A quasi-Newton versus a homotopy method for nonlinear structural analysis

Abstract

The globally convergent quasi-Newton minimization algorithm and the homotopy algorithms are discussed in detail and their effectiveness in solving certain classes of highly nonlinear problems of structural analysis is demonstrated. The application of the double dogleg strategy controls the directions and step-lengths of the quasi-Newtonian algorithm and overcomes the problem of nonpositive definite Hessians being produced during the iteration process. The algorithms are applied to a centrally loaded clamped beam, the snap-through of a shallow arch, and a shallow reticulated dome.