A new second-order approximation method for optimum design of structures

ABSTRACT In this study, a new method called Second-order Consistent Exponential Approximation (SCEA) is developed to generate the high-quality nonlinear approximation of the structural problems. For this purpose, some important parameters are designed by employing design sensitivities to enhance its consistency with various structural optimisation problems. In the optimisation process, the design variables for which sensitivity of the objective function is zero, are eliminated in the corresponding iteration. In addition, in approximating the design constraints, the zero design sensitivities are limited to a small value. In the presented approach, the primary optimisation problem is replaced with a sequence of explicit sub-problems. Each sub-problem is efficiently solved using the sequential quadratic programming (SQP) algorithm. For reducing computational cost and enhancing the efficiency and capability of the proposed method, a corrective technique is applied for tolerance on the constraint violation, the function value, and the design variables in the SQP algorithm. Several structural examples and highly nonlinear problems were utilised to demonstrate the efficiency of the proposed method. Optimal solutions were compared to the conventional approximation methods and some of the metaheuristic approaches. Results illustrate that the accuracy of the optimum design is improved and the rate of the convergence speeds up.