Modeling methods for the design of 3D broadcloth composite parts

With the advent of lighter and stronger composite materials over the last two decades, more and more metals have been replaced by composite materials in aircraft and other vehicles. It is not suprising that the airframes of certain aircraft (e.g. Lear Fan 2100) are totally fabricated from composite materials. Composites consist of a reinforcing material suspended in a “matrix” material (e.g. epoxy) that bonds it to adjacent reinforcing materials. The three major composite forms are chopped fiber, unidirectional tape, and (bidirectional) broadcloth. Today’s aircraft mostly employ broadcloth composites partly because they have outstanding strength-to-weight ratio, and partly because their structural properties may be tailored to the expected load in different directions [16]. Broadcloth composites have both vertical and horizontal threads (weft and warp) interwoven to form a sheet of cloth as seen in Fig 1. They strongly resist stretching along thread directions, but can be deformed flexibly along thread diagonals by changing the angle between vertical and horizontal threads. This allows a composite broadcloth to be “formed” into virtually any curved surface. In order to reinforce aircraft structures, multiple sheets (plies) of broadcloth composites are usually laid one on top of the other, a lamination process. With this trend of replacing metals with composite materials, new lamination technologies have been developed to manufacture composite materials in order to form an airframe. During the lamination process, plies of composite sheets must be cut to the required size, with the required fiber orientation, and laid up onto the surface of a die or molding tool prior to curing. It is this process of deforming a broadcloth composite sheet into a 3D shape by pressing it onto a mold that we will refer to as a “fitting.” Unfortunately, the cutting and orientation process has not yet been fully automated, and it has been mostly implemented with manual procedures. It is therefore a time-consuming, non-reproducable, and inaccurate process in need of design automation tools. In this paper we present a number of modeling methods that may be used to automate the design of 3D broadcloth composite parts. First, we describe a model (a Tchebychev net) which allows us to simulate the deformation of woven materials into a specific 3D shape. Two algorithms are described for performing the actual fitting. The first algorithm simulates the fit by solving the Tchebychev net formula using a finite difference technique. The second algorithm simulates the fit by reducing the problem to a surface-surface intersection problem. Once we establish the techniques for simulating a fit, we can discuss the quality and acceptibility of the fit. In general, a good fit is the one that consumes the smallest area of the material, that has the smallest deformation energy, and that is free of manufacturing anomalies such as wrinkles and breaks. We will present mathematical tools that allow us to measure the “goodness” of a fit with a Tchebychev net, and that allow us to visually identify where a possible anomalous event may occur. Specifically, we will introduce a path-dependent Gaussian curvature integral that is defined at an arbitrary point in a surface region. With a path-dependent Gaussian curvature integral, we will show that it is possible not only to predict anomalous events, or wrinkles in particular, but to provide a solution to preventing them. Finally, we will propose three methods for preventing anomalous events: (1) automatic generation of a good initial condition, (2) dart insertion, and (3) surface shape modification. Providing different methods for preventing