On the Membrane Approximation for Thin Elastic Shells in the Hyperbolic Case
PALENCIA E. Sánchez · Revista Matemática Complutense · 1993
Wc consider ¡he variational formulation of ¡he probiena of elastic shells in the membrane approxima¡ion, when ¡he medium surface is hyperboiic.It appears tiat ¡he corresponding bilinear form behaves as sorne kind of two dimensional elasticity wi¡hout shear rigidi¡y.This amounts te saying ¡bat ¡he membrane behaves rather as a net made of elastic strings disposed aiong ¡he asymptotic curves of ¡he surface ¡han as an elas¡ic ¡wo-dimensionai medium, The mathematicai and physicai reasons of tEis behavior are explauned and consequences are thrown concerning ¡be admissibie appiied forces and ¡he behavior of ¡he solutions.The normal cornponen¡ of ¡he dispiacement is somewha¡ non smoo¡h.Our approach gives a description of the problem in somewhat general situations concerning ¡he boundary conditions, whereas ¡he classical approach in terms of a hyperbolic system of total order 4 with 2 deubíe characteristics (¡he asymptotic unes) only works in ¡he case when ¡he boundary condiiions lead te eitEer Cauchy or Ooursat problems.