%0 Report
%T Optimal Shells Formed on a Sphere. The Topological Derivative Method
%+ Mathematical Analysis and Numerical Simulation of Non-Linear Models (NUMATH)
%A Lewinski, Tomasz
%A Sokolowski, Jan
%N RR-3495
%P 62
%I INRIA
%8 1998
%D 1998
%K shape optimization
%K shape derivative
%K topological derivative
%K asymptotic expansion
%K inverse problem
%Z Computer Science [cs]/Other [cs.OH]Reports
%X The subject of the paper is the analysis of sensitivity of a thin elastic spherical shell to the change of its shape associated with forming a small circular opening, far from the loading applied. The analysis concerns the elastic potential of the shell. The sensitivity of this functional is measured as a topological derivative, introduced for the plane elasticity problem by Sokolowski and $\buildrel . \over {\hbox{Z}}$ochowski (1997) and extended here to the case of a spherical shell. A proof is given that : i) the first derivative of the functional with respect to the radius of the opening vanishes, and : ii) the second derivative does not blow up. A partially constructive formula for the second derivative or for the topological derivative is put forward. The theoretical considerations are confirmed by the analysis of a special case of a shell loaded rotationally symmetric, weakened by an opening at its north-pole. The whole treatment is based on the Niordson-Koiter theory of spherical shells, belonging to the family of correct first order shell models of Love.
%G English
%2 https://inria.hal.science/inria-00073191/document
%2 https://inria.hal.science/inria-00073191/file/RR-3495.pdf
%L inria-00073191
%U https://inria.hal.science/inria-00073191
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