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Area moment of inertia of a “flower-shaped” cross section and generalization for N-fold rotational symmetry and multipole moments
Citation Link: https://doi.org/10.15480/882.3066
Publikationstyp
Technical Report
Date Issued
2020-12-10
Sprache
English
TORE-DOI
TORE-URI
Citation
Technische Universität Hamburg (2020)
Motivated by three-point bending tests with a nanoindenter and the necessary analysis, the area moment of inertia of tiny bending specimens, with a special “flower-shaped” cross section, is calculated analytically. If such cross sections have a four-fold rotational symmetry, it can be shown that a rotation of the cross section by any angle, with respect to the reference plane, does not change the result. By demonstrating that this is valid also for N-fold rotational symmetry with N ≥ 3 and by generalization for multipole moments of any order, some interesting equations and principles are found. (Originally, the chapters 1–4 were an internal communication in the Institute of Advanced Ceramics, TUHH. Later on, the chapters 5–7 and the appendices were added, and the introduction was extended. Although the calculations are standard, they are perhaps also of interest to others. In order not to lose track of the idea and the calculations, they are published in this format.)
Subjects
bending test
area moment of inertia
rotational symmetry
second moment of area
central binomial coefficient
trigonometric identity
DDC Class
600: Technik
620: Ingenieurwissenschaften
More Funding Information
Deutsche Forschungsgemeinschaft (DFG)
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Name
TUHH-Moment-of-Inertia-2020-Jelitto.pdf
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1.04 MB
Format
Adobe PDF