Harwell-Boeing Sparse Collection

BCSSTRUC1: BCS Structural Engineering Matrices (eigenvalue matrices)

BCSSTRUC1
Source:	John Lewis, Boeing Computer Services, Seattle, Washington.
Discipline:	Dynamic analyses in structural engineering
Accession:	Summer 1982

These matrices all represent dynamic analyses in structural engineering. They have been extracted from various structural engineering packages such as GT-STRUDL, MSC/NASTRAN, and BCS ATLAS. All of these matrices come in pairs. The first matrix, K, is the stiffness matrix while the second, M, is the mass matrix for the dynamic modelling of structures. Structural engineering requires the computations of a few modes, usually the lowest, of the generalized eigenvalue problem, . Most of the matrices were extracted in the years 1980 to 1982.

Some of the collected problems demonstrate the effect of standard structural engineering techniques. BCSSTK02 and BCSSTM02 are the result of applying ``static condensation'' to the oil rig model represented by BCSSTK04 and BCSSTM04. Static condensation can be applied in cases where the mass matrix is singular to reduce the problem order while preserving the spectrum. However, the reduced stiffness matrix is usually dense, which is the case here. Good sparse eigenvalue codes should be able to solve a large sparse problem much more quickly than a dense code can solve the reduced problem of order one-half or one-third the original. This problem is probably too small to demonstrate that effect.

Matrices BCSSTK06 and BCSSTM06 represent the ``lumped'' (diagonal) mass formulation for the same problem for which BCSSTK07 and BCSSTM07 form the ``consistent'' mass formulation. BCSSTK11, BCSSTM11, BCSSTK12, and BCSSTM12 represent the lumped and consistent mass formulation for an ore car model. In both cases, the consistent mass formulations lead to non-diagonal mass matrices. The eigenvalues from the two formulations of a model should be similar, but not necessarily equal.

Matrices BCSSTK08 and BCSSTM08 have several clusters of eigenvalues where a doubleton (eigenvalue with multiplicity 2) is very close to a third eigenvalue.