A shape optimization approach based on natural design variables and shape functions
Computer Methods in Applied Mechanics and Engineering
Shape optimization of connecting rod pin end using a generic model
Finite Elements in Analysis and Design - Special NASTRAN issue
Volume-preserving free-form solid
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Fast volume-preserving free form deformation using multi-level optimization
Proceedings of the fifth ACM symposium on Solid modeling and applications
Implicit functions with guaranteed differential properties
Proceedings of the fifth ACM symposium on Solid modeling and applications
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
Erep: An editable, high-level representation for geometric design and analysis
Selected and Expanded Papers from the IFIP TC5/WG5.2 Working Conference on Geometric Modeling for Product Realization
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
B-rep SE: simplicially enhanced boundary representation
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Shape sensitivity of constructively represented geometric models
Computer Aided Geometric Design
A framework for preservable geometry-centric artifacts
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Distance functions and skeletal representations of rigid and non-rigid planar shapes
Computer-Aided Design
Optimization of continuous heterogeneous models
Heterogeneous objects modelling and applications
On the long-term retention of geometry-centric digital engineering artifacts
Computer-Aided Design
Hi-index | 0.01 |
Most solid models are archived using boundary representations, but they are created, edited, and optimized using high level constructive methods that rely on parameterized Boolean set operations and feature-based techniques. Downstream applications often require optimization of integral-valued performance measures over such models that include volume, mass, and energy properties, as well as more general distributed fields (stress, temperature, etc.). A key computational utility in all such applications is the computation of the sensitivity of the performance measure with respect to the parameters in the solid's construction history. We show that for a class of performance measures defined as domain integrals, the sensitivity with respect to a parameter requires integration over a subset of the solid's boundaries that is affected by that parameter. In contrast to earlier methods, the proposed approach for computing sensitivities does not require solid's boundary to remain homeomorphic, and may be used with most types of constructive representations, including CSG and feature-based representations, where the defining Boolean expression may not be known. Simplicity and effectiveness of the proposed technique are illustrated on several common shape optimization problems.