A comparison of three Algorithms for Tracing Nonlinear Equilibrium Paths of Structural Systems

The relative efficiencies of the Riks/Wempner, Crisfield, and normal flow solution algorithms for tracking nonlinear equilibrium paths of structural systems are compared. It is argued that the normal flow algorithm maybe both more computationally efficient and more robust compared to the other two algorithms when tracing the path through severe nonlinearities such as those associated with structural collapse. This is demonstrated qualitatively by comparing the relative behaviors of each algorithm in the vicinity of a severe nonlinearity. Quantitative results are presented for the collapse a blade stiffened panel

Structural Design using Cellular Automata

Traditional parallel methods for structural design do not scale well. This paper discusses the application of massively scalable cellular automata (CA) techniques to structural design. There are two sets of CA rules, one used to propagate stresses and strains, and one to perform design analysis. These rules can be applied serially,periodically,or concurrently, and Jacobi or Gauss- Seidel style updating can be done. These options are compared with respect to convergence,speed, and stability

An interior point method for isogeometric contact

The interior point method is applied to frictionless contact mechanics problems and is shown to be a viable alternative to the augmented Lagrangian approach. The method is derived from a mixed formulation which induces a contact discretization scheme in the spirit of the mortar method and naturally delivers slack variables that help constrain the solution to the feasible region. The derivation of the algorithm as well as its robustness benefits from the contact interface description that is induced by NURBS-based isogeometric volume discretizations. Various interior point algorithms are discussed, including a primal-dual approach that satisfies the unilateral contact constraints exactly, in addition to two primal approaches that retain an arbitrary barrier parameter. The developed algorithms can easily be pursued starting from an augmented Lagrangian implementation. Numerical investigations on benchmark problems demonstrate the efficiency and the robustness of the framework, but also highlight current limitations that suggest paths for future research. Overall, the results indicate that the interior point method can challenge the augmented Lagrangian method in contact mechanics, even displaying potential for higher efficiency and robustness. © 2014 Elsevier B.V