Issue 78

M. Habashneh et alii, Fracture and Structural Integrity, 78 (2026) 409-431; DOI: 10.3221/IGF-ESIS.78.24

C ONCLUSIONS

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his study investigated the influence of mesh size, evolutionary rate, and filter radius on geometrically nonlinear BESO topology optimization. Three benchmark problems were considered: an L-shaped beam, a pinned plate, and a U-shaped plate. A one-parameter-at-a-time approach was adopted to isolate the effect of each parameter on the optimized topology, convergence behavior, and structural stiffness. In addition to the topological results, displacement at the load application point was used to quantify the stiffness of the optimized designs. The main findings can be summarized as follows:  The primary load-transfer mechanism remained stable across all parameter variations. Although local details changed, the dominant force-flow paths were preserved in all three benchmark problems.  Mesh size mainly affected the resolution of secondary structural members. Finer meshes generated more detailed bracing systems, whereas coarser meshes produced simpler topologies with thicker members.  The influence of mesh size on stiffness was generally limited. However, the U-shaped plate showed greater sensitivity because of its geometric complexity. The maximum displacement variation due to mesh refinement reached approximately 9.3%.  The evolutionary rate had a strong effect on topology development. Lower values produced more refined layouts with better-defined secondary members and smoother convergence behavior.  Increasing the evolutionary rate progressively simplified the optimized layouts and reduced structural efficiency. In the pinned plate example, high evolutionary rates altered the load-transfer mechanism by partially disengaging the corner supports. For the U-shaped plate, the maximum stiffness reduction reached 12%.  The filter radius strongly influenced both topology and structural performance. Changes in the filter radius modified the number of internal load paths and the level of geometric detail throughout the optimized structures.  Larger filter radii promoted smoother and more consolidated layouts by suppressing small structural features. While this improved geometric regularity, it often reduced the completeness of the load-transfer network.  The effects of filter radius and evolutionary rate were different in origin but similar in outcome. Both parameters tended to simplify the topology and reduce the efficiency of the optimized design when excessively large values were used. Overall, the results show that mesh size, evolutionary rate, and filter radius should be selected carefully in geometrically nonlinear BESO optimization. Parameter values commonly used in linear formulations may not always be suitable for nonlinear problems. The consistent trends observed across the three benchmark structures indicate that the findings are not limited to a specific geometry and may be applicable to a broader range of large-deformation topology optimization problems. Future work may focus on extending the proposed framework to dynamic loading conditions, elasto-plastic material behavior, and three-dimensional structures. The coupled influence of mesh size, evolutionary rate, and filter radius should also be investigated through systematic multi-parameter or factorial design studies to quantify interaction effects that cannot be identified using the present one-parameter-at-a-time approach. Developing adaptive parameter-selection strategies represents another promising direction for further research. Future studies should also incorporate practical design criteria, including manufacturing complexity and cost, surface-protection requirements, and fatigue performance under dynamic loading, to investigate the trade-off between structural efficiency and the practical complexity of optimized topologies.

A CKNOWLEDGMENTS

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he authors thank the support of the EKÖP-26-4-II-SZE-8, University Research Fellowship Program of the Ministry for Culture and Innovation, funded by the National Research, Development, and Innovation Fund.

R EFERENCES

[1] Ghabraie, K. (2015). An improved soft-kill BESO algorithm for optimal distribution of single or multiple material phases, Structural and Multidisciplinary Optimization, 52(4), pp. 773–790. DOI: https://doi.org/10.1007/S00158-015-1268-2/FIGURES/23.

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