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 Nth-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.

提供了有关弹性尖角标准和棱形壳和杆（尤其是尖角板）以及相应的奇异偏微分方程和系统的文献的最新综合探索性调查。压缩，拉伸和弯曲情况下的静力学和动力学方程的控制系统是从I. Vekua的通用N阶逼近的层次模型得出的，特别是对于有尖角的弹性板。在静态情况下，研究了夹板的基本BVP的适定性。通常，尖角处的BC是非经典的，并且取决于细化的类型。建立相应的标准。在特殊情况下，BVP以显式形式求解。