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Solving Interval Constraints by Linearization in Computer-Aided Design

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Reliable Computing

Abstract

Current parametric CAD systems require geometric parameters to have fixed values. Specifying fixed parameter values implicitly adds rigid constraints on the geometry, which have the potential to introduce conflicts during the design process. This paper presents a soft constraint representation scheme based on nominal interval. Interval geometric parameters capture inexactness of conceptual and embodiment design, uncertainty in detail design, as well as boundary information for design optimization. To accommodate under-constrained and over-constrained design problems, a double-loop Gauss-Seidel method is developed to solve linear constraints. A symbolic preconditioning procedure transforms nonlinear equations to separable form. Inequalities are also transformed and integrated with equalities. Nonlinear constraints can be bounded by piecewise linear enclosures and solved by linear methods iteratively. A sensitivity analysis method that differentiates active and inactive constraints is presented for design refinement.

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  1. NSF Center for e-Design, University of Central Florida, 4000 Central Florida Blvd, Orlando, FL, 32816, USA

    Yan Wang

  2. NSF Center for e-Design, University of Pittsburgh, 1048 Benedum Hall, Pittsburgh, PA, 15261, USA

    Bartholomew O. Nnaji

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  1. Yan Wang
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Wang, Y., Nnaji, B.O. Solving Interval Constraints by Linearization in Computer-Aided Design. Reliable Comput 13, 211–244 (2007). https://doi.org/10.1007/s11155-006-9023-4

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