Design Optimization based on the Redundancy Matrix
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The degree of static indeterminacy and its spatial distribution characterize load-bearing structures independent of a specific load case. The redundancy matrix contains the distribution of the static indeterminacy on its main diagonal [1], and offers thereby the possibility to use this property for the assessment of structures. In this presentation, quantitative design criteria for the robustness and the assemblability of structures based on the redundancy matrix are proposed. For both a detailed matrix-based derivation is given. Design criteria based on the redundancy matrix are especially suitable in early planning stages for design exploration. They can be directly used an objective function for a design optimization. Efficient implementation of the calculation or updating of the redundancy matrix significantly reduces the computational effort [2, 3]. The application is showcased with different examples using shape or sizing optimization of truss system. REFERENCES [1] M. von Scheven, E. Ramm, M. Bischoff. Quantification of the redundancy distribution in truss and beam structures. International Journal of Solids and Structures 213, pp. 41–49, 2021. [2] T. Krake, M. von Scheven, J. Gade, M. Abdelaal, D. Weiskopf, and M. Bischoff. Efficient Update of Redundancy Matrices for Truss and Frame Structures. Journal of Theoretical, Computational and Applied Mechanics, 2022. [3] A. Tkachuk, T. Krake, J. Gade, M. von Scheven. Efficient Computation of Redundancy Matrices for Moderately Redundant Truss and Frame Structures. Journal of Theoretical, Computational and Applied Mechanics, 2023.