Optimum Design by Partitioning Into Substructures

Abstract

A method is developed for the optimum design of large framed structures. Optimization is carried out iteratively by partitioning the structure and thus dividing the optimization problem into a number of smaller subproblems. In the solution of a subproblem only part of the design variables and constraints are considered. Analysis is performed by the stiffness method. An approximate method for reanalysis of the substructures is suggested. The partitioning approach and the reanalysis method are based on the fact that changes of a design variable of one substructure do not appreciably affect the behavior of the other substructures. The cost function is set up for the whole structure and the subproblems are optimized by a direct search technique using external penalty functions on the constraints. Numerical examples of beam and beam grid structures demonstrate applications of the method.