Solving the Boundary Value Problem of Curves With Prescribed Geodesic Curvature Based on a Cubic B-Spline Element Method

Composite manufacturing processes such as automated tape placement (ATP) and filament winding process (FW) put forward specific requirements for the geodesic curvature along layup paths of composite tows tapes. In this paper, a non-uniform cubic b-spline element method is proposed solving boundary value problem curves with prescribed curvature. The differential equation system target curve discretized through point collocation method, quasi-Newton iteration scheme adopted to approach real solution from an initial approximation. proved have third order accuracy, which shows more superiorities comparing existing numerical methods. Simulations experiments on series parametric surfaces are performed investigate performance results verify high efficiency. could cope BVP no matter their vanishes or not. At same time, computed natural smooth that interpolation technique unnecessary ensure continuity curves. One potential application trajectory optimization process.