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A Finite Element based on a Generalized Laminated Plate Theory

Konačni element zasnovan na Opštoj laminatnoj teoriji ploča

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2006
Grafar_Cetkovic_2006_M.pdf (14.75Mb)
Authors
Vuksanović, Đorđe
Ćetković, Marina
Book part (Published version)
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Abstract
In this paper a plate bending element based on Generalized layerwise plate theory (GLPT) is formulated. The finite element accounts for transverse shear deformationa and layer-wise description of in-plane displacement components and a constant transverse displacement through the thickness. Mathematical model allows indenpendent in-plane and through the thickness interpolations, thus requiring less numerical operations than conventional 3D elasticity model. Basic element equations are derived using displacement-based finite element formulation. Starting from assumed displacement field, shear stresses are computed by satisfying constitutive equations of laminae, traction free boundary conditions and 3D equilibrium equations of laminate. Deformation and stresses are analyzed in simply supported statically loaded plate. The obtained results had shown excellent agreement with closed form solution of GLPT.
U ovom radu formulisan je konačni element zasnovan na opštoj laminatnoj teoriji ploča. Pomenutim modelom uzima se u obzir smičuća deformacija i realna raspodela komponenata pomeranja kao i konstantno pomeranje po debljini ploče. Matematički model dopušta nezavisnu interpolaciju polja pomeranja u ravni i po debljini ploče, što značajno smanuje računski obim posla u odnosu na uobičajeni 3D model teorije elastičnosti. Osnovne jednačine konačnog elementa formulisane su po metodi deformacije. Polazeći od pretpostavljenog polja pomeranja, polje smičućih napona sračunato je iz uslova da zadovolji konstitutivne jednačine lamine, granične uslove po naponima i 3D uslove ravnoteže laminata. Analizirano je stanje deformacija i naprezanja u slobodno oslonjenoj ploči pri statičkom opterećenju. Dobijena rešenja pokazala su izuzetno slaganje sa tačnim rešenjem opšte laminatne teorije ploča.
Keywords:
laminated plates / static analysis / finite element / MATLAB program / layerwise plate theory
Source:
Theoretical and Experimental Research of Elasto─Plastic Behaviour of Engineering Structures─Monograph Dedicated to Professor Milić Milićević, 2006, 71-84
Publisher:
  • University of Niš─Civil Engineering and Architectural Faculty of Niš
Funding / projects:
  • Contemporary problems of mechanics of deformable bodies/ IO 1749//RS

ISBN: 86-80295-71-X

[ Google Scholar ]
Handle
https://hdl.handle.net/21.15107/rcub_grafar_1875
URI
https://grafar.grf.bg.ac.rs/handle/123456789/1875
Collections
  • Radovi istraživača / Researcher's publications
  • Катедра за техничку механику и теорију конструкција
Institution/Community
GraFar
TY  - CHAP
AU  - Vuksanović, Đorđe
AU  - Ćetković, Marina
PY  - 2006
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1875
AB  - In this paper a plate bending element based on Generalized layerwise plate theory (GLPT) is formulated. The finite element accounts for transverse shear deformationa and layer-wise description of in-plane displacement components and a constant transverse displacement through the thickness. Mathematical model allows indenpendent in-plane and through the thickness interpolations, thus requiring less numerical operations than conventional 3D elasticity model. Basic element equations are derived using displacement-based finite element formulation. Starting from assumed displacement field, shear stresses are computed by satisfying constitutive equations of laminae, traction free boundary conditions and 3D equilibrium equations of laminate. Deformation and stresses are analyzed in simply supported statically loaded plate. The obtained results had shown excellent agreement with closed form solution of GLPT.
AB  - U ovom radu formulisan je konačni element zasnovan na opštoj laminatnoj teoriji ploča. Pomenutim modelom uzima se u obzir smičuća deformacija i realna raspodela komponenata pomeranja   kao i konstantno pomeranje   po debljini ploče. Matematički model dopušta nezavisnu interpolaciju polja pomeranja u ravni i po debljini ploče, što značajno smanuje računski obim posla u odnosu na uobičajeni 3D model teorije elastičnosti. Osnovne jednačine konačnog elementa formulisane su po metodi deformacije. Polazeći od pretpostavljenog polja pomeranja, polje smičućih napona sračunato je iz uslova da zadovolji konstitutivne jednačine lamine, granične uslove po naponima i 3D uslove ravnoteže laminata. Analizirano je stanje  deformacija i naprezanja u slobodno oslonjenoj ploči pri statičkom opterećenju. Dobijena rešenja pokazala su izuzetno slaganje sa tačnim rešenjem opšte laminatne teorije ploča.
PB  - University of Niš─Civil Engineering and Architectural Faculty of Niš
T2  - Theoretical and Experimental Research of Elasto─Plastic Behaviour of Engineering Structures─Monograph Dedicated to Professor Milić Milićević
T1  - A Finite Element based on a Generalized Laminated Plate Theory
T1  - Konačni element zasnovan na Opštoj laminatnoj teoriji ploča
EP  - 84
SP  - 71
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1875
ER  - 
@inbook{
author = "Vuksanović, Đorđe and Ćetković, Marina",
year = "2006",
abstract = "In this paper a plate bending element based on Generalized layerwise plate theory (GLPT) is formulated. The finite element accounts for transverse shear deformationa and layer-wise description of in-plane displacement components and a constant transverse displacement through the thickness. Mathematical model allows indenpendent in-plane and through the thickness interpolations, thus requiring less numerical operations than conventional 3D elasticity model. Basic element equations are derived using displacement-based finite element formulation. Starting from assumed displacement field, shear stresses are computed by satisfying constitutive equations of laminae, traction free boundary conditions and 3D equilibrium equations of laminate. Deformation and stresses are analyzed in simply supported statically loaded plate. The obtained results had shown excellent agreement with closed form solution of GLPT., U ovom radu formulisan je konačni element zasnovan na opštoj laminatnoj teoriji ploča. Pomenutim modelom uzima se u obzir smičuća deformacija i realna raspodela komponenata pomeranja   kao i konstantno pomeranje   po debljini ploče. Matematički model dopušta nezavisnu interpolaciju polja pomeranja u ravni i po debljini ploče, što značajno smanuje računski obim posla u odnosu na uobičajeni 3D model teorije elastičnosti. Osnovne jednačine konačnog elementa formulisane su po metodi deformacije. Polazeći od pretpostavljenog polja pomeranja, polje smičućih napona sračunato je iz uslova da zadovolji konstitutivne jednačine lamine, granične uslove po naponima i 3D uslove ravnoteže laminata. Analizirano je stanje  deformacija i naprezanja u slobodno oslonjenoj ploči pri statičkom opterećenju. Dobijena rešenja pokazala su izuzetno slaganje sa tačnim rešenjem opšte laminatne teorije ploča.",
publisher = "University of Niš─Civil Engineering and Architectural Faculty of Niš",
journal = "Theoretical and Experimental Research of Elasto─Plastic Behaviour of Engineering Structures─Monograph Dedicated to Professor Milić Milićević",
booktitle = "A Finite Element based on a Generalized Laminated Plate Theory, Konačni element zasnovan na Opštoj laminatnoj teoriji ploča",
pages = "84-71",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1875"
}
Vuksanović, Đ.,& Ćetković, M.. (2006). A Finite Element based on a Generalized Laminated Plate Theory. in Theoretical and Experimental Research of Elasto─Plastic Behaviour of Engineering Structures─Monograph Dedicated to Professor Milić Milićević
University of Niš─Civil Engineering and Architectural Faculty of Niš., 71-84.
https://hdl.handle.net/21.15107/rcub_grafar_1875
Vuksanović Đ, Ćetković M. A Finite Element based on a Generalized Laminated Plate Theory. in Theoretical and Experimental Research of Elasto─Plastic Behaviour of Engineering Structures─Monograph Dedicated to Professor Milić Milićević. 2006;:71-84.
https://hdl.handle.net/21.15107/rcub_grafar_1875 .
Vuksanović, Đorđe, Ćetković, Marina, "A Finite Element based on a Generalized Laminated Plate Theory" in Theoretical and Experimental Research of Elasto─Plastic Behaviour of Engineering Structures─Monograph Dedicated to Professor Milić Milićević (2006):71-84,
https://hdl.handle.net/21.15107/rcub_grafar_1875 .

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