Optimal design by a homotopy method

Abstract

An optimal design problem is formulated as a system of nonlinear equations rather than the extremum of a functional. Based on a new homotopy method, an algorithm is developed for solving the nonlinear system which is globally convergent with probability one. Since no convexity is required, the nonlinear system may have more than one solution. The algorithm will produce an optimal design solution for a given starting point. For most engineering problems, the initial prototype design is already well conceived and close to the global optimal solution. Such a starting point usually leads to the optimal design by the homotopy method, even though Newton's method may diverge from that starting point. A simple example is given.

Keywords:

• Optimal structural design
• uniform energy density
• generalized plane stress
• homotopy method
• globally convergent
• Chow-Yorke algorithm.

†The work of this author was partially supported by NSF Grant MCS 7821337.

†The work of this author was partially supported by NSF Grant MCS 7821337.

Notes

†The work of this author was partially supported by NSF Grant MCS 7821337.