A Two-Node Finite Element for LinearMagneto-Electric Laminated Timoshenko Beams

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Abstract

A new finite element is presented for linear magnetoelectric straight laminated beamsubject to the assumptions of quasi-steady electromagnetic state. The mechanicalmodel is based upon Timoshenko beam theory to account for shear deformation influences.The electromagnetic stacking sequence is proved to enter the equivalentelastic problem by affecting both the stiffness properties of the beam, in terms of axialand flexural coupling, and by modifying the mechanical boundary conditions as distributedloads. Shape functions are first written for the generalized beam mean-linekinematical quantities in such a way the obtained strain field fulfills the homogeneousgoverning equations of the equivalent elastic problem. The weak form of the governingequations are then obtained by integrating over the element length the equation ofmotion of the beam opportunely multiplied by the virtual mean-line axial and transversedisplacements and by the virtual cross-sectional rotation. Both the virtual andactual kinematical quantities are then expressed in terms of virtual and actual nodalvariables by means of the proposed shape functions. By so doing, the definitions ofthe element mass and stiffness matrices and of the equivalent force vector are straightforwardlyobtained. Lastly, numerical results are presented to assess the soundness ofthe proposed formulation.
Lingua originaleEnglish
Numero di pagine13
Stato di pubblicazionePublished - 2012

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Stiffness matrix
Shear deformation
Stiffness
Boundary conditions

All Science Journal Classification (ASJC) codes

  • Environmental Engineering
  • Civil and Structural Engineering
  • Computational Theory and Mathematics
  • Artificial Intelligence

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title = "A Two-Node Finite Element for LinearMagneto-Electric Laminated Timoshenko Beams",
abstract = "A new finite element is presented for linear magnetoelectric straight laminated beamsubject to the assumptions of quasi-steady electromagnetic state. The mechanicalmodel is based upon Timoshenko beam theory to account for shear deformation influences.The electromagnetic stacking sequence is proved to enter the equivalentelastic problem by affecting both the stiffness properties of the beam, in terms of axialand flexural coupling, and by modifying the mechanical boundary conditions as distributedloads. Shape functions are first written for the generalized beam mean-linekinematical quantities in such a way the obtained strain field fulfills the homogeneousgoverning equations of the equivalent elastic problem. The weak form of the governingequations are then obtained by integrating over the element length the equation ofmotion of the beam opportunely multiplied by the virtual mean-line axial and transversedisplacements and by the virtual cross-sectional rotation. Both the virtual andactual kinematical quantities are then expressed in terms of virtual and actual nodalvariables by means of the proposed shape functions. By so doing, the definitions ofthe element mass and stiffness matrices and of the equivalent force vector are straightforwardlyobtained. Lastly, numerical results are presented to assess the soundness ofthe proposed formulation.",
author = "Alberto Milazzo",
year = "2012",
language = "English",

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TY - CONF

T1 - A Two-Node Finite Element for LinearMagneto-Electric Laminated Timoshenko Beams

AU - Milazzo, Alberto

PY - 2012

Y1 - 2012

N2 - A new finite element is presented for linear magnetoelectric straight laminated beamsubject to the assumptions of quasi-steady electromagnetic state. The mechanicalmodel is based upon Timoshenko beam theory to account for shear deformation influences.The electromagnetic stacking sequence is proved to enter the equivalentelastic problem by affecting both the stiffness properties of the beam, in terms of axialand flexural coupling, and by modifying the mechanical boundary conditions as distributedloads. Shape functions are first written for the generalized beam mean-linekinematical quantities in such a way the obtained strain field fulfills the homogeneousgoverning equations of the equivalent elastic problem. The weak form of the governingequations are then obtained by integrating over the element length the equation ofmotion of the beam opportunely multiplied by the virtual mean-line axial and transversedisplacements and by the virtual cross-sectional rotation. Both the virtual andactual kinematical quantities are then expressed in terms of virtual and actual nodalvariables by means of the proposed shape functions. By so doing, the definitions ofthe element mass and stiffness matrices and of the equivalent force vector are straightforwardlyobtained. Lastly, numerical results are presented to assess the soundness ofthe proposed formulation.

AB - A new finite element is presented for linear magnetoelectric straight laminated beamsubject to the assumptions of quasi-steady electromagnetic state. The mechanicalmodel is based upon Timoshenko beam theory to account for shear deformation influences.The electromagnetic stacking sequence is proved to enter the equivalentelastic problem by affecting both the stiffness properties of the beam, in terms of axialand flexural coupling, and by modifying the mechanical boundary conditions as distributedloads. Shape functions are first written for the generalized beam mean-linekinematical quantities in such a way the obtained strain field fulfills the homogeneousgoverning equations of the equivalent elastic problem. The weak form of the governingequations are then obtained by integrating over the element length the equation ofmotion of the beam opportunely multiplied by the virtual mean-line axial and transversedisplacements and by the virtual cross-sectional rotation. Both the virtual andactual kinematical quantities are then expressed in terms of virtual and actual nodalvariables by means of the proposed shape functions. By so doing, the definitions ofthe element mass and stiffness matrices and of the equivalent force vector are straightforwardlyobtained. Lastly, numerical results are presented to assess the soundness ofthe proposed formulation.

UR - http://hdl.handle.net/10447/76230

M3 - Other

ER -