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Chain Models and Finite Element Analysis: An Executable Chains Formulation of Plane Stress
 Computer Aided Geometric Design
, 1994
"... Algebraictopological kchains defined over finite cell complexes have been proposed as a uniform computational means of representing physical objects, systems and properties. This article introduces Chains, a computer language whose basic datatypes are cells, cell complexes, and kchains. To illus ..."
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Algebraictopological kchains defined over finite cell complexes have been proposed as a uniform computational means of representing physical objects, systems and properties. This article introduces Chains, a computer language whose basic datatypes are cells, cell complexes, and kchains. To illustrate how Chains may be used in numerical computing, we develop a two page Chains program that completely specifies a finite element solution to plane strain, including symbolic definition of quadratic shape functions, the related "element stiffness matrices," and an algebraictopological specification of the assembly process. In contrast to a textbook derivation of the finite element method (which it closely resembles), this program is a fully formal finite element computation, and hence is a step towards the goal of improving the process of creating software for scientific computing by raising the semantic level at which physical systems are specified. 1 Introduction The chain models[PS9...