Advances in Computational Design

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Numerical solution of beam equation using neural networks and evolutionary optimization tools

  • Babaei, Mehdi (Department of Civil Engineering, University of Bonab) ;
  • Atasoy, Arman (Department of Civil Engineering, Istanbul Rumeli University) ;
  • Hajirasouliha, Iman (Department of Civil & Structural Engineering, The University of Sheffield) ;
  • Mollaei, Somayeh (Department of Civil Engineering, University of Bonab) ;
  • Jalilkhani, Maysam (Department of Civil Engineering, Urmia University of Technology)
  • Received : 2021.04.05
  • Accepted : 2021.09.03
  • Published : 2022.01.25
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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 toolsin solving beam ODEs can efficiently lead to accurate solutions with low computational costs, and should prove useful to solve more complex practical applications.

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References

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