Effect of General Sparse Matrix Algorithm on Optimization of Space Structures

摘要

The global stiffness matrix of a structural analysis problem is a sparse matrix with many zero elements. The number of zeros in this matrix increases with the size of the structure. The zero terms inside the stiffness matrix slow down the processing speed of the computations due to unnecessary operations performed on them. To overcome these problems, banded and skyline (envelope or variable band) methods of data structures were developed and are in use for storage of stiffness coefficients and their subsequent operations. However, as the size of the structure increases, the bandwidth will also increase, and the number of zeros within the band becomes large for large structures with hundreds or thousands of members. In this case, the solution by the banded or the skyline method may not be the most efficient one. In this work, we investigate the effect of a general sparse matrix approach on the optimization of large structures using the optimalily criteria approach and the Cholesky lower-upper (LU) decomposition method for the solution of the resulting linear simultaneous equations.