Sparse null basis computations in structural optimization (Q1115103)

We study the computation of sparse null bases of equilibrium matrices in the context of the force method in structural optimization. Two classes of structural problems are considered. For the class of rigid joined skeletal structures, we use a partitioning method suggested by \textit{J. C. de C. Henderson} and \textit{E. A. W. Maunder} [J. Inst. Math. Appl. 5, 254- 269 (1969; Zbl 0197.214)] to partition the problem into a set of independent null basis computations. For the class of structures represented by a continuum, we compute a sizable fraction of the null vectors in a basis from a consideration of the finite element formulation and the bipartite graph of the equilibrium matrix. The remaining null vectors are computed by the triangular algorithm of \textit{T. E. Coleman} and the author [SIAM J. Alg. Disc. Meth. 8, 544-563 (1987; Zbl 0642.65028)]. The new algorithms find sparser bases than the triangular algorithm and are also faster.