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  • Na prostoru symetrických, pozitivně definintních matic (prostor deformačních tenzorù) lze zavést Riemannovu metriku tak, že exponenciála matice reprezentuje geodetiku, tj. zobecněnou přímku (nebo-li nejkratší spojnici dvou bodù), vycházející z poèátečního bodu - jednotkové matice, směrem určeným vektorem - zadanou maticí. Ukážeme, že logaritmický tenzor přetvoření lze tak interpretovat jako vektor určený geodetikou, která spojuje nedeformovaný a deformovaný stav. (cs)
  • On the space of all symmetric positive definite matrices (the space of deformation tensor fields) one can introduce a Riemannian geometry, so that the matrix exponential represents ageodesic (i.e. a generalised straight line, the shortest connecting line of two points) emanating from an initial point - the identity matrix, in a direction given by a vector - the prescribed matrix. Based on this approach, we prove that the logarithmic strain can be interpreted as a vector, determined by a geodesic connecting an undeformed and a deformed states.
  • On the space of all symmetric positive definite matrices (the space of deformation tensor fields) one can introduce a Riemannian geometry, so that the matrix exponential represents ageodesic (i.e. a generalised straight line, the shortest connecting line of two points) emanating from an initial point - the identity matrix, in a direction given by a vector - the prescribed matrix. Based on this approach, we prove that the logarithmic strain can be interpreted as a vector, determined by a geodesic connecting an undeformed and a deformed states. (en)
Title
  • Matrix exponential and geometrical meaning of logarithmic strain
  • Matrix exponential and geometrical meaning of logarithmic strain (en)
  • Exponenciála matice a geometrický význam pole logaritmického tenzoru přetvoření (cs)
skos:prefLabel
  • Matrix exponential and geometrical meaning of logarithmic strain
  • Matrix exponential and geometrical meaning of logarithmic strain (en)
  • Exponenciála matice a geometrický význam pole logaritmického tenzoru přetvoření (cs)
skos:notation
  • RIV/68378297:_____/07:00087614!RIV08-AV0-68378297
http://linked.open.../vavai/riv/strany
  • 55;64
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • Z(AV0Z20710524)
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
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http://linked.open...iv/duvernostUdaju
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  • 432385
http://linked.open...ai/riv/idVysledku
  • RIV/68378297:_____/07:00087614
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • finite deformations; logarithmic strain; Riemannian geometry (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...ontrolniKodProRIV
  • [C9E29D15314B]
http://linked.open...v/mistoKonaniAkce
  • Svratka
http://linked.open...i/riv/mistoVydani
  • Praha
http://linked.open...i/riv/nazevZdroje
  • Engineering Mechanics 2007
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...UplatneniVysledku
http://linked.open...iv/tvurceVysledku
  • Fiala, Zdeněk
http://linked.open...vavai/riv/typAkce
http://linked.open.../riv/zahajeniAkce
http://linked.open...n/vavai/riv/zamer
number of pages
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  • Ústav termomechaniky AV ČR
https://schema.org/isbn
  • 978-80-87012-06-2
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