Plates and Junctions in Elastic Multi-structures: An Asymptotic Analysis |
Contents
The twodimensional equations of a nonlinearly | 1 |
VI | 3 |
Introduction | 65 |
Copyright | |
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applied force densities assume assumptions asymptotic expansions boundary conditions boundary value problem Chapter Ciarlet compatibility conditions components computed constitutive equation converges de-scaled defined denotes Destuynder DIEGO dimensional displacement approach displacement vector displacement-stress approach eigenvalue elastic plates equations found equations PVW(0 equivalent existence fadys force densities formal expansion found in Theorem given givida Green's formula H¹(N H¹(w H²(w h₂dy Hence hidy independent of ɛ Kármán equations L²(N Lamé constants lateral surface leading terms uº linearized elasticity method of asymptotic middle surface naß Ñº nonlinear nonlinearly elastic Piola-Kirchhoff stress tensor plate theory proof Rabier reference configuration satisfy scaled stress Sect solution solves the following space V(N strain tensor three-dimensional problem two-dimensional displacement two-dimensional equations unknowns variational equations variational problem vector field VH(w Vu(ɛ αβ