Solving Interval Constraints by Linearization in Computer-Aided Design |
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Authors: | Yan Wang Bartholomew O Nnaji |
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Affiliation: | (1) NSF Center for e-Design, University of Central Florida, 4000 Central Florida Blvd, Orlando, FL 32816, USA;(2) NSF Center for e-Design, University of Pittsburgh, 1048 Benedum Hall, Pittsburgh, PA 15261, USA |
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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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