Plates and shells: Asymptotic expansions and hierarchical models
نویسندگان
چکیده
Concerning thin structures such as plates and shells, the idea of reducing the equations of elasticity to twodimensional models defined on the mid-surface seems relevant. Such a reduction was first performed thanks to kinematical hypotheses about the transformation of normal lines to the mid-surface. As nowadays, the asymptotic expansion of the displacement solution of the three-dimensional linear model is fully known at least for plates and clamped elliptic shells, we start from a description of these expansions in order to introduce the twodimensional models known as hierarchical models: These models extend the classical models, and pre-suppose the displacement to be polynomial in the thickness variable, transverse to the mid-surface. Because of the singularly perturbed character of the elasticity problem as the thickness approaches zero, boundaryor internal layers may appear in the displacements and stresses, and so may numerical locking effects. The use of hierarchical models, discretized by higher degree polynomials (p-version of finite elements) may help to overcome these severe difficulties.
منابع مشابه
Plates and Shells: Asymptotic Expansions and Hierarchic Models
Concerning thin structures, such as plates and shells, the idea of reducing the equations of elasticity to two-dimensional models defined on the midsurface seems relevant. Such a reduction was first performed thanks to kinematicalhypotheses about the transformation of normal lines to the midsurface. As nowadays, the asymptotic expansion of thedisplacement solution of the three-dimen...
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