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Volume 7, Number 1, January 2022 , pages 001-17 DOI: https://doi.org/10.12989/acd.2022.7.1.001 |
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Numerical solution of beam equation using neural networks and evolutionary optimization tools |
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Mehdi Babaei, Arman Atasoy, Iman Hajirasouliha, Somayeh Mollaei and Maysam Jalilkhani
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| Abstract | ||
| In this study, a new strategy is presented to transmit the fundamental elastic beam problem into the modern optimization platform and solve it by using artificial intelligence (AI) tools. As a practical example, deflection of Euler-Bernoulli beam is mathematically formulated by 2nd-order ordinary differential equations (ODEs) in accordance to the classical beam theory. This fundamental engineer problem is then transmitted from classic formulation to its artificial-intelligence presentation where the behavior of the beam is simulated by using neural networks (NNs). The supervised training strategy is employed in the developed NNs implemented in the heuristic optimization algorithms as the fitness function. Different evolutionary optimization tools such as genetic algorithm (GA) and particle swarm optimization (PSO) are used to solve this non-linear optimization problem. The step-by-step procedure of the proposed method is presented in the form of a practical flowchart. The results indicate that the proposed method of using AI tools in solving beam ODEs can efficiently lead to accurate solutions with low computational costs, and should prove useful to solve more complex practical applications. | ||
| Key Words | ||
| artificial neural networks; elastic beam deflection; euler-bernoulli beam; genetic algorithm; ordinary differential equation; particle swarm optimization | ||
| Address | ||
| Mehdi Babaei: Department of Civil Engineering, University of Bonab, Bonab, Iran Arman Atasoy: Department of Civil Engineering, Istanbul Rumeli University, Istanbul, Turkey Iman Hajirasouliha: Department of Civil & Structural Engineering, The University of Sheffield, Sheffield, U.K. Somayeh Mollaei: Department of Civil Engineering, University of Bonab, Bonab, Iran Maysam Jalilkhani: Department of Civil Engineering, Urmia University of Technology, Urmia, Iran | ||
