Title

Solving interval constraints by linearization in computer-aided design

Authors

Authors

Y. Wang;B. O. Nnaji

Comments

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Abbreviated Journal Title

Reliab. Comput.

Keywords

NONLINEAR-SYSTEMS; EXISTENCE VERIFICATION; GEOMETRIC CONSTRAINTS; DECOMPOSITION PLANS; BOUNDARY EVALUATION; MECHANICAL DESIGN; PARAMETRIC; DESIGN; SINGULAR ZEROS; BEZIER CURVES; NEWTON METHOD; Mathematics, Applied

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.

Journal Title

Reliable Computing

Volume

13

Issue/Number

2

Publication Date

1-1-2007

Document Type

Review

Language

English

First Page

211

Last Page

244

WOS Identifier

WOS:000252303100005

ISSN

1385-3139

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