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2025
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| Online Access: | https://doi.org/10.5281/zenodo.17906182 |
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| _version_ | 1866901253126094848 |
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| author | Sakib, S M Nazmuz |
| author_facet | Sakib, S M Nazmuz |
| contents | <p>This paper introduces the S M Nazmuz Sakib Non-Commutative Stiffness History Index (Sakib-Index), a scalar, dimensionless measure of the non-commutativity of tangent stiffness matrices along a structural loading or environmental history. Given a sequence of symmetric positive-definite stiffness matrices, the Sakib-Index is constructed from normalized Frobe-nius norms of pairwise commutators and then averaged over the entire history. The index is invariant under orthogonal changes of basis, vanishes if and only if the stiffness matrices commute pairwise (i.e. share a common eigenbasis), and increases when stiffness principal directions rotate or stiffness is redistributed in a path-dependent manner. We formalize this as the S M Nazmuz Sakib Non-Commutative Stiffness History Principle and propose the associated Sakib-Index as a damage complexity indicator complementary to classical eigenfrequency-, mode-shape-and flexibility-based damage indices. Using published data from the Z24 Bridge progressive damage test and a set of controlled numerical experiments on low-order stiffness matrices, we illustrate how frequency-based indicators can remain relatively small while the Sakib-Index grows, reflecting increased geometric or material path dependence. We also investigate sampling and noise sensitivity. Mathematically, the proposed index specializes and adapts known Frobenius-norm commu-tator measures to the context of structural health monitoring (SHM); in the SHM literature, 1 S M Nazmuz Sakib Non-Commutative Stiffness History Index Sakib-Index however, an explicit non-commutativity-based global stiffness history index of this form does not appear to have been reported. The present work thus frames and names a new structural damage-complexity index built on these ideas.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17906182 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | S M Nazmuz Sakib Non-Commutative Stiffness History Index: A Path-Dependent Damage-Complexity Measure for Structural Systems Sakib, S M Nazmuz <p>This paper introduces the S M Nazmuz Sakib Non-Commutative Stiffness History Index (Sakib-Index), a scalar, dimensionless measure of the non-commutativity of tangent stiffness matrices along a structural loading or environmental history. Given a sequence of symmetric positive-definite stiffness matrices, the Sakib-Index is constructed from normalized Frobe-nius norms of pairwise commutators and then averaged over the entire history. The index is invariant under orthogonal changes of basis, vanishes if and only if the stiffness matrices commute pairwise (i.e. share a common eigenbasis), and increases when stiffness principal directions rotate or stiffness is redistributed in a path-dependent manner. We formalize this as the S M Nazmuz Sakib Non-Commutative Stiffness History Principle and propose the associated Sakib-Index as a damage complexity indicator complementary to classical eigenfrequency-, mode-shape-and flexibility-based damage indices. Using published data from the Z24 Bridge progressive damage test and a set of controlled numerical experiments on low-order stiffness matrices, we illustrate how frequency-based indicators can remain relatively small while the Sakib-Index grows, reflecting increased geometric or material path dependence. We also investigate sampling and noise sensitivity. Mathematically, the proposed index specializes and adapts known Frobenius-norm commu-tator measures to the context of structural health monitoring (SHM); in the SHM literature, 1 S M Nazmuz Sakib Non-Commutative Stiffness History Index Sakib-Index however, an explicit non-commutativity-based global stiffness history index of this form does not appear to have been reported. The present work thus frames and names a new structural damage-complexity index built on these ideas.</p> |
| title | S M Nazmuz Sakib Non-Commutative Stiffness History Index: A Path-Dependent Damage-Complexity Measure for Structural Systems |
| url | https://doi.org/10.5281/zenodo.17906182 |