Title

Solving Interval Constraints By Linearization In Computer-Aided Design

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. © Springer Science + Business Media B.V. 2007.

Publication Date

4-1-2007

Publication Title

Reliable Computing

Volume

13

Issue

2

Number of Pages

211-244

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s11155-006-9023-4

Socpus ID

33846280144 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/33846280144

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