Computational Algorithms For Modeling of One-Dimensional Contours Through k In Advance Given Points

In this paper have been proposed theoretical bases for formation one-dimensional contours of the first order smoothness, passing through k in advance given points, including requirements to the contour in general, and the contour’s arcs in particular, as well as representations for tangents in extreme and intermediate contour sections, which determine the contour arc shape. Based on this theoretical material have been developed computational algorithms for simulation of closed (A5, A6) and open (A1-A4) contours according to postulated conditions, which allow form irregular composite curves and surfaces with different degree of complexity, docked together on the first order smoothness. The proposed computational algorithms can also be used to construct contours of higher orders smoothness using arcs of the same ratio curves. For analytical description of computational algorithms for one-dimensional contours simulation is used the mathematical apparatus of BN-calculation (Balyuba – Naidysh point calculation). The obtained algorithms have been presented in a point form, which is a symbolic form. For transition from point equations to a system of parametric equations, it is necessary to perform a coordinate-by-coordinate calculation, which can be presented geometrically as population of projections on the global coordinate system’s axes. As an example has been presented a computational algorithm that provides the use a system of parametric equations instead of symbolic point recording. The proposed algorithms have been successfully used for computer modeling and prediction for the impact of geometric shape imperfections on the strength and stability of engineering structures’ thin-walled shells. In particular, a numerical study method for a stress-strain state of steel vertical cylindrical reservoirs with regard to imperfections of theirs geometric shapes has been proposed.