An interpolatory subdivision algorithm for surfaces over arbitrary triangulations

In this paper, an interpolatory subdivision algorithm for surfaces over ar-bitrary triangulations is introduced and its convergence properties over nonuni-form triangulations studied. The so called Butterfly Scheme (interpolatory) is a special case of this algorithm. In our analysis of the algorithm over uniform triangulations, a matrix approach is employed and the idea, of "Cross Differ-ence of Directional Divided Difference" analysis is presented. This method is a generalization of the technique used by Dyn, Gregory and Levin etc. to analyse univariate subdivision algorithms. While for nonuniform data, an extraordi-nary point analysis is introduced and the local subdivision matrix analysis is presented. It is proved that the algorithm produces smooth surfaces over ar-bitrary triangular networks provided the shape parameters are kept within an appropriate range

Non-uniform corner cutting

The convergence of a non-uniform corner cutting process is investigated. It is shown that the limit curve will be differentiable provided the proportions of the corner cuts are kept within appropriate constraints. Keywords Subdivision, corner cuttin

A 10-point interpolatory recursive subdivision algorithm for the generation of parametric surfaces

In this paper, an interpolatory subdivision algorithm for surfaces over arbitrary triangulations is introduced and its properties over uniform triangulations studied. The Butterfly Scheme, which is introduced by Dyn, Gregory and Levin is a special case of this algorithm. In our analysis, the matrix approach is employed and the idea of "Cross Difference of Directional Divided Difference" analysis is presented. This method is a generalization of the technique used by Dyn, Gregory and Levin etc. to analyse univariate subdivision algorithms. It is proved that the algorithm produces smooth surfaces provided the shape parameters are kept within an appropriate range

The 3D version of the finite element program FESTER

In this report, a detailed description of the 3-D version finite element pro-gram FESTER is given. This includes: 1. A brief introduction to the package FESTER; 2. Preparing an input data file for the 3D version of FESTER; 3. Principal stress and stress invariant analyses; 4. 2D joint element (surface contact) characterisation and its mathematical formulation; 5. Formulations of the 3D stress-strain analyses for both isotropic and anisotropic materials, plane of weakness and cracking criteria; 6. 3D brick elements, infinity elements and their corresponding shape and mapping functions; 7. Large-displacement formulations; 8. Modifications to the subroutines INVAR, JNTB, TMAT, MOD2 etc; 9. Numerical examples; and 10. Conclusions

Integrated Optimization of Mars Hybrid Solar-Electric/Chemical Propulsion Trajectories

NASAs Human Exploration and Operation Mission Directorate is developing a reusable hybrid transportation architecture in which both chemical and solar-electric propulsion systems are used to deliver crew and cargo to the Martian sphere of influence. By combining chemical and solar-electric propulsions into a single spacecraft and applying each where it is the most effective, the hybrid architecture enables a series of Mars trajectories that are more fuel efficient than an all chemical propulsion architecture without significant increase to trip time. Solving the complex problem of low-thrust trajectory optimization coupled with the vehicle sizing requires development of an integrated trajectory analysis frame- work. Previous studies have utilized a more segmented optimization framework due to the limitation of the tools available. A new integrated optimization framework was recently developed to address the deficiencies of the previous methods that enables higher fidelity analysis to be performed and increases the efficiency of large design space explorations