Abstract
An efficient computational procedure is proposed for identifying singular points in global bifurcation analysis of the static behavior of symmetric discrete structures such as symmetric truss domes. Assuming group equivariance of the system of equations describing the steady state, and making use of group representation theory, the proposed method decomposes the Jacobian matrix (or tangent stiffness matrix) into block-diagonal form, with possibly repeated occurrences of identical blocks, by means of a suitable “local” coordinate transformation. The “local” transformation is computationally favorable in that it requires a small amount of computation and preserves the sparsity of the original Jacobian matrix fairly well. A concrete procedure is described for symmetric truss structures which are equivariant to dihedral groups; an explicit formula is given to the number of diagonal blocks into which the Jacobian matrix splits, and an estimate of the required number of computations shows the efficiency of the proposed method.
Published Version
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