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

Kufner T, Leugering G, Semmler J, Stingl M, Strohmeyer C (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Book Volume: 52

Pages Range: 2409-2431

Journal Issue: 6

DOI: 10.1051/m2an/2018065

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.

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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. Mathematical Modelling and Numerical Analysis, 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." Mathematical Modelling and Numerical Analysis 52.6 (2019): 2409-2431.

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