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.
Topology Optimization of Large Motion Rigid Body Mechanisms With Nonlinear Kinematics
The modern design process of mechanical structures is increasingly influenced by highly sophisticated methods of topology optimization that can automatically synthesize optimal design variants. However, the typically finite-element-based methods are limited to design tasks with comparably small deflections and simple kinematics. They are not directly applicable to the difficult development process of large motion mechanisms, which remains mainly a manual task based on the engineer’s experience, intuition, and ingenuity. There, optimization techniques are only, if at all, used in the process of dimensional synthesis, where the geometrical properties and the orientation of individual links of a fixed mechanism topology are determined. In this work, two different approaches to optimization-based topology synthesis of large motion rigid body mechanisms are presented and investigated. The goal is to automatically synthesize a combination of linkage topology and joint types that represent the most suitable mechanism layout for a particular task. The first approach is based on a trusslike ground structure that represents an overdetermined system of rigid bars from which the most appropriate topology can be extracted from this ground structure by means of gradient-based optimization algorithms. In the second approach, a genetic algorithm is used to solve the intrinsically combinatorial problem of topology synthesis. Along with several examples, both approaches are explained, their functionality is shown, and their advantages, limitations, and their capability to improve the overall design process is discussed.