Summary
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 jointed skeletal structures, we use a partitioning method suggested by Henderson and Maunder 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 in [6]. The new algorithms find sparser bases than the triangular algorithm and are also faster.
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This research was partially supported by NSF grant CCR-8701723 and AFOSR grant 88-0161
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Pothen, A. Sparse null basis computations in structural optimization. Numer. Math. 55, 501–519 (1989). https://doi.org/10.1007/BF01398913
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DOI: https://doi.org/10.1007/BF01398913