Shape sensitivity of constructively represented geometric models

Chen, Jiaqin; Freytag, Michael; Shapiro, Vadim

doi:10.1016/j.cagd.2008.01.005

Cited by 24 publications

(10 citation statements)

References 20 publications

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“…Currently, Boundary Representation (B-rep) is extensively used in a geometric data model [31,32]. It describes the geometry of an object in terms of its boundaries, namely the vertexes, edges and surfaces which represent entities of zero dimension, one dimension and two dimension, respectively [33].…”

Section: Unified Data Modelmentioning

confidence: 99%

A CAD/CAE incorporate software framework using a unified representation architecture

Xia

Wang

et al. 2015

Advances in Engineering Software

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Section: Unified Data Modelmentioning

confidence: 99%

A CAD/CAE incorporate software framework using a unified representation architecture

Xia

Wang

et al. 2015

Advances in Engineering Software

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“…One approach to obtain these geometric sensitivities (also found in the literature as design velocities [10]) is to compute finite differences between the CAD model before and after a parameter perturbation. This approach has been identified by some researchers [11,12,13] to lack robustness against topology and labelling changes, which can occur even under small parameter perturbations. Nevertheless, Queen's University of Belfast (QUB) has developed an approach based on projections between discrete representations of the CAD geometries [14], which is efficient, robust and has been successfully applied to CFD [15].…”

Section: Introductionmentioning

confidence: 99%

“…In Fig. 1(b), which is taken from [13], the arrows represent the design velocities as the boundary changes from the solid to the dashed line. Due to the convention adopted throughout this paper that the boundary normals are pointing outwards, a positive design velocity represents an outward movement of the boundary, and negative is inward.…”

Section: Introductionmentioning

confidence: 99%

Linking Parametric Cad With Adjoint Surface Sensitivities

Vasilopoulos

Agarwal²,

Meyer

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. The goal of this work is to present an efficient CAD-based adjoint process chain for calculating parametric sensitivities (derivatives of the objective function with respect to the CAD parameters) in timescales acceptable for industrial design processes. The idea is based on linking parametric design velocities (geometric sensitivities computed from the CAD model) with adjoint surface sensitivities. A CAD-based design velocity computation method has been implemented based on distances between discrete representations of perturbed geometries. This approach differs from other methods due to the fact that it works with existing commercial CAD packages (unlike most analytical approaches) and it can cope with the changes in CAD model topology and face labeling. Use of the proposed method allows computation of parametric sensitivities using adjoint data at a computational cost which scales with the number of objective functions being considered, while it is essentially independent of the number of design variables. The gradient computation is demonstrated on test cases for a Nozzle Guide Vane (NGV) model and a Turbine Rotor Blade model. The results are validated against finite difference values and good agreement is shown. This gradient information can be passed to an optimization algorithm, which will use it to update the CAD model parameters.

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“…Some researchers have elected not to work with the CAD geometry, but still make use of the CAD model parameters for optimization. Methods include determining the movement of the boundary by differentiating parametric expressions for the feature shapes based on the parameters in the construction history [1], or calculating the change in component performance due to a variation in parameter directly [5]. These approaches require access to the underlying CAD modeler kernel and are currently not available for all feature types, therefore at this time they cannot be utilized by a designer in industry.…”

Section: Adjoint Sensitivity Mapsmentioning

confidence: 99%

Optimizing Parameterized CAD Geometries Using Sensitivities Based on Adjoint Functions

Robinson¹,

Armstrong²,

Chua³

et al. 2012

Computer-Aided Design and Applications

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An approach is presented for determining which parameters defining the features in a CAD model need to be modified, and by what amount, to optimize component performance. It uses sensitivities computed for the parameters to determine the change required in each to optimize the component. Parametric sensitivity is computed by combining a measure of boundary movement due to a parameter perturbation, known as design velocity, and an adjoint sensitivity map over the boundary. The sensitivity map results from an adjoint analysis and approximates the change in objective function (performance) due to a movement of the boundary. Gradient based optimization is used based on the parametric sensitivities.This presented method is significantly less computationally expensive than alternative approaches, and has the advantage that optimization is based on the parameters defining the CAD model, allowing it to be integrated into design workflows. The efficiency of the approach allows all of the parameters in the CAD model to be used as optimization variables, potentially offering better optimization. The work is immune to many of the issues hampering existing approaches.

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Shape sensitivity of constructively represented geometric models

Cited by 24 publications

References 20 publications

A CAD/CAE incorporate software framework using a unified representation architecture

A CAD/CAE incorporate software framework using a unified representation architecture

Linking Parametric Cad With Adjoint Surface Sensitivities

Optimizing Parameterized CAD Geometries Using Sensitivities Based on Adjoint Functions

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