The Earthquake Engineering Online Archive

The design of steel energy-absorbing restrainers and their incorporation into nuclear power plants for enhanced safety (final technical report, vol 1C): Numerical method for dynamic substructure analysis

Dickens, John Martin; Wilson, Edward L.

UCB/EERC-80/20, Earthquake Engineering Research Center, University of California, Berkeley, 1980-06, 220 pages (530/D38/1980/v.1C)

This report presents several new or improved numerical methods for the dynamic response analysis of large, complex structural systems. The methods presented are primarily concerned with linear dynamic analysis. However, one of the significant results of the research is the development of efficient numerical methods for large systems with a small number of nonlinear members. The technique of dynamic substructure analysis is used to accurately model the behavior of the linear part of the system. This approach allows the behavior of the linear structural members to be reduced to a small number of generalized dynamic coordinates. These linear dynamic coordinates are then used in direct combination with the nonlinear members to approximate the solution of the large nonlinear problem. The methods presented can be applied to structures of arbitrary geometry. However, the use of techniques such as cyclic symmetry can further decrease the numerical effort. The specific numerical algorithms which are studied, modified, and extended are (1) The standard nodal truncation response analysis procedure is reviewed. Either a static or a dynamic correction term is added which will greatly reduce the number of nodes required for an analysis. (2) A time domain formulation for the response of a structure for an arbitrary periodic loading is given. (3) Dynamic substructuring procedures and symmetry methods are reviewed. An alternate derivation for cyclic symmetry is given which is numerically efficient. (4) The subspace iteration algorithm is reviewed and compared to other algorithms which have been used for dynamic substructure analysis. A numerically efficient formulation for Guyen reduction is given. An extension of the subspace iteration for structures comprised of substructures is detailed and problems with the extension are discussed. (5) An efficient numerical technique is presented for solving the eigenvalue problem of a structure described by substructures. (6) An algorithm for the efficient numerical solution of the limited nonlinearity problem is developed based primarily on the concepts presented in two of the report chapters.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-80-20.pdf (5 MB)