Modeling of the 2nd Order Curves and Surfaces of Engineering Structures Shells Based on Their Basis

Abstract

The paper describes an example of modeling an arc of a 2nd order curve using an engineering discriminant and its analytical description based on a graphical algorithm for constructing a curve in point calculus. Examples of modeling the surfaces of engineering structures shells on an elliptical and rectangular plan are given. Research methods include geometric algorithms: modeling of 2nd order curves passing through 3 predetermined points in advance and having tangents at the start and end points, and shell surfaces based on them; analytical definition of curves arcs and sections of surfaces using the mathematical apparatus point calculation in a given parametrization and taking into account all predetermined geometric conditions. This approach can be widely used in the practice of modeling the shells of engineering structures for various technical purposes. It allows the designer to choose the best curvature of the shell surface, which will have the necessary strength characteristics, technical aesthetics and artistic expressiveness. The possibility of dividing the surface of the shell into finite elements of a given amount is also provided for studying the stress-strain state of the shell under the action of various loads in the systems of finite element analysis.