Remarks on the Stress Version of Topology Optimization of Truss Structures
Based on numerical solutions that minimize the total potential energy of trusses subjected to static loads, with specified displacements at selected support nodes and simultaneous fulfillment of the isoperimetric condition on the structure’s volume, several properties of optimally designed structur...
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Institute of Fundamental Technological Research Polish Academy of Sciences
2025-03-01
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| Series: | Computer Assisted Methods in Engineering and Science |
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| Online Access: | https://cames.ippt.pan.pl/index.php/cames/article/view/1759 |
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| author | Sławomir Czarnecki |
| author_facet | Sławomir Czarnecki |
| author_sort | Sławomir Czarnecki |
| collection | DOAJ |
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Based on numerical solutions that minimize the total potential energy of trusses subjected to static loads, with specified displacements at selected support nodes and simultaneous fulfillment of the isoperimetric condition on the structure’s volume, several properties of optimally designed structures are revealed. The most significant finding is the relatively frequent occurrence of non-unique global solutions, represented as vectors of cross-sectional areas of members in the stress-based version of topology optimization problem. A key aspect of the presented method is the objective function, derived from Castigliano’s theorem, which minimizes the total potential energy. Unlike traditional approaches that optimize transverse areas of the members, this method uses statically admissible forces in the truss members as design variables. This formulation allows for a free search of solutions, including cases where certain members can disappear in the optimal design. Numerous tests have revealed an interesting property of the objective function, indicating that global solutions are located at the bottom of a long valley in its graph within the space Rr +1, where r denotes the size of the kernel of the equilibrium matrix governing the force balance equations of the nodes of the truss structure.
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| format | Article |
| id | doaj-art-820f19d436e94e54b6ff4716b6072f5c |
| institution | Matheson Library |
| issn | 2299-3649 2956-5839 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Institute of Fundamental Technological Research Polish Academy of Sciences |
| record_format | Article |
| series | Computer Assisted Methods in Engineering and Science |
| spelling | doaj-art-820f19d436e94e54b6ff4716b6072f5c2025-07-09T10:21:00ZengInstitute of Fundamental Technological Research Polish Academy of SciencesComputer Assisted Methods in Engineering and Science2299-36492956-58392025-03-0132110.24423/cames.2025.1759Remarks on the Stress Version of Topology Optimization of Truss StructuresSławomir Czarnecki0Department of Structural Mechanics and Computer Aided Engineering, Faculty of Civil Engineering, Warsaw University of Technology, Warsaw Based on numerical solutions that minimize the total potential energy of trusses subjected to static loads, with specified displacements at selected support nodes and simultaneous fulfillment of the isoperimetric condition on the structure’s volume, several properties of optimally designed structures are revealed. The most significant finding is the relatively frequent occurrence of non-unique global solutions, represented as vectors of cross-sectional areas of members in the stress-based version of topology optimization problem. A key aspect of the presented method is the objective function, derived from Castigliano’s theorem, which minimizes the total potential energy. Unlike traditional approaches that optimize transverse areas of the members, this method uses statically admissible forces in the truss members as design variables. This formulation allows for a free search of solutions, including cases where certain members can disappear in the optimal design. Numerous tests have revealed an interesting property of the objective function, indicating that global solutions are located at the bottom of a long valley in its graph within the space Rr +1, where r denotes the size of the kernel of the equilibrium matrix governing the force balance equations of the nodes of the truss structure. https://cames.ippt.pan.pl/index.php/cames/article/view/1759topology optimizationtrussesprescribed displacementsnon-uniqueness of optimal solutionsnarrow valley |
| spellingShingle | Sławomir Czarnecki Remarks on the Stress Version of Topology Optimization of Truss Structures Computer Assisted Methods in Engineering and Science topology optimization trusses prescribed displacements non-uniqueness of optimal solutions narrow valley |
| title | Remarks on the Stress Version of Topology Optimization of Truss Structures |
| title_full | Remarks on the Stress Version of Topology Optimization of Truss Structures |
| title_fullStr | Remarks on the Stress Version of Topology Optimization of Truss Structures |
| title_full_unstemmed | Remarks on the Stress Version of Topology Optimization of Truss Structures |
| title_short | Remarks on the Stress Version of Topology Optimization of Truss Structures |
| title_sort | remarks on the stress version of topology optimization of truss structures |
| topic | topology optimization trusses prescribed displacements non-uniqueness of optimal solutions narrow valley |
| url | https://cames.ippt.pan.pl/index.php/cames/article/view/1759 |
| work_keys_str_mv | AT sławomirczarnecki remarksonthestressversionoftopologyoptimizationoftrussstructures |