Optimal Design of a Medical Staple Using Shape Memory Alloy

Abstract

This paper presents the mechanical design of a medical staple using shape memory alloy (SMA) material. The design problem was formulated as an optimization problem minimizing an energy functional. The constraints were the length of wire, the properties of the SMA material, and the required clamping force. The Euler-Lagrange equation of this isoperimetric calculus of variation problem was derived, which was a fourth order two-point boundary value problem. An analytical solution was constructed and verified. A numerical optimization technique was applied to generate other possible solutions for the boundary value problem. The objective was to minimize the error of the solution for specific boundary conditions. The sequential quadratic programming algorithm was applied with Runge-Kutta integration to solve the boundary value problem. The design procedure described in this paper could be applied to the design of other mechanical components of wire form using SMA material.