The Signorini perturbation scheme in an abstract setting

Abstract

SynopsisThe Signorini perturbation scheme is a series expansion algorithm that locates solution branches for a class of symmetry-breaking bifurcation problems in nonlinear elastostatics. The relationship of the formal steps in the algorithm to geometric aspects of the problem is brought out in work of J. E. Marsden and Y.-H. Wan, where an abstract formulation is also considered. In this paper, the abstract algorithm and its geometry are explored further: the logical structure is clarified, and it is shown how the scheme adapts to the presence of additional symmetry constraints.