Volume 15, Issue 3 (8-2025)
IJOCE 2025, 15(3): 359-388 |
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Kaveh A. OPTIMAL ANALYSIS OF SKELETAL STRUCTURES VIA FORCE METHOD: A REVIEW. IJOCE 2025; 15 (3) :359-388
URL: http://ijoce.iust.ac.ir/article-1-644-en.html
URL: http://ijoce.iust.ac.ir/article-1-644-en.html
School of Civil Engineering, Iran University of Science and Technology, Tehran, Iran
Abstract: (1729 Views)
In this paper, a review is provided for the optimal analysis of structures using the graph theoretic force method. An analysis is defined as “optimal” if the corresponding structural matrices (flexibility or stiffness) are sparse, well-structured, and well-conditioned. An expansion process together with the union-intersection theorem is utilized for generating subgraphs, forming a special cycle basis, corresponding to highly localized self equilibration systems. Admissibility checks are used in place of the more common independence checks to speed up the formation of the basis. An efficient solution requires organizing the non-zero entries into various well-defined patterns. Algorithms are provided to form matrices having banded matrices and small profiles. Though the paper considers mainly skeletal structures, the presented concepts are easily extensible to other finite element models. References for such generalizations have been provided. A brief review of swift analysis methods that skirt the harder problem of matrix conditioning is also provided. The iterative nature of optimal structural design via metaheuristic algorithms rewards any speedup in the analysis process. This review recommends utilizing the force method instead of the alternative displacement method to achieve said speedup. The work concludes with a discussion of future challenges in the field of optimal analysis.
Keywords: Optimal Analysis, Sparse Structural Matrices, Well-Structured Matrices, Well-Conditioned Matrices, Graph Theory, Force Method, Optimal Design Using Metaheuristic Algorithms
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