An Assessment Of Quasi-Newton Sparse Update Techniques For Nonlinear Structural Analysis

In this paper an attempt is made to evaluate the performance of a few algorithms for unconstrained minimization of nonlinear functions that exploit sparsity of the Hessians of such functions. The evaluation is centered around large scale, geometrically nonlinear problems of structural analysis in general. In particular, the snap-through response of finite element models of a shallow elastic arch under a concentrated load at the crown is considered. The sensitivity of these algorithms to varying degrees of refinement of these finite element models as well as to the sparsity pattern of the Hessian of the potential surface in question are examined. The paper concludes by making recommendations on the choice of an algorithm based on the scale of the problem and the degree and type of nonlinearity.