Simulation and structural optimization of 3d Timoshenko beam networks based on fully analytic network solutions
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 6, pp. 2409-2431.

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.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2018065
Classification : 34B45, 68U20, 74P05, 90C30, 90C90
Mots-clés : Timoshenko beam network, analytic solutions, topology optimization, multi-material optimization
Kufner, Tobias 1 ; Leugering, Günter 1 ; Semmler, Johannes 1 ; Sting, Michael 1 ; Strohmeyer, Christoph 1

1 
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     author = {Kufner, Tobias and Leugering, G\"unter and Semmler, Johannes and Sting, Michael and Strohmeyer, Christoph},
     title = {Simulation and structural optimization of 3d {Timoshenko} beam networks based on fully analytic network solutions},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {2409--2431},
     publisher = {EDP-Sciences},
     volume = {52},
     number = {6},
     year = {2018},
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Kufner, Tobias; Leugering, Günter; Semmler, Johannes; Sting, Michael; Strohmeyer, Christoph. Simulation and structural optimization of 3d Timoshenko beam networks based on fully analytic network solutions. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 6, pp. 2409-2431. doi : 10.1051/m2an/2018065. http://www.numdam.org/articles/10.1051/m2an/2018065/

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