Influence of Heat Transfer on Stress Components in Metallic Plates Weakened by Multi-Curved Holes
This manuscript addresses an application study by employing a mathematical model of a thermoelastic plate weakened by multi-curved holes under the effect of stress forces in the presence of heat conduction. When the initial heat flow is directed to the plate system, complex variable procedures are u...
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MDPI AG
2025-05-01
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| author | Faizah M. Alharbi Nafeesa G. Alhendi |
| author_facet | Faizah M. Alharbi Nafeesa G. Alhendi |
| author_sort | Faizah M. Alharbi |
| collection | DOAJ |
| description | This manuscript addresses an application study by employing a mathematical model of a thermoelastic plate weakened by multi-curved holes under the effect of stress forces in the presence of heat conduction. When the initial heat flow is directed to the plate system, complex variable procedures are used to compute the basic Goursat functions, taking into account the time-dependent variables through conformal mapping, which transfers the domain to the exterior of a unit circle. The problem reduces to a general form of a contact problem in two dimensions, which is called an integrodifferential equation of the second type with the Cauchy kernel. Additionally, different hole shapes are generated using Maple 2023. Computational simulations are performed to determine the normal and shear stress components in the presence and absence of heat effects at various times. Furthermore, numerical calculations of Goursat functions are carried out and graphically displayed for some specific materials. This investigation provides valuable information about industries, such as those regarding ceramic tile, glass, rubber, paint, ceramic pigment, and metal alloys. |
| format | Article |
| id | doaj-art-96bfe26bd9644540ae699c4d0bdd6337 |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-96bfe26bd9644540ae699c4d0bdd63372025-08-20T01:56:17ZengMDPI AGAxioms2075-16802025-05-0114536910.3390/axioms14050369Influence of Heat Transfer on Stress Components in Metallic Plates Weakened by Multi-Curved HolesFaizah M. Alharbi0Nafeesa G. Alhendi1Mathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah 24227, Saudi ArabiaMathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah 24227, Saudi ArabiaThis manuscript addresses an application study by employing a mathematical model of a thermoelastic plate weakened by multi-curved holes under the effect of stress forces in the presence of heat conduction. When the initial heat flow is directed to the plate system, complex variable procedures are used to compute the basic Goursat functions, taking into account the time-dependent variables through conformal mapping, which transfers the domain to the exterior of a unit circle. The problem reduces to a general form of a contact problem in two dimensions, which is called an integrodifferential equation of the second type with the Cauchy kernel. Additionally, different hole shapes are generated using Maple 2023. Computational simulations are performed to determine the normal and shear stress components in the presence and absence of heat effects at various times. Furthermore, numerical calculations of Goursat functions are carried out and graphically displayed for some specific materials. This investigation provides valuable information about industries, such as those regarding ceramic tile, glass, rubber, paint, ceramic pigment, and metal alloys.https://www.mdpi.com/2075-1680/14/5/369complex variableGoursat functionsconformal mappingstress componentsflowing heat |
| spellingShingle | Faizah M. Alharbi Nafeesa G. Alhendi Influence of Heat Transfer on Stress Components in Metallic Plates Weakened by Multi-Curved Holes Axioms complex variable Goursat functions conformal mapping stress components flowing heat |
| title | Influence of Heat Transfer on Stress Components in Metallic Plates Weakened by Multi-Curved Holes |
| title_full | Influence of Heat Transfer on Stress Components in Metallic Plates Weakened by Multi-Curved Holes |
| title_fullStr | Influence of Heat Transfer on Stress Components in Metallic Plates Weakened by Multi-Curved Holes |
| title_full_unstemmed | Influence of Heat Transfer on Stress Components in Metallic Plates Weakened by Multi-Curved Holes |
| title_short | Influence of Heat Transfer on Stress Components in Metallic Plates Weakened by Multi-Curved Holes |
| title_sort | influence of heat transfer on stress components in metallic plates weakened by multi curved holes |
| topic | complex variable Goursat functions conformal mapping stress components flowing heat |
| url | https://www.mdpi.com/2075-1680/14/5/369 |
| work_keys_str_mv | AT faizahmalharbi influenceofheattransferonstresscomponentsinmetallicplatesweakenedbymulticurvedholes AT nafeesagalhendi influenceofheattransferonstresscomponentsinmetallicplatesweakenedbymulticurvedholes |