SIMULATION AND STRUCTURAL OPTIMIZATION OF 3D TIMOSHENKO BEAM NETWORKS BASED ON FULLY ANALYTIC NETWORK SOLUTIONS

Journal article


Publication Details

Author(s): Kufner T, Leugering G, Semmler J, Stingl M, Strohmeyer C
Journal: Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique
Publication year: 2019
Volume: 52
Journal issue: 6
Pages range: 2409-2431
ISSN: 0764-583X


Abstract

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.


FAU Authors / FAU Editors

Kufner, Tobias
Professur für Angewandte Mathematik (Kontinuierliche Optimierung)
Leugering, Günter Prof. Dr.
Lehrstuhl für Angewandte Mathematik
Semmler, Johannes
Lehrstuhl für Angewandte Mathematik
Stingl, Michael Prof. Dr.
Professur für Angewandte Mathematik (Kontinuierliche Optimierung)
Strohmeyer, Christoph
Lehrstuhl für Angewandte Mathematik


How to cite

APA:
Kufner, T., Leugering, G., Semmler, J., Stingl, M., & Strohmeyer, C. (2019). SIMULATION AND STRUCTURAL OPTIMIZATION OF 3D TIMOSHENKO BEAM NETWORKS BASED ON FULLY ANALYTIC NETWORK SOLUTIONS. Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique, 52(6), 2409-2431. https://dx.doi.org/10.1051/m2an/2018065

MLA:
Kufner, Tobias, et al. "SIMULATION AND STRUCTURAL OPTIMIZATION OF 3D TIMOSHENKO BEAM NETWORKS BASED ON FULLY ANALYTIC NETWORK SOLUTIONS." Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique 52.6 (2019): 2409-2431.

BibTeX: 

Last updated on 2019-20-07 at 07:22