Zusammenfassung:
The present work addresses the problem of maximizing a structure load-bearing capacity subject to given material strengthproperties and a material volume constraint. This problem can be viewed as an extension to limit analysis problemswhich consist in finding the maximum load capacity for a fixed geometry. We show that it is also closely linked to theproblem of minimizing the total volume under the constraint of carrying a fixed loading. Formulating these topologyoptimization problems using a continuous field representing a fictitious material density yields convex optimizationproblems which can be solved efficiently using state-of-the-art solvers used for limit analysis problems. We further analyzethese problems by discussing the choice of the material strength criterion, especially when considering materials withasymmetric tensile/compressive strengths. In particular, we advocate the use of a L1-Rankine criterion which tends topromote uniaxial stress fields as in truss-like structures. We show that the considered problem is equivalent to a constrainedMichell truss problem. Finally, following the idea of the SIMP method, the obtained continuous topology is post-processedby an iterative procedure penalizing intermediate densities. Benchmark examples are first considered to illustrate the methodoverall efficiency while final examples focus more particularly on no-tension materials, illustrating how the method is ableto reproduce known structural patterns of masonry-like structures. This paper is accompanied by a Python package based onthe FEniCS finite-element software library
(PDF) Topology optimization of load-bearing capacity. Available from: https://www.researchgate.net/publication/352735567_Topology_optimization_of_load-bearing_capacity
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