Article: Solution of structural mechanic's problems by machine learning Journal: International Journal of Hydromechatronics (IJHM) 2022 Vol.5 No.1 pp.22 - 43 Abstract: This article proposes an analysis procedure of structural mechanics' problem as integral formulation. The methodology is novel which can be suitably applied for finding the solution of engineering problems with required accuracy either it is linear or nonlinear range (plastic range) of the material behaviour. This methodology, which was proposed as a stress-based analysis procedure, exploits the unfolded part of the structural analysis problems which were not so easy to solve such as geometric and material nonlinearity together with simple integration technique (Gaur and Srivastav, 2021). In fracture mechanics, it has already unfolded the misery of physically exploiting the plastic behaviour of structures before the start of the crack for elastic materials (Gaur et al., 2021). The formulation is an integral formulation rather than a differential formulation in which whole stress-strain behaviour is utilised in the analysis procedure by using a neural network as a regression tool. In this article, the one-dimensional problem of uniaxial bar, beam bending problem and plane strain axis-symmetric problem of a cylinder subjected to internal pressure is solved. The results are compared with the existing differential formulation or linear theory. Inderscience Publishers - linking academia, business and industry through research

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Title: Solution of structural mechanic's problems by machine learning

Authors: Himanshu Gaur; Basim Khidhir; Ram Kishore Manchiryal

Addresses: Institute of Structural Mechanics, Bauhaus-Universität Weimar, Marienstrasse 15, D-99423 Weimar, Germany; Middle East College, Knowledge Oasis Muscat, P.B. No. 79, Al Rusayl, Muscat, 124, Sultanate of Oman ' Middle East College, Knowledge Oasis Muscat, P.B. No. 79, Al Rusayl, Muscat, 124, Sultanate of Oman ' Middle East College, Knowledge Oasis Muscat, P.B. No. 79, Al Rusayl, Muscat, 124, Sultanate of Oman

Abstract: This article proposes an analysis procedure of structural mechanics' problem as integral formulation. The methodology is novel which can be suitably applied for finding the solution of engineering problems with required accuracy either it is linear or nonlinear range (plastic range) of the material behaviour. This methodology, which was proposed as a stress-based analysis procedure, exploits the unfolded part of the structural analysis problems which were not so easy to solve such as geometric and material nonlinearity together with simple integration technique (Gaur and Srivastav, 2021). In fracture mechanics, it has already unfolded the misery of physically exploiting the plastic behaviour of structures before the start of the crack for elastic materials (Gaur et al., 2021). The formulation is an integral formulation rather than a differential formulation in which whole stress-strain behaviour is utilised in the analysis procedure by using a neural network as a regression tool. In this article, the one-dimensional problem of uniaxial bar, beam bending problem and plane strain axis-symmetric problem of a cylinder subjected to internal pressure is solved. The results are compared with the existing differential formulation or linear theory.

Keywords: computational methods; continuum mechanics; machine learning; plastic analysis; elastic materials.

DOI: 10.1504/IJHM.2022.122459

International Journal of Hydromechatronics, 2022 Vol.5 No.1, pp.22 - 43

Received: 17 Sep 2021
Accepted: 04 Nov 2021
Published online: 25 Apr 2022 *

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Title: Solution of structural mechanic's problems by machine learning

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