Design of deployable structures using limit analysis of partially rigid frames with quadratic yield functions
The linear programming approach to generating deployable structures is extend to allow a hinge rotating around an axis in arbitrary direction. Plastic limit analysis problem with quadratic yield function with respect to member-end moments is solved to generate hinges in arbitrary directions of a partially rigid frame. The directions of hinges are obtained from the member-end momemts along the local axes. Using the proposed method, three-dimensional mechanisms and deployable structures with small number of hinges are successfully obtained. The manufacturability of a deployable structure is confirmed by assembling a small-scale model.
ANALYSIS OF STABILITY AND MECHANISM OF FRAMES WITH PARTIALLY RIGID CONNECTIONS
A method is presented for stability analysis and finding mechanisms of frames with partially rigid connections. Equilibrium equations are formulated with respect to the reduced vector of member-end forces, for which linear constraints are assigned. The modes of self-equilibrium forces and unstable mechanisms are found using singular value decomposition of the matrix representing equilibrium equations and constraints. An infinitesimal mechanism with small degree of kinematic indeterminacy can be found using limit analysis for an artificial proportional loading condition. The effectiveness of proposed method is demonstrated through examples of frames with rectangular and hexagonal grids.
Matrix formulation of macro-elements for deployable structures
Abstract This paper deals with the computer analysis of a particular class of deployable structures, which we have developed over recent years. These structures consist only of rods, hinged together to form a deployable backbone, of some passive cables, which are slack when the backbone is fully or partially folded but become taut when it is fully deployed, and one or more active cables, which activate deployment and set up suitable states of prestress, once the structure is in its fully deployed configuration. We discuss one aspect of the computer analysis of these structures, namely the task of setting up the equilibrium and flexibility matrices required for the deployment, prestressing and structural response computations of three macro-elements: the active cable, i.e. a slender, constant-tension element consisting of two or more straight segments; the pantograph unit, consisting of two coplanar, straight beams joined by a shear connector; and the backbone module for the octahedral mast, which consists of a flat, square cross of rods and an additional rod going through a pivot-and-slider joint at the centre of the cross. Compact matrices for these elements are derived using a recently developed matrix reduction technique. Three applications of these macro-elements are given, illustrating their use in simple deployable structures.