James Gloyd
Georgia Institute of Technology
Discrete lattices employ individually manufactured unit cells which are assembled to form the final structure of the lattice; this differs from traditional lattice construction as monolithic entities. Doing so, the quality of the final structure is not significantly influenced by the scale of the structure since the constituent unit cells can be manufactured with the same precision regardless of overall structure scale, unlike most monolithic construction methods in which the likelihood of defects increases with scale. Moreover, since the unit cells are assembled after manufacture, the scale of the structure is not bound by the footprint of the equipment used, as is the case with most manufacturing. This scalability was demonstrated by the Coded Structures Laboratory (CSL) at NASA in multiple projects. Given the practicality and efficiency of manufacturing these systems, design and optimization of target structures becomes an interesting endeavor.
Tuning the elastic behavior of materials and structures provides the possibility for significant application weight savings since the mechanisms become integrated with the structure, that is the structure acts as both the load bearing system and the mechanization involved in operation. Some prior work demonstrated discrete lattices as aircraft wings, capable of warping to provide control authority instead of ailerons. These were developed using primitive heuristics based on trial and error with conventional finite element modeling. The goal of this project is to develop a direct method of obtaining a lattice structure which deforms in a prescribed manner when a given set of forces is applied. Obtaining the necessary structural configuration for desired deformation behavior allows engineers to perform optimizations on these designs, such as minimizing the mass or other useful goals. Such a method will allow faster and broader application of morphing discrete lattice technology in aerospace applications and beyond, to any application where form has a significant effect on function. From morphing chassis in terrestrial vehicles to space stations and satellites capable of dynamically changing their shape or compliant mechanisms in robotics, there is a wide breadth of potential applications and benefits for morphing discrete structures.
Modeling of discrete lattices, and indeed any discrete design, is accomplished by treating the individual unit cells or other building blocks as their own structural elements, and in this way the full structure can be easily modeled by an assembly of the repeating unit cell or cells, as done with finite element analysis. With such a model, the stiffness matrix for the entire discrete structure can be cast as a function of design variables relating to the components as an affine combination of the elements. This representation of the stiffness matrix allows implementation of structural optimization methods, so by choosing an objective function and applying optimization algorithms, a breadth of possible goals for the structure can be easily sought. Moreover, by rearranging the same affine combination, the structure’s displacements can be prescribed, which define a design space that guarantees the prescribed displacements are satisfied. Within such a design space, structural optimization methods can be used to obtain different structures depending on the desired purpose and goal of the discrete structure.