Geometric and structural design of foldable structures

Abstract

This paper initially investigates the previous works on foldable structures. Subsequently, generation and geometric (architectural) design of compatible foldable structures with scissor-like elements is formulated for various shapes of barrels with no geometric limitations (free forms) for the purpose of configuration processing. Special cases for configuration processing based on given formulation are studied to obtain different geometries. For example, the division of the sum of the internal angles of duplets leads to different geometries. The method employed for this division could be equal between duplets, according to arithmetic or geometric progression, or using algebraic equations. These methods are used to divide the sum of internal angles and radius of curvature; Corresponding geometries are then created and compared. The method to generate a geometry imposed by architectural requirements is also proposed in this work. Using such ordering, one can create and model free form foldable structures. To provide changeability for geometry of the structure, a special mid-connection (pivot) is proposed and a prototype model is constructed to demonstrate the efficiency. To construct real scale foldable structures, some connections and a simple method to analyze and design of this type of connections are proposed. A graph of maximum displacement vs. height of the structure is illustrated. A design-construct methodology for foldable structures is proposed.