A method for planar development of free-form surfaces made of anisotropic materials

Abstract

This paper presents a method for planar development of free-form surfaces especially made of anisotropic materials. A free-form surface is first tessellated into a set of triangular elements (i.e., facet model). If necessary, a facet refinement technique using Euler operators is applied to create a more reliable model that approximates the original surface as closely as possible. The facet model is then roughly flattened on a 2D plane. Next, the roughly flattened model is used as an initial guess for subsequent optimization during which the strain energy method using constant strain triangles (CST) is applied to yield an optimal 2D contour. In fact, various resulting 2D contours can be obtained while varying elasticity ratios between two material axes or development angles. To compare these resulting 2D contours, a contour alignment technique for error estimation is also presented. In this paper, anisotropic materials are considered to be orthotropic as a first approximation. A specific example (lateral surface of a shoe last) is shown to validate the proposed method.

A free‐form surface flattening algorithm that minimizes geometric deformation energy

“…According to the principle of geometric mapping, x ps0 = x s0 , y ps0 = y s0 , so the flatten coordinate of the starting point p s0 is (x s0 , y s0 ). According to the principle of keeping the edge length constant, the coordinate of point p s1 can be calculated by Equation (1).…”

“…In terms of using different numerical solvers, Shin et al. [1] presented a method for planar flattening of free‐form surfaces especially made of anisotropic materials. The free‐form surface was first tessellated into a set of triangular elements, a facet refinement technique using Euler operators was applied to create a more reliable model that approximated the original surface as closely as possible.…”