Finite Element In-Depth Verification: Base Displacements of a Spherical Dome Loaded by Edge Forces and Moments
Nowadays, engineers possess a wealth of numerical packages in order to design civil engineering structures. The finite element method offers a variety of sophisticated element types, nonlinear materials, and solution algorithms, which enable engineers to confront complicated design problems. However...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Modelling |
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| Online Access: | https://www.mdpi.com/2673-3951/5/1/3 |
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| author | Vasiliki G. Terzi Triantafyllos K. Makarios |
| author_facet | Vasiliki G. Terzi Triantafyllos K. Makarios |
| author_sort | Vasiliki G. Terzi |
| collection | DOAJ |
| description | Nowadays, engineers possess a wealth of numerical packages in order to design civil engineering structures. The finite element method offers a variety of sophisticated element types, nonlinear materials, and solution algorithms, which enable engineers to confront complicated design problems. However, one of the difficult tasks is the verification of the produced numerical results. The present paper deals with the in-depth verification of a basic problem, referring to the axisymmetric loading by edge forces/moments of a spherical dome, truncated at various roll-down angles, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="sans-serif">φ</mi><mi mathvariant="normal">o</mi></msub></mrow></semantics></math></inline-formula>. Two formulations of analytical solutions are derived by the bibliography; their results are compared with those produced by the implementation of the finite element method. Modelling details, such as the finite element type, orientation of joints, application of loading, boundary conditions, and results’ interpretation, are presented thoroughly. Four different ratios of the radius of curvature, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">r</mi></mrow></semantics></math></inline-formula> and shell’s thickness, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">t</mi></mrow></semantics></math></inline-formula> are examined in order to investigate the compatibility between the implementation of the finite element method to the “first-order” shell theory. The discussion refers to the differences not only between the numerical and analytical results, but also between the two analytical approaches. Furthermore, it emphasizes the necessity of contacting even linear elastic preliminary verification numerical tests as a basis for the construction of more elaborated and sophisticated models. |
| first_indexed | 2024-04-24T17:59:37Z |
| format | Article |
| id | doaj.art-a0c8be1a57234db88cf697fc418204cf |
| institution | Directory Open Access Journal |
| issn | 2673-3951 |
| language | English |
| last_indexed | 2024-04-24T17:59:37Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Modelling |
| spelling | doaj.art-a0c8be1a57234db88cf697fc418204cf2024-03-27T13:56:29ZengMDPI AGModelling2673-39512023-12-0151375410.3390/modelling5010003Finite Element In-Depth Verification: Base Displacements of a Spherical Dome Loaded by Edge Forces and MomentsVasiliki G. Terzi0Triantafyllos K. Makarios1Institute of Structural Analysis and Dynamics of Structures, School of Civil Engineering, Aristotle University of Thessaloniki, 56124 Thessaloniki, GreeceInstitute of Structural Analysis and Dynamics of Structures, School of Civil Engineering, Aristotle University of Thessaloniki, 56124 Thessaloniki, GreeceNowadays, engineers possess a wealth of numerical packages in order to design civil engineering structures. The finite element method offers a variety of sophisticated element types, nonlinear materials, and solution algorithms, which enable engineers to confront complicated design problems. However, one of the difficult tasks is the verification of the produced numerical results. The present paper deals with the in-depth verification of a basic problem, referring to the axisymmetric loading by edge forces/moments of a spherical dome, truncated at various roll-down angles, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="sans-serif">φ</mi><mi mathvariant="normal">o</mi></msub></mrow></semantics></math></inline-formula>. Two formulations of analytical solutions are derived by the bibliography; their results are compared with those produced by the implementation of the finite element method. Modelling details, such as the finite element type, orientation of joints, application of loading, boundary conditions, and results’ interpretation, are presented thoroughly. Four different ratios of the radius of curvature, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">r</mi></mrow></semantics></math></inline-formula> and shell’s thickness, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">t</mi></mrow></semantics></math></inline-formula> are examined in order to investigate the compatibility between the implementation of the finite element method to the “first-order” shell theory. The discussion refers to the differences not only between the numerical and analytical results, but also between the two analytical approaches. Furthermore, it emphasizes the necessity of contacting even linear elastic preliminary verification numerical tests as a basis for the construction of more elaborated and sophisticated models.https://www.mdpi.com/2673-3951/5/1/3finite element methodthin shellspherical domeverificationmodelling assumptions |
| spellingShingle | Vasiliki G. Terzi Triantafyllos K. Makarios Finite Element In-Depth Verification: Base Displacements of a Spherical Dome Loaded by Edge Forces and Moments Modelling finite element method thin shell spherical dome verification modelling assumptions |
| title | Finite Element In-Depth Verification: Base Displacements of a Spherical Dome Loaded by Edge Forces and Moments |
| title_full | Finite Element In-Depth Verification: Base Displacements of a Spherical Dome Loaded by Edge Forces and Moments |
| title_fullStr | Finite Element In-Depth Verification: Base Displacements of a Spherical Dome Loaded by Edge Forces and Moments |
| title_full_unstemmed | Finite Element In-Depth Verification: Base Displacements of a Spherical Dome Loaded by Edge Forces and Moments |
| title_short | Finite Element In-Depth Verification: Base Displacements of a Spherical Dome Loaded by Edge Forces and Moments |
| title_sort | finite element in depth verification base displacements of a spherical dome loaded by edge forces and moments |
| topic | finite element method thin shell spherical dome verification modelling assumptions |
| url | https://www.mdpi.com/2673-3951/5/1/3 |
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