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Two-dimensional model of fifth order in thickness for plates

type de publication      communication internationale avec actes publiés
date de publication 2013
auteur(s) Pruchnicki Erick
  
conférence SSTA The 10th Conference-2013
     dates de 16-10-2013 à 18-10-2013
     lieu Gdansk, Poland
     nom des actes Shell STructures: Theory and Applications
  
  Sous presse
résumé For the homogeneous plate, the highest order term of transverse shear and normal stresses is of second order in thickness. To take this effect into account, we show that the thickness wise expansion of the potential energy must be truncated at least from fifth order in thickness. The equilibrium equation imply local constraints on the through-thickness derivatives of the zero-order displacement field. These lead to an analytical expression for the two-dimensional potential energy in terms of the zero-order displacement field. These lead to an analytical expression for the two dimensional potential energy in terms of the zero-order displacement field and its derivatives that includes non-standard shearing and transverse normal energies and coupled strechtching-shearing, bending-shearing, stretching-transverse normal energies. As a consequence, this potential energy satisfies the stability condition of Legendre-Hadamard which is necessary for the existence of minimizer.
mots clés Two-dimensional model, plate, fifth order
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