Surface parameterization complex geometry

Abstract

Among thin-walled structures, including building structures and constructions, shells of complex geometry are effective in their rigidity and strength characteristics, which are also distinguished by architectural harmony. For a wider application of shells of complex geometry, it is necessary to reliably assess their stress-strain state. In this case, an integral part of the calculation is the parametrization stage of the median surface of shells of complex geometry. There are shells of complex geometry of canonical and non-canonical forms. For shells of non-canonical shape, the median surface cannot be defined by analytical formulas. At the same time, difficulties arise at the stage of specifying (parameterizing) the shape of the median surface. The task becomes more complicated when the shell fragment has a complex contour and one or more surface points have fixed coordinates. For building structures, this is, for example, the presence of additional internal supports. Information about the spline version of the FEM is presented. Some well-known parametrization methods are noted. The approach of parametrization of a minimal surface of a complex shape bounded by four curved contours and a given (fixed) coordinate of one inner point of the surface is considered. An algorithm for constructing a spatial network, as well as determining coordinates, metric tensor components and Christoffel symbols necessary for solving parametrization problems in the spline version of the finite element method is described.