Direct manipulation of free-form deformation using curve-pairs

Given the importance of structural integrity of aerodynamic shapes, the necessity of including a cross-sectional area equality constraint among other geometrical and aerodynamic ones arises during the optimization process of an airfoil. In this work an airfoil optimization scheme is presented, based on Area-Preserving Free-Form Deformation (AP FFD), which serves as an alternative technique for the fulfillment of a cross-sectional area equality constraint. The AP FFD is based on the idea of solving an area correction problem, where a minimum possible offset is applied on all free-to-move control points of the FFD lattice, subject to the area preservation constraint. Due to the linearity of the area constraint in each axis, the extraction of an inexpensive closed-form solution to the area preservation problem is possible by using Lagrange Multipliers. A parallel Differential Evolution (DE) algorithm serves as the optimizer, assisted by two Artificial Neural Networks as surrogates. The use of multiple surrogate models, in conjunction with the inexpensive solution to the area correction problem, render the optimization process time efficient. The application of the proposed methodology for wind turbine airfoil optimization demonstrates its applicability and effectiveness.

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Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows

Journal of Scientific Computing ◽

10.1007/s10915-013-9807-8 ◽

2013 ◽

Vol 60 (3) ◽

pp. 537-563 ◽

Cited By ~ 16

Author(s):

Francesco Ballarin ◽

Andrea Manzoni ◽

Gianluigi Rozza ◽

Sandro Salsa

Keyword(s):

Shape Optimization ◽

Numerical Solution ◽

Existence Results ◽

Free Form ◽

Stokes Flows ◽

Free Form Deformation

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Fully Free-Form Deformation Features (δ-F4) Incorporating Discontinuities

Volume 1: 30th Design Automation Conference ◽

10.1115/detc2004-57225 ◽

2004 ◽

Cited By ~ 2

Author(s):

Vincent Cheutet ◽

Jean-Philippe Pernot ◽

Jean-Claude Leon ◽

Bianca Falcidieno ◽

Franca Giannini

Keyword(s):

Surface Deformation ◽

Geometric Constraints ◽

Free Form ◽

Initial Surface ◽

Cad Systems ◽

Free Form Deformation ◽

Deformation Features ◽

Generate Surface ◽

Prototype Software ◽

Free Form Surfaces

To limit low-level manipulations of free-form surfaces, the concept of Fully Free Form Deformation Features (δ-F4) have been introduced. They correspond to shapes obtained by deformation of a surface area according to specified geometric constraints. In our work, we mainly focused on those features aimed at enforcing the visual effect of the so-called character lines, extensively used by designers to specify the shape of an object. Therefore, in the proposed approach, 3D lines are used to drive surface deformation over specified areas. Depending on the wished shape and reflection light effects, the insertion of character lines may generate surface tangency discontinuities. In CAD systems, such kind of discontinuities is generally created by a decomposition of the initial surface into several patches. This process can be tedious and very complex, depending on the shape of the deformation area and the desired surface continuity. Here, a method is proposed to create discontinuities on a surface, using the trimming properties of surfaces. The corresponding deformation features produce the resulting surface in a single modification step and handle simultaneously more constraints than current CAD systems. The principle of the proposed approach is based on arbitrary shaped discontinuities in the parameter domain of the surface to allow the surface exhibiting geometric discontinuities at user-prescribed points or along lines. The proposed approach is illustrated with examples obtained using our prototype software.

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