Sensitivity analysis and design optimization of 3T rotating thermoelastic structures using IGBEM

Mohamed Abdelsabour Fahmy; Mohammed O. Alsulami; Ahmed E. Abouelregal; Mohamed Abdelsabour Fahmy; Mohammed O. Alsulami; Ahmed E. Abouelregal

doi:10.3934/math.20221090

AIMS Mathematics

2022, Volume 7, Issue 11: 19902-19921. doi: 10.3934/math.20221090

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Sensitivity analysis and design optimization of 3T rotating thermoelastic structures using IGBEM

1.
Adham University College, Umm Al-Qura University, Adham 28653, Makkah, Saudi Arabia
2.
Faculty of Computers and Informatics, Suez Canal University, New Campus, 41522 Ismailia, Egypt
3.
Department of Mathematical Sciences, Faculty of Applied Sciences Umm Al-Qura University, Makkah 24381, Saudi Arabia
4.
Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayyat 72388, Saudi Arabia
5.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received: 20 June 2022 Revised: 08 August 2022 Accepted: 16 August 2022 Published: 08 September 2022
MSC : 35Qxx, 65Zxx

In this study, the isogeometric boundary element method (IGBEM) based on non-uniform rational basis spline (NURBS) is used to perform shape design sensitivity and optimization of rotating three-temperature (3T) thermoelastic structures. During the optimization process, the shape design sensitivity within the IGBEM formulation was derived to include precise geometries and greater continuities. It was found through the application of the IGBEM that the shape design velocity has a significant effect on accuracy of the obtained shape design sensitivity. As a result, the developed shape design sensitivity analysis (SDSA) technique based on the considered IGBEM formulation outperforms the computational solution based on the traditional SDSA method. The isogeometric shape sensitivity and optimal design for a complicated three-temperature thermoelastic problem in rotating structures are investigated. The impact of rotation on the thermal stress sensitivity, optimal three-temperature, optimal displacement and optimal three temperature thermal stress distributions are established. It is shown that the SDSA derived using IGBEM is efficient and applicable for most three-temperature thermoelastic optimization problems.
- sensitivity,
- optimization,
- three-temperature,
- rotation,
- thermoelastic structures,
- isogeometric boundary element method
Citation: Mohamed Abdelsabour Fahmy, Mohammed O. Alsulami, Ahmed E. Abouelregal. Sensitivity analysis and design optimization of 3T rotating thermoelastic structures using IGBEM[J]. AIMS Mathematics, 2022, 7(11): 19902-19921. doi: 10.3934/math.20221090

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Abstract

In this study, the isogeometric boundary element method (IGBEM) based on non-uniform rational basis spline (NURBS) is used to perform shape design sensitivity and optimization of rotating three-temperature (3T) thermoelastic structures. During the optimization process, the shape design sensitivity within the IGBEM formulation was derived to include precise geometries and greater continuities. It was found through the application of the IGBEM that the shape design velocity has a significant effect on accuracy of the obtained shape design sensitivity. As a result, the developed shape design sensitivity analysis (SDSA) technique based on the considered IGBEM formulation outperforms the computational solution based on the traditional SDSA method. The isogeometric shape sensitivity and optimal design for a complicated three-temperature thermoelastic problem in rotating structures are investigated. The impact of rotation on the thermal stress sensitivity, optimal three-temperature, optimal displacement and optimal three temperature thermal stress distributions are established. It is shown that the SDSA derived using IGBEM is efficient and applicable for most three-temperature thermoelastic optimization problems.

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