Location of Repository

International audienceThe linear static problem for a thin shell made of a homogeneous and isotropic elastic material is analyzed. It is assumed that the shell thickness $2\epsilon$ is constant, the neutral shell surface $S\coloneq\bftheta(\omega)$ is bounded connected and elliptic and the shell edge $\Gamma$ is clamped. The solution ${\bf u}(\epsilon)$ of the three-dimensional problem is compared with the solution $\bfzeta$ of the corresponding two-dimensional membrane problem. The following estimate is proved for $\epsilon$ small enough: $$||{\bf u}(\epsilon)-\bfzeta ||_ {H^1(\Omega)\times H^1(\Omega)\times L^2(\Omega)}\le C\epsilon^a,\quad a={1\over6},\tag1$$where $\Omega=\omega\times(-1,\,1)\subset{\bf R}^3$. Here $\bftheta\colon\ \omega\to{\bf R}^3$ is a mapping of class $C^3$, the external body forces $f^i\in L^2(\Omega)$ with $\partial_{\alpha}f^{\alpha}\in L^2(\Omega)$, and $\bfzeta(y,x_3)=\bfzeta(y)\in{\bf H}^2(\Omega)$. It is also shown that inequality (1) cannot hold with $a>{5\over6}$ even for smooth enough functions $\bf f$

Topics:
Shells, elasticity, asymptotics, error estimates, three-dimensional model, [
MATH
]
Mathematics [math], [
MATH.MATH-AP
]
Mathematics [math]/Analysis of PDEs [math.AP], [
MATH.MATH-FA
]
Mathematics [math]/Functional Analysis [math.FA], [
MATH.MATH-MP
]
Mathematics [math]/Mathematical Physics [math-ph], [
PHYS.MECA.SOLID
]
Physics [physics]/Mechanics [physics]/Mechanics of the solides [physics.class-ph]

Publisher: IOS Press

Year: 1998

OAI identifier:
oai:HAL:hal-01478594v1

Provided by:
Hal-Diderot

Download PDF:To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.