This paper presents an eigensolution method by the power method (or the inverse power method) and the preconditioned conjugate gradient method in the symmetric matrices. The proposed method has been derived retaining the advantages of the conjugate gradient method. This method is particularly useful for the case where the largest (or the smallest) eigenvalue and the corresponding eigenvector are required to obtain. Some numerical illustrations are presented to verify the proposed method.
The design method of steel sheet pile wall is usually based on the assumption that this type of structure behaves like a beam on elastic support. Some relationships between deflection of a beam and subgrade reaction have been presented. Especially the Chang’s assumption that the relationship is linear is generally appropriate. However, there are few studies about variation of ground properties in depth direction. In some cases where stiffness of ground varies arbitrarily in depth direction, to determine the stiffness requires engineer’s experiences and considerations. In order to overcome these difficulties, an approximate method that can represent all layers comes to be necessary. As one of solutions, in this paper we deal with finite element method using stiffness of ground interpolated by a spline function. A finite element method using this stiffness is illustrated by application to a continuous ground and multi-layered grounds. The former is an example which can be solved analytically, and the latter is one which approximately reproduced by random numbers. As a result of calculations, this method provides sufficient accuracy about horizontal displacement. Moreover, we discuss about applicability of cubic spline to curve fitting of shear force. This method provides sufficient accuracy about location in which maximum shear force occurred.