Optimization of Ring Trusses for Antenna Structures Using Line Geometry

Abstract

Two types of trusses were optimized using the simple, yet powerful, mathematical technique of employing line geometry as defined by the mathematicians Plucker and Grassmann. The key benefit to this design methodology is simplicity. Multiple-node designs were analyzed, with particular focus placed on the triangular truss. The methodology is based on a geometric stability criterion called the quality index. This approach allowed for a simple equation to be created that identifies the optimal geometry based on the exterior angles and the number of sides. Trusses with single and double connecting points are considered using the quality index. An example of a double connection truss is the triangular truss. In this case, each node (either on the top or the base) has two structural elements connecting to the other nodes. It is shown that there are optimal design criteria for the upper, lower, and separation dimensions. These optimal geometric designs yield conical trusses. Further consideration of the 3-3 truss produced a closed-form solution. This equation holds significant potential for truss designs, providing a clear comparison between single and double connections.