Equal force density method-based shape finding method for cable section of geodesic line between two points of curved surface

Abstract

The invention provides an equal force density method-based shape finding method for a cable section of a geodesic line between two points of a curved surface. The method comprises the main steps of giving a curved surface equation, cable section initial point coordinate values and an inter-initial point discrete node number; equally dividing a horizontal projection straight line between two initial points to obtain discrete node coordinates of the cable section on the curved surface; establishing a force balance equation set of all cable section nodes; calculating out new node coordinates; and judging whether a difference value of two node coordinates meets a convergence condition or not, and if the condition is met, outputting all node information of the cable section of the geodesic line, or otherwise, returning to iteratively solve coordinate values of the cable section nodes. According to the shape finding method, the shape finding of the cable section of the geodesic line between the two points of the curved surface is realized by utilizing an equal force density algorithm, and the node information of the cable section of the geodesic line between the two points is obtained, so that a complex geodesic line cable net structure of the curved surface can be designed.

Description

technical field [0001] The invention belongs to the field of geodesic clue section form-finding, in particular to a geodesic clue section form-finding method between two points on a curved surface based on an isodynamic density method. Background technique [0002] Definition of a geodesic: A curve on a surface is called a geodesic if its geodesic curvature is zero at each point. The geodesic has an important position similar to that of the plane straight line on the curved surface, and the geodesic equations on the curved surface are second-order differential equations. The problem of finding geodesic clue segments is the problem of solving the coordinates of some discrete nodes on geodesic clue segments. Suppose there is a tensioned cable on a surface connecting two given points, and the cable can slide freely on a smooth surface. Since a geodesic is a geodesic on a surface, the cable will tend to the geodesic connecting the two points. The force exerted by the surface ...

AI Technical Summary

Problems solved by technology

The entire calculation process is complex, and proper meshing of the surface is a difficult problem. Improper meshing will lead to large solution errors or failure to solve

Images