A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
Shape optimal design using high-order elements
Computer Methods in Applied Mechanics and Engineering
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
A CAD-based design parameterization for shape optimization of elastic solids
Advances in Engineering Software
Finite elements, genetic algorithms and &bgr;-splines: a combined technique for shape optimization
Finite Elements in Analysis and Design
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Finite Elements in Analysis and Design
Multimorphing: A tool for shape synthesis and analysis
Advances in Engineering Software
NPV-based decision support in multi-objective design using evolutionary algorithms
Engineering Applications of Artificial Intelligence
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Optimum design introduces strong emphasis on compact geometry parameterization in order to reduce the dimensionality of the search space and consequently optimization run-time. This paper develops a decision support system for optimum shape which integrates geometric knowledge acquisition using 3D scanning and evolutionary shape re-engineering by applying genetic-algorithm based optimum search within a distributed computing workflow. A shape knowledge representation and compaction method is developed by creating 2D and 3D parameterizations based on adaptive chaining of piecewise Bezier curves and surfaces. Low-degree patches are used with adaptive subdivision of the target domain, thereby preserving locality. C^1 inter-segment continuity is accomplished by generating additional control points without increasing the number of design variables. The control points positions are redistributed and compressed towards the sharp edges contained in the data-set for better representation of areas with sharp change in slopes and curvatures. The optimal decomposition of the points cloud or target surface into patches is based on the requested modeling accuracy, which works as lossy geometric data-set compression. The proposed method has advantages in non-recursive evaluation, possibility of chaining patches of different degrees, options of prescribing fixed values at selected intermediate points while maintaining C^1 continuity, and uncoupled processing of individual patches. The developed procedure executes external application nodes using mutual communication via native data files and data mining. This adaptive interdisciplinary workflow integrates different algorithms and programs (3D shape acquisition, representation of geometry with data-set compaction using parametric surfaces, geometric modeling, distributed evolutionary optimization) such that optimized shape solutions are synthesized. 2D and 3D test cases encompassing holes and sharp edges are provided to prove the capacity and respective performance of the developed parameterizations, and the resulting optimized shapes for different load cases demonstrate the functionality of the overall distributed workflow.