Energy minimizers of the coupling of a Cosserat rod to an elastic continuum

We formulate the static mechanical coupling of a geometrically exact Cosserat rod to an elastic continuum. The coupling conditions accommodate for the difference in dimension between the two models. Also, the Cosserat rod model incorporates director variables, which are not present in the elastic continuum model. Two alternative coupling conditions are proposed, which correspond to two different configuration trace spaces. For both we show existence of solutions of the coupled problems. We also derive the corresponding conditions for the dual variables and interpret them in mechanical terms

Fast interior point solution of quadratic programming problems arising from PDE-constrained optimization

Interior point methods provide an attractive class of approaches for solving linear, quadratic and nonlinear programming problems, due to their excellent efficiency and wide applicability. In this paper, we consider PDE-constrained optimization problems with bound constraints on the state and control variables, and their representation on the discrete level as quadratic programming problems. To tackle complex problems and achieve high accuracy in the solution, one is required to solve matrix systems of huge scale resulting from Newton iteration, and hence fast and robust methods for these systems are required. We present preconditioned iterative techniques for solving a number of these problems using Krylov subspace methods, considering in what circumstances one may predict rapid convergence of the solvers in theory, as well as the solutions observed from practical computations

Sparsing in Real Time Simulation

Modelling of mechatronical systems often leads to large DAEs with stiff components. In real time simulation neither implicit nor explicit methods can cope with such systems in an efficient way: explicit methods have to employ too small steps and implicit methods have to solve too large systems of equations. A solution of this general problem is to use a method that allows manipulations of the Jacobian by computing only those parts that are necessary for the stability of the method. Specifically, manipulation by sparsing aims at zeroing out certain elements of the Jacobian leading t a structure that can be exploited using sparse matrix techniques. The elements to be neglected are chosen by an a priori analysis phase that can be accomplished before the real-time simulaton starts. In this article a sparsing criterion for the linearly implicit Euler method is derived that is based on block diagnonalization and matrix perturbation theor

Mixed-mode Integration for Real-time Simulation

The new possibilities of multi-domain hierarchical modelling often lead to models with both fast and slow parts. In this paper a new approach to simulate such systems is discussed that is especially useful in real-time applications. Mixed-mode integration represents a middle course between implicit and explicit integration. The main idea is to split up the system into a fast and a slow part and to apply implicit discretization only to the fast part. The partitioning of the system can be performed offline using a newly developed automatic selection routine, before real-time simulation starts. Mixed-mode integration was applied to several Modelica models from different fields, e.g. models of a diesel engine and an industrial robot and tested using Dymola. Speedup factors from about 4-16 were recorded. In this paper, mixed-mode integration is introduced, the selection routine is described and numerical results are presented

Wear Testing of Knee Implants

Hardware wear tests for knee implants, necessary for market authorization, are expensive and time-consuming. Faster than realtime wear simulations have the potential to speed up the design process for implants by providing frequent and early feedback

Hölder Continuity and Optimal Control for Nonsmooth Elliptic Problems

The well known De Giorgi result on Hölder continuity for solutions of the Dirichlet problem is re-established for mixed boundary value problems, provided that the underlying domain is a Lipschitz domain and the border between the Dirichlet and the Neumann boundary part satisfies a very general geometric condition. Implications of this result for optimal control theory are presented