Draping simulation using optimization techniquesDraping simulation using optimization techniques H. de Boer and F. van Keulen Delft University of Technology Faculty of Mechanical Engineering

Draping simulation using optimizationtechniques

H. de Boer and F. van Keulen

Delft University of TechnologyFaculty of Mechanical EngineeringP.O. Box 5033, NL 2600 GA Delft

phone +31-(0)15-2786512, email [email protected]

IntroductionSimulation of deep drawing of fabric reinforced com-posites is investigated. Numerical simulation is, forinstance, required to enable structural analysis. Anenhanced geometrical algorithm on the basis of opti-mization techniques is presented.

ApproachGeometrical methods make use of the fact that oncetwo perpendicular yarns are located, the completefabric is uniquely defined. The problem of coveringa product surface with fabric is herewith reduced tofinding the location of these yarns. That is: define thecurvature of a yarn as a function of a material coordi-nate y (See Figure 1).

In the optimization based method the curvature is de-termined by:

� Mould surface ! curvature in normal plane.� Control variables ! curvature in tangent plane.

Governing equation:

i;y = �(s)j� (i � n;y)n

Physical reliable values for the control variables s aredetermined by using optimization techniques.

Advantages of the optimization based approach:

� Computational efficient.� Flexible

i(y)n(y)

j(y)x(y)

Tangent plane

Normal planeYarn

y

Figure 1 : Geometry of a yarn.

ResultsDraping of a closed semi-cylinder is examined. Thefitness of each intermediate covering (Figure 2) iscomputed by an objective and constraint function.Currently, the objective function is a weighted meanshear angle, while the constraint function eliminateswrinkles.

Figure 2 : Intermediate coverings and final solution

DiscussionIt is possible to formulate the problem of simulatingforming processes as a constraint optimization prob-lem. The forming process to be simulated is reflectedby objective and constraint functions.

References1. De Boer, H. and Van Keulen, F. Simulating forming pro-

cesses of fabric reinforced composites by applying optimiza-tion. In: 7th AIAA/USAF/NASA/ISSMO Symposium on Mul-tidisciplinary Analysis and Optimization, St. Louis, Missouri,September 2-4, 1998, Part 2, AIAA-98-4842, 1045-1055.