SIMULATION AND STRUCTURAL OPTIMIZATION OF 3D TIMOSHENKO BEAM NETWORKS BASED ON FULLY ANALYTIC NETWORK SOLUTIONS - Kufner, Tobias; Leugering, Günter; Semmler, Johannes; Stingl, Michael; Strohmeyer, Christoph (Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique, 2019)
This article is concerned with the efficient and accurate simulation and optimization of linear Timoshenko beam networks subjected to external loads. A solution scheme based on analytic ansatz-functions known to provide analytic solutions for the deformation and rotation of a single beam with given boundary data is extended to the full network. It is demonstrated that the analytic approach is equivalent to a finite element (FE) method where only one element with a suitably chosen shape function per beam is required. The solution of the FE-type system provides analytic solutions at the nodes, from which the solutions along the beams can be reconstructed. Consequently analytic solutions for the network can be computed by a numerical scheme without applying a spacial discretization. While the assembly of the local stiffness matrices is slightly more expensive compared to an FE model using, e.g., linear ansatz-functions, the complexity of the solution of the FE-system is not. This is particularly interesting for topology and material optimization problems formulated on the network. In order to demonstrate the efficiency of the approach a numerical comparison to the case of linear ansatz-functions is provided followed by a series of studies with topology and multi-material optimization problems on networks.
CRIS-Team WoS Importer:2019-03-29

Towards a lifecycle oriented design of infrastructure by mathematical optimization - Kufner, Tobias; Leugering, Günter; Martin, Alexander; Medgenberg, J.; Schelbert, Jakob; Schewe, Lars; Stingl, Michael; Strohmeyer, Christoph; Walther, Maximilian (Optimization and Engineering, 2019)
Today’s infrastructures are mainly designed heuristically using state-of-the-art simulation software and engineering approaches. However, due to complexity, only part of the restrictions and costs that show up during the lifecycle can be taken into account. In this paper, we focus on a typical and important class of infrastructure problems, the design of high-pressure steam pipes in power plants, and describe a holistic approach taking all design, physical, and technical constraints and the costs over the full lifecycle into account. The problem leads to a large-scale mixed-integer optimization problem with partial differential equation (PDE) constraints which will be addressed hierarchically. The hierarchy consists of a combinatorial and a PDE-constrained optimization problem. The final design is evaluated with respect to damage, using beam models that are nonlinear with respect to kinematics as well as constitutive law. We demonstrate the success of our approach on a real-world instance from our industrial partner Bilfinger SE.<br
Keywords: Structural optimization; Lifecycle oriented design; Mixed integer nonlinear programming