New Approximation Method for Structural Optimization

Abstract

The main difficulty with the use of mathematical programming for structural optimization problems in which the structural form is specific is the formulation of constraints, such as displacement and stress limitations, as explicit functions of the design variables. In this research, a new method, called Consistent Approximation (CONAP), was developed to explicitly formulate constraints and objective functions based on an efficient approximation concept. In the proposed method, some important parameters are designed using design sensitivities to increase the method’s flexibility and consistency in various optimization problems. It is shown that existing methods based on approximation concepts can be easily derived from CONAP with the definition of special values for the designed parameters. In the presented approach, the primary optimization problem is replaced with a sequence of explicit sub-problems. Each sub-problem is efficiently solved using the Sequential Quadratic Programming (SQP) method. Several examples are given to demonstrate the capability and applicability of the method. It is shown that the proposed method speeds up the convergence of the optimization process.