Building flexible user interfaces for solving PDEs

FEniCS is a collection of software tools for the automated solution of differential equations by finite element methods. In this note, we describe how FEniCS can be used to solve a simple nonlinear model problem with varying levels of automation. At one extreme, FEniCS provides tools for the fully automated and adaptive solution of nonlinear partial differential equations. At the other extreme, FEniCS provides a range of tools that allow the computational scientist to experiment with novel solution algorithms. © 2010 American Institute of Physics.

Solving problems in production scheduling

Traditionally, production scheduling has been viewed as a problem-solving task that involves a single problem - generation of a suitable schedule. This paper presents an alternative model in which individual difficulties are viewed as problems, and the task is to maintain a suitable schedule by resolving as many of these problems as possible. Decision support software is described that has facilities for defining policies to handle numerous minor problems and complete problem-solving strategies to deal with major problems. The paper then discusses the potential for this style of decision support to improve the performance of human schedulers. © 1995.

On Solving Non-Standard H-/H2/H-Infinity Fault Detection Problems

We discuss solvability issues of H_-/H_2/infinity optimal fault detection problems in the most general setting. A solution approach is presented which successively reduces the initial problem to simpler ones. The last computational step generally may involve the solution of a non-standard H_-/H_2/infinity optimization problem for which we discuss possible solution approaches. Using an appropriate definition of the H- index, we provide a complete solution of this problem in the case of H2-norm. Furthermore, we discuss the solvability issues in the case of H-infinity-norm.

Effects of constraint curvature on structural instability: tensile buckling and multiple bifurcations

Bifurcation of an elastic structure crucially depends on the curvature of the constraints against which the ends of the structure are prescribed to move, an effect which deserves more attention than it has received so far. In fact, we show theoretically and we provide definitive experimental verification that an appropriate curvature of the constraint over which the end of a structure has to slide strongly affects buckling loads and can induce: (i.) tensile buckling; (ii.) decreasing- (softening), increasing- (hardening), or constant-load (null stiffness) postcritical behaviour; (iii.) multiple bifurcations, determining for instance two bifurcation loads (one tensile and one compressive) in a single-degree-of-freedom elastic system. We show how to design a constraint profile to obtain a desired postcritical behaviour and we provide the solution for the elastica constrained to slide along a circle on one end, representing the first example of an inflexional elastica developed from a buckling in tension. These results have important practical implications in the design of compliant mechanisms and may find applications in devices operating in quasi-static or dynamic conditions.