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An exact multiple‐level dynamic substructure technique was developed by a combination of WYD algorithm and static multiple‐level substructuring technique. This method is essentially different from the traditional mode component synthesis. The eigenvalues and eigenvectors created by the method are the eigenpairs for the whole structure and not for the components of structure. On the other hand, the dynamic response by using mode superposition can also be implemented in substructure level. This algorithm actually is an exact substructuring technique which means that substructuring itself did not introduce any additional error except the round‐off when a structure was split into some arbitrary subdomains and the error of WYD or mode superposition themselves. It is no longer necessary to assume any connective condition on the interface between substructures. This method makes the capacity of dynamic analysis of a structural analysis program unlimited. It is especially attractive for the programs on microcomputers. Of course, the method leads to a frequent I/O for a subsequent search of the files from each substructure. It is time consuming compared to the mode component synthesis. But the potential still exists to improve the efficiency by using parallel computation on concurrent computers. In this paper the theory and procedure of the algorithm are presented.

The advantages of a direct superposition of the Ritz vector in dynamic response analysis (developed by Wilson, Yuan, and Dickens in 1982 and termed the WYD method) are that: no iteration is involved; the method is at least four times faster than the subspace iteration method; and fewer Ritz vectors are necessary for the mode superposition of dynamic response analysis than exact eigenvectors are used. The major purpose of this paper is to illustrate that the WYD method can also be used as a general approximate algorithm to calculate eigenvalues and eigenvectors. The WYD and Lanczos algorithms are very similar and a formula that relates the two is given in this paper. Although the exact algebraic value of only a single eigenvector of a multi‐eigenvalue can be calculated using either the WYD or Lanczos methods, an artificial round‐off is presented that can be used to solve the eigenvalue problem. A method of estimating the error introduced by the WYD method is also developed. A dynamic substructuring technique, based on the WYD method, and which assumes that the connectivities on the interfaces among the substructures need not be considered is also presented.

Gives a bibliographical review of the finite element meshing and remeshing from the theoretical as well as practical points of view. Topics such as adaptive techniques for meshing and remeshing, parallel processing in the finite element modelling, etc. are also included. The bibliography at the end of this paper contains 1,727 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1990 and 2001.