Optimal pick-up locations for transport and handling of limp materials

Optimization procedures are developed to solve for pick-up locations that minimize a measure of the deformation of flat limp parts. The limp parts are modeled as shells undergoing large deformations and rotations using a geometrically exact nonlinear shell finite element formulation. The strain energy is the objective function minimized and is computed from a finite element solution for the deformation of the limp part. The optimal locations are found by solving the corresponding bound constrained minimization problem using gradient based algorithms. The ability to automatically mesh the domain of the limp part determines whether the problem can be solved as a continuous problem. Meshes for one dimensional and square/rectangular two dimensional domains are automatically generated and the optimal locations are solved using continuous optimization algorithms based on the Broyden, Fletcher, Goldfarb and Shanno (BFGS) update of the Hessian. Optimal locations for all other two dimensional domains are obtained by solving a discrete optimization problem on a fixed mesh by a new gradient based algorithm. Results are obtained for one dimensional strips and various two dimensional shapes of limp material. These include shapes obtained from apparel and datawear products.