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One-dimensional models of fourth and sixth orders for rods derived from three-dimensional elasticity

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2017
auteur(s) Pruchnicki Erick
journal (abréviation) Mathematics and mechanics of solids (Math Mech Solid)
volume (numéro) 22 (2)
pages 158 – 175
résumé The displacement field in rods can be approximated by using a Taylor- Young expansion in transverse dimension of the rod. These involve that the highest order term of shear is of second-order in transverse dimension of the rod. Then we show that transverse shearing energy is removed by the fouth order truncation of the potential energy and so we revisit the model presented by Pruchnicki [11]. Then we consider the sixth order truncation of the potential which includes transverse shearing and transverse normal stress energies. For this two models we show that the potential energies satisfy the stability condition of Legendre-Hadamard which is necessary for the existence of aminimizer and then we give the Euler-Lagrange equations and the natural boundary conditions associated with these potential energies. For the sake of simplicity we consider the the cross-section of the rod has double symmetry axes.
mots clés Rods, Linear elasticity, Strain gradients, Transverse shearing, one dimensional model
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