This paper examines the utilization of a load dependent vector basis generated by a block Lanczos algorithm for dynamic analysis of offshore structures. The block-version is an extension of the single-vector Lanczos method for dealing with dynamic loadings represented by linear combinations of load patterns. such as wave trains with distinct periods and phase angles. The procedure is shortly presented and then applied to the analysis of a steel jacket platform model.
Other techniques have been proposed for generation of an M-orthogonal basis of vectors Φ taking into account the loading (Wilson et al. 1982, Bayo et al., 1984, Arnold et al, 1985, Leger et al.. 1990), without solving the eigen problem (3), which uses to be a computationally-intensive task. Lanczos algorithm (Lanczos, 1950, Parlett, 1980) has been Widely used both in eigen problems solution (Hughes, 1981, Marques and Landau, 1990a) and in the generation of a load-dependent vector basis for structural dynamic response (Nom--Omid and Clough, 1984, Coutinho et al., 1987). The Lanczos procedure can be also implemented in a blocked form so that an improvement in the convergence characteristics for clustered and/or multiple eigen solutions is verified (MSC/NASTRAN, 1985, Marques and Landau, 1990b). The aim of this work is to investigate the utilization of a block type Lanczos algorithm in the generation of a load-dependent vector basis when the loading is defined as a linear combination of load patterns. In the following sections some aspects of the procedure are firstly outlined. Then, some results concerning the application of the method to the linear analysis of a 312 degrees of freedom platform model are presented.
The block Lanczos algorithm for generation of a load-dependent vector basis (Nour-Omid and Clough, 1985) is somewhat similar to the basic algorithm (Nour-Omid and Clough, 1984).