splines - From SIAM News, Volume 38, Number 4, May 2005 The...

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From SIAM News , Volume 38, Number 4, May 2005 The Extensive Use of Splines at Boeing By Thomas A. Grandine Splines are used extensively at Boeing and throughout much of the industrial world. There are very few remaining areas in either manufacturing or engineering in which these interesting functions have yet to play a role, and their use continues to grow at a rapid rate. A spline, for the purposes of this article, is defined as any function made up of one or more polynomial pieces joined together to satisfy given (and possibly different) differentiability requirements. At Boeing, these functions are used not only to represent geometric designs, by modeling curves and surfaces that describe the edges and faces of geometric solids, but also to model engineering analysis and performance data. As an example of the latter, splines can be used to model airplane drag as a function of mach number, the speed of the airplane with respect to the free stream airflow. Ideal Modeling Technology In these contexts, Boeing uses splines in four very different kinds of applications. The most familiar is computer-aided design, where splines are used to represent the geometric entities that form the basis of product-definition data. A related application, common across many industries, is computer-aided manufacturing. Here, in addition to representing geometric parts, splines can be used to represent machine tool cutter paths. They can also be used as engineering data modeling functions. Compensation tables on machine tools, for example, can be represented this way; compensation tables themselves are used to model positional corrections to a large variety of environmental or external conditions, such as temperature. A third application class, engineering an-alysis and simulation, is especially important at a large engineering company like Boeing. Examples range from sophisticated computational fluid dynamics simulations to simple linear analysis codes involving simplified physical models. In many cases, splines are required to represent geometry or geometric boundary conditions. In others, splines are called on to model material properties and thicknesses, atmospheric chemical composition and reactivity, and experimental results, such as wind tunnel data. Some codes use them to calibrate other computations, while others use the B-splines that form a basis for any given spline function space as finite elements. In the finite element case, engineering codes create spline approximations to the solution of ordinary differential equations, partial differential equations, integral equations, and differential– algebraic equations, an approach popularized by de Boor and Swartz in 1973.
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splines - From SIAM News, Volume 38, Number 4, May 2005 The...

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