Abstract
This paper is devoted to the theoretical and numerical study of singular perturbation problems for elliptic inhibited shells. We present a reduction of the classical membrane equations to a partial differential equation with respect to the bending displacement, which is well adapted to the study of singularities of the limit problem. For a discontinuous loading or when the boundary of the loading domain presents corners, we put in a prominent position the existence of two kinds of singularities. One of them is not classical; it reduces to a logarithmic point singularity at the corner of the loading domain. To finish numerical simulations are performed with a finite element software coupled with an anisotropic adaptive mesh generator. They enable to visualize precisely the singularities predicted by the theory with only a very small number of elements.
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Béchet, F., Sanchez-Palencia, E. & Millet, O. Computing singular perturbations for linear elliptic shells. Comput Mech 42, 287–304 (2008). https://doi.org/10.1007/s00466-007-0204-8
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DOI: https://doi.org/10.1007/s00466-007-0204-8