Brian Tatting

CELLULAR AUTOMATA FOR DESIGN OF TWO-DIMENSIONAL CONTINUUM STRUCTURES

The implementation of Cellular Automata (CA) techniques for the analysis and design of two-dimension al continuum structures under in-plane loading is presented. The paper summarizes the basic elements of the CA and the specific formulation used for thin isotropic plates. Analysis and design rules are presented that satisfy static equilibrium and fulfill a fully-stressed material failure condition. The update rules are based on the deformation of an equivalent truss structure, and the relation between the thickness of the isotropic plate and the cross-sectional areas of the truss members are derived so mat the strain energy due to in-plane deformation is modeled correctly. Example results are presented which verify the accuracy of the modeling technique by a comparison to a closedform stress functional solution. Additionally, design studies based on topology optimization and thickness sizing are performed, which demonstrate the applicability of the CA environment for efficient design of structures.

Cellular Automata for design of truss structures with linear and nonlinear response

The feasibility of the use of Cellular Automata (CA) techniques for the design of two-dimensional structural problems, such as trusses and continuum structures under static loading, is investigated. The study implements an integrated analysis and design approach using the methods of CA to achieve an optimal structural configuration. The paper summarizes the basic features of the CA and demonstrates a formulation for the design of twodimensional truss structures that exhibit linear and geometrically nonlinear response characteristics. The solution variables chosen for the approach include the in-plane displacements of the cells, which represent nodal points of the truss, and the cross sectional areas of the members that connect the neighboring cells. Equations derived from local equilibrium are used as the rules that govern the cell displacements, and simple rules that are based on fully stressed design conditions are used for sizing of the members. In addition to the theoretical formulation, an investigation into the numerical implementation of the CA was performed. Initially the Mathematica programming language was used for demonstration purposes. For large-scale problems, an efficient and flexible Fortran 90 computer code capable of modeling complex two-dimensional geometries was developed. Examples demonstrating the capabilities of the design tools are included.

Tow-Placement Technology and Fabrication Issues for Laminated Composite Structures

‡A review of fabrication issues encountered during the manufacture of tow-steered laminates is presented. Tow-steering is a novel laminate design concept that attempts to tailor the stiffness of a traditional composite laminate by using non-traditional curvilinear fiber paths within the plane of a ply. Manufacture of such tow-steered plies has been demonstrated with advanced tow-placement machines, and a representative machine is used to provide an example of the fabrication process. Stiffness tailoring of the composite laminate is achieved through spatial variation of the fiber orientation angle. The resulting curvilinear tow paths are based on constant curvature arcs, which provide simple numerical solutions as well as direct correspondence with the limiting turning radius constraint of the tow-placement machine. A basic framework for a general constant curvature path is presented, along with additional concepts to extend the fiber angle definition throughout the entire domain of the ply. These construction techniques generate gaps and/or overlaps between neighboring tow courses, which must be adequately considered during both the structural analysis and fabrication phases. The major concerns within the analysis portion due to the presence of tow-steered plies involve the balancing and symmetry of the laminate. Balancing is an issue due to the variable stiffness nature of each ply, and proper configurations are introduced which are required to obtain a globally balanced laminate. Symmetry about the middle surface of the laminate ensures that unintentional curvature does not arise during the curing process. For laminates using plies with overlaps, both the lay-down order of the tow courses and the alignment of the layers on the mandrel surface play an important role for this symmetry issue. Appropriate modifications to the stiffness measures of Classical Lamination Theory are discussed so that better correlation between the modeling and the actual part can be achieved. Relevant information concerning the fabrication of such laminates is based on previous production of several prototype flat panels which were built to validate the tow-steering design concept. The fabrication of these panels provided many opportunities to improve several details of the tow-steering concepts, as well as assess and correct unforeseen complications that the manufacturing phase brought into focus. The most important of these issues involves the minimization of the gaps that exist due to the curvilinear nature of the tow paths and the tow-dropping between neighboring courses. The presence of these lamina irregularities can often lead to degraded performance of the structure, therefore a coverage parameter and an interweaving technique are introduced which aim to diminish the effect of the gaps. Examples from actual parts are employed to demonstrate the usefulness of the techniques to produce a more reliable structure. Similarly, the interweaving technique applied to plies that permit overlaps instead of tow-dropping is shown to smooth out the thickness variation that occurs due to the extra plies within the overlap regions.