Localising the smallest stiffness and its direction of a homogeneous structure by spectral and optimisation approaches

Henyš, Petr; Sutula, Danas; Kopal, Jiří; Kuchař, Michal; Čapek, Lukáš

doi:10.1016/j.engstruct.2020.111842

Cited by 3 publications

(16 citation statements)

References 17 publications

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“…Interpretation of eigenvectors with respect to static stiffness: The smallest static stiffness can be approximated by modal stiffness if there exist a load and kinematic boundary conditions that produce a deformation of bone, which is similar to an eigenvector. This relation was already demonstrated in the authors' previous study 21 and in 32 . This relation can be also explained by a so-called modal reduction technique, where the quantities of interest are projected on to a reduced space spanned by a few eigenvectors to decrease computational complexity while maintaining model as accurate as possible 21 .…”

Section: Discussionsupporting

confidence: 79%

“…This relation was already demonstrated in the authors' previous study 21 and in 32 . This relation can be also explained by a so-called modal reduction technique, where the quantities of interest are projected on to a reduced space spanned by a few eigenvectors to decrease computational complexity while maintaining model as accurate as possible 21 . Eigenmetrics predict sex, although are only moderately correlated with anthropometric measures.…”

Section: Discussionsupporting

confidence: 79%

“…One interpretation could be in an analogy with an alternative model with suitable boundary conditions defined that produces a deformation corresponding to FEMP-II eigenvector. This hypothesis was partially touched in previous author's study on beam bending analysis 21 . Relation of eigenmetrics and modal analysis: The static stiffness is related to modal stiffness in following way.…”

Section: Discussionmentioning

confidence: 83%

“…The static stiffness at point with index k is computed in virtue of modal superposition described in 21 and can be expressed as:…”

Section: Eigenmetrics Definitionmentioning

confidence: 99%

“…The proposed definitions of modal stiffness s i as well as static stiffness S were based on the theoretical and computational study 21 .…”

Section: Eigenmetrics Definitionmentioning

confidence: 99%

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Mechanical Metric for Skeletal Biomechanics Derived from Spectral Analysis of Stiffness matrix

Henyš

Kuchař

Hájek

et al. 2021

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A new metric for the quantitative and qualitative evaluation of bone stiffness is introduced. It is based on the spectral decomposition of stiffness matrix computed with finite element method. The here proposed metric is defined as an amplitude rescaled eigenvalues of stiffness matrix. The metric contains unique information on the principal stiffness of bone and reflects both bone shape and material properties. The metric was compared with anthropometrical measures and was tested for sex sensitivity on pelvis bone. Further, the smallest stiffness of pelvis was computed under a certain loading condition and analyzed with respect to sex and direction. The metric complements anthropometrical measures and provides a unique information about the smallest bone stiffness independent from the loading configuration and can be easily computed by state-of-the-art subject specified finite element algorithms.

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Section: Discussionsupporting

confidence: 79%