A survey of results on cusped standard and prismatic shells, in particular plates, and bars and on the corresponding singular PDEs. (English) Zbl 1537.74001
Summary: An updated comprehensive exploratory survey of the literature on elastic cusped standard and prismatic shells and bars, in particular, cusped plates, and to the corresponding singular partial differential equations and systems is given. The governing systems of equations of statics and dynamics in the cases of compression-tension and bending are derived from I. Vekua’s hierarchical models of the generic \(N\)th-order approximation, in particular, for cusped elastic plates. In the static case, the well-posedness of the basic BVPs for cusped plates is investigated. The BCs at the cusped edge are non-classical, in general, and depend on the kind of thinning. The corresponding criteria are established. In the special cases, the BVPs are solved in the explicit form.
MSC:
| 74-02 | Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids |
| 74K25 | Shells |
| 74K20 | Plates |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
Keywords:
cusped standard and prismatic shells; cusped plates; cusped beams; I. Vekua’s hierarchical models; singular partial differential equationsReferences:
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