Construction of the Transverse-Vertical Shapes of the Orthopedic Boot-Tree by Means of the Solution to Singular Dirichlet Boundary Value Problem

摘要

The paper describes the problem of approximate construction of the transverse-vertical shapes of the orthopedic boot-tree. In the footwear industry, great attention is paid to the design of boot-trees. The task is much harder, when we deal with the design and production of the orthopedic boot-tree. It is well-known that from a geometrical standpoint, the boot-tree has a complex shape, and its description by using methods of mathematical research is a fairly long and arduous process. To solve the mentioned problem, that is, to provide approximate construction of the transverse-vertical shapes of the orthopedic boot-tree, the authors of this paper used the integral curves of the solutions to singular Dirichlet boundary value problem. Coupling and connection of the sections of the mentioned curves allow us to construct not only the approximate sections of the transverse-vertical shapes, but also to change the shapes of the transverse-vertical sections of boot-trees in unlimited numbers and with high degree of accuracy transfer one size of the boot-tree to another size. The latter is particularly relevant in the design and production of orthopedic footwear.