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.

KEYWORDS:

• Exponential approximation
• consistent
• optimum design structures
• second-order

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Hosein Ahmadvand

Hosein Ahmadvand received his BSc from the Isfahan University of Technology in Iran and MSc in Structural Engineering from Shahid Bahonar University in Iran. He is currently PhD Student in Structural Engineering at Kurdistan University under the supervision of Prof. Ali Reza Habibi. His PhD thesis is focused on structural optimisation. His research interests include structural optimisation, and seismic vulnerability evaluation of structures.

Alireza Habibi

Alireza Habibi is a Professor of Structural Engineering in the Department of Civil Engineering at Shahed University in Iran. He received his BSc from the Bou-Ali Sina University in Iran, MSc from the Shahid Bahonar University in Iran, and PhD from the Tarbiat Modares University in Iran. His research interests are structural optimisation, nonlinear analysis, damage analysis, and sensitivity analysis.