The article considers the problems of the formation of a neck in a sample of complex shape and Lüders slip bands in a square plate with a central circular hole in a plane-deformed state in finite deformations, taking into account the perfectly plastic flow. The statement of tasks is presented. Due to the symmetry, quarters of the models were considered. Numerical results were obtained in the CAE Fidesys package using the finite element method for the first and second orders, as well as for the spectral element method: for seven orders for the necking problem and the third-order elements for the Lüders slip bands problem. Based on the results obtained, the analysis of the capabilities of the spectral element method relative to the finite element method is carried out. The results of the conducted research can be useful when deciding on the use of the spectral element method in industrial problems.

本文考虑了在有限变形中平面变形状态下具有中心圆孔的方板中复杂形状样品中颈部的形成和吕德斯滑带的形成问题，同时考虑了完美塑性流动。提出任务说明。由于对称性，考虑了四分之一的模型。在 CAE Fidesys 包中使用有限元法获得一阶和二阶以及谱元法的数值结果：颈缩问题的七阶和吕德斯滑带问题的三阶元素。根据所得结果，对谱元法相对于有限元法的能力进行了分析。