Structural optimization using Newton modified barrier method

Abstract

The Newton Modified Barrier Method (NMBM) was applied to a structural optimization problem with large numbers of design variables and constraints. This mathematical optimization algorithm was based on Modified Barrier Function (MBF) theory and the global converging step version of the Newton Method for smooth unconstrained optimization. For illustrating the convergence characteristics of this method to structural optimization, a truss structure with 721 design variables with constraints on displacements and minimum size requirements was solved. The convergence to the optimum was found to be monotonic. The rate of convergence was compared with solving the same problem with ASTROS and optimality criteria approach.