Mathematical Modeling and Well-Posedness of Three-Dimensional Shell in Disorders of Human Vascular System
Aortic dissection is the most common aortic emergency requiring surgical intervention. Whether the elective endovascular repair of abdominal aortic aneurysm reduces long-term morbidity and mortality, as compared with traditional open repair, remains uncertain. The foundation of shell element based o...
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| Formato: | Capítulo de libro |
| Lenguaje: | inglés |
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IntechOpen
2020
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| Acceso en línea: | https://www.intechopen.com/chapters/70721 |
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| _version_ | 1879164694190620672 |
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| author | Jadaun, Vishakha Singh, Nitin Raja |
| author_browse | Jadaun, Vishakha Singh, Nitin Raja |
| author_facet | Jadaun, Vishakha Singh, Nitin Raja |
| author_sort | Jadaun, Vishakha |
| building | IntechOpen |
| collection | Acceso abierto |
| description | Aortic dissection is the most common aortic emergency requiring surgical intervention. Whether the elective endovascular repair of abdominal aortic aneurysm reduces long-term morbidity and mortality, as compared with traditional open repair, remains uncertain. The foundation of shell element based on the Reissner-Mindlin kinematics assumption is widely applicable, but this cannot model applications of shell surface stresses as needed in analysis of shell in human vascular system. The analysis is designed to assess progression of initial lesion in aortic dissection. Using general shell element analysis and tensor calculus, a higher order differential geometry-based model is proposed. Since the shell is thin, a variational formulation for initial lesion is proposed. The variational formulation for initial lesion is well posed. The weak convergence of the solution to initial lesion model is mathematically substantiated. Asymptotic analysis shows that initial lesion is membrane-dominated and bending-dominated when pure bending is inhibited and noninhibited, respectively. At least two observations are to be noted. First, the mathematical analysis of the initial lesion model is distinct from classical shell models. Second, the asymptotic analysis of the initial lesion model is based on degenerating three-dimensional continuum to bending strains in order to assess initial lesion behavior. |
| doi_str_mv | 10.5772/intechopen.89866 |
| first_indexed | 2026-10-15T21:38:24Z |
| format | Book Chapter |
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<dc:title>Mathematical Modeling and Well-Posedness of Three-Dimensional Shell in Disorders of Human Vascular System</dc:title>
<dc:creator>Vishakha Jadaun</dc:creator>
<dc:creator>Nitin Raja Singh</dc:creator>
<dc:subject>Physical Sciences, Engineering and Technology</dc:subject>
<dc:description>Aortic dissection is the most common aortic emergency requiring surgical intervention. Whether the elective endovascular repair of abdominal aortic aneurysm reduces long-term morbidity and mortality, as compared with traditional open repair, remains uncertain. The foundation of shell element based on the Reissner-Mindlin kinematics assumption is widely applicable, but this cannot model applications of shell surface stresses as needed in analysis of shell in human vascular system. The analysis is designed to assess progression of initial lesion in aortic dissection. Using general shell element analysis and tensor calculus, a higher order differential geometry-based model is proposed. Since the shell is thin, a variational formulation for initial lesion is proposed. The variational formulation for initial lesion is well posed. The weak convergence of the solution to initial lesion model is mathematically substantiated. Asymptotic analysis shows that initial lesion is membrane-dominated and bending-dominated when pure bending is inhibited and noninhibited, respectively. At least two observations are to be noted. First, the mathematical analysis of the initial lesion model is distinct from classical shell models. Second, the asymptotic analysis of the initial lesion model is based on degenerating three-dimensional continuum to bending strains in order to assess initial lesion behavior.</dc:description>
<dc:publisher>IntechOpen</dc:publisher>
<dc:date>2020-01-03</dc:date>
<dc:type>Chapter, Part Of Book</dc:type>
<dc:identifier>https://www.intechopen.com/chapters/70721</dc:identifier>
<dc:identifier>doi:10.5772/intechopen.89866</dc:identifier>
<dc:language>en</dc:language>
<dc:relation>ISBN:978-1-78985-471-8</dc:relation>
<dc:rights>https://creativecommons.org/licenses/by/3.0/</dc:rights>
<dc:source>https://www.intechopen.com/books/7662 ; Nonlinear Systems -Theoretical Aspects and Recent Applications</dc:source>
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| id | intech-70721 |
| institution | IntechOpen |
| isbn | 978-1-78985-471-8 |
| language | English |
| last_indexed | 2026-10-15T21:38:24Z |
| publishDate | 2020 |
| publishDateRange | 2020 |
| publishDateSort | 2020 |
| publisher | IntechOpen |
| publisherStr | IntechOpen |
| record_format | oai_dc |
| spelling | intech-707212020-01-03 Mathematical Modeling and Well-Posedness of Three-Dimensional Shell in Disorders of Human Vascular System Vishakha Jadaun Nitin Raja Singh Physical Sciences, Engineering and Technology Aortic dissection is the most common aortic emergency requiring surgical intervention. Whether the elective endovascular repair of abdominal aortic aneurysm reduces long-term morbidity and mortality, as compared with traditional open repair, remains uncertain. The foundation of shell element based on the Reissner-Mindlin kinematics assumption is widely applicable, but this cannot model applications of shell surface stresses as needed in analysis of shell in human vascular system. The analysis is designed to assess progression of initial lesion in aortic dissection. Using general shell element analysis and tensor calculus, a higher order differential geometry-based model is proposed. Since the shell is thin, a variational formulation for initial lesion is proposed. The variational formulation for initial lesion is well posed. The weak convergence of the solution to initial lesion model is mathematically substantiated. Asymptotic analysis shows that initial lesion is membrane-dominated and bending-dominated when pure bending is inhibited and noninhibited, respectively. At least two observations are to be noted. First, the mathematical analysis of the initial lesion model is distinct from classical shell models. Second, the asymptotic analysis of the initial lesion model is based on degenerating three-dimensional continuum to bending strains in order to assess initial lesion behavior. IntechOpen 2020-01-03 Chapter, Part Of Book https://www.intechopen.com/chapters/70721 doi:10.5772/intechopen.89866 en ISBN:978-1-78985-471-8 https://creativecommons.org/licenses/by/3.0/ https://www.intechopen.com/books/7662 ; Nonlinear Systems -Theoretical Aspects and Recent Applications |
| spellingShingle | Physical Sciences, Engineering and Technology Jadaun, Vishakha Singh, Nitin Raja Mathematical Modeling and Well-Posedness of Three-Dimensional Shell in Disorders of Human Vascular System |
| title | Mathematical Modeling and Well-Posedness of Three-Dimensional Shell in Disorders of Human Vascular System |
| title_full | Mathematical Modeling and Well-Posedness of Three-Dimensional Shell in Disorders of Human Vascular System |
| title_fullStr | Mathematical Modeling and Well-Posedness of Three-Dimensional Shell in Disorders of Human Vascular System |
| title_full_unstemmed | Mathematical Modeling and Well-Posedness of Three-Dimensional Shell in Disorders of Human Vascular System |
| title_short | Mathematical Modeling and Well-Posedness of Three-Dimensional Shell in Disorders of Human Vascular System |
| title_sort | mathematical modeling and well posedness of three dimensional shell in disorders of human vascular system |
| topic | Physical Sciences, Engineering and Technology |
| url | https://www.intechopen.com/chapters/70721 |
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