled systems such as complicated piping systems, the majority of computation time is consumed in the solution of simultaneous linear equations. Equation solvers are classified by direct solvers based on Gauss elimination and iterative solvers derived from the optimization theory. In this thesis, efficient direct and iterative equation solvers for large sparse symmetric matrix are studied. An efficient in-and out-of-core direct column solver utilizing moving memory scheme is developed. Comparing with existing blocking methods the proposed algorithm is simple and this solver automatically performs solution within the core or outside core. Recently, many researches for iterative solvers such as conjugate gradient method have been performed. Conjugate gradient method has superlinearly convergence and finite step convergence properties. And because the stiffness matrix can be compactly stored, it can be an efficient solver for large sparse matrices. Especially, for adaptive refinement analyses or parallel processing analyses, it is very efficient method.
