Details
| Original language | English |
|---|---|
| Title of host publication | Current Trends and Open Problems in Computational Mechanics |
| Publisher | Springer International Publishing AG |
| Pages | 463-474 |
| Number of pages | 12 |
| ISBN (electronic) | 9783030873127 |
| ISBN (print) | 9783030873110 |
| Publication status | Published - 13 Mar 2022 |
Abstract
This work deals with infinitesimal deformations of an isotropic elastic shell in a differential geometry framework. It provides an introduction to differential geometry of embedded surfaces in the Euclidean three-dimensional space and serves as a tangible and practical “recipe” for those, particularly students, who are interested in invoking the old art of working with curvilinear coordinates. It seems that the fundamental concepts in this field have remained obscure and vague for many students and they do not dare employ this elegant tool. With regard to this, a shell structure composed of only a single element is taken into consideration represented geometrically exact in a curvilinear setting. The stress/strain are computed at the Gauss points using the framework of differential geometry and the results are validated against ones predicted by ANSYS as a commercial software. One should notice that, nowadays, this approach is not implemented in commercial software such as ANSYS due to its complications. Rather, such software prefers to use the so-called solid degenerated shell elements. Using such approach, one can circumvent dealing directly with objects such as Christoffel symbols which naturally emerge as soon as the derivative are taken in a curvilinear coordinate system.
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Current Trends and Open Problems in Computational Mechanics. Springer International Publishing AG, 2022. p. 463-474.
Research output: Chapter in book/report/conference proceeding › Contribution to book/anthology › Research › peer review
}
TY - CHAP
T1 - Differential Geometry of Surfaces with Application to Shell Structures
AU - Sahraee, Shahab
AU - Soleimani, Meisam
PY - 2022/3/13
Y1 - 2022/3/13
N2 - This work deals with infinitesimal deformations of an isotropic elastic shell in a differential geometry framework. It provides an introduction to differential geometry of embedded surfaces in the Euclidean three-dimensional space and serves as a tangible and practical “recipe” for those, particularly students, who are interested in invoking the old art of working with curvilinear coordinates. It seems that the fundamental concepts in this field have remained obscure and vague for many students and they do not dare employ this elegant tool. With regard to this, a shell structure composed of only a single element is taken into consideration represented geometrically exact in a curvilinear setting. The stress/strain are computed at the Gauss points using the framework of differential geometry and the results are validated against ones predicted by ANSYS as a commercial software. One should notice that, nowadays, this approach is not implemented in commercial software such as ANSYS due to its complications. Rather, such software prefers to use the so-called solid degenerated shell elements. Using such approach, one can circumvent dealing directly with objects such as Christoffel symbols which naturally emerge as soon as the derivative are taken in a curvilinear coordinate system.
AB - This work deals with infinitesimal deformations of an isotropic elastic shell in a differential geometry framework. It provides an introduction to differential geometry of embedded surfaces in the Euclidean three-dimensional space and serves as a tangible and practical “recipe” for those, particularly students, who are interested in invoking the old art of working with curvilinear coordinates. It seems that the fundamental concepts in this field have remained obscure and vague for many students and they do not dare employ this elegant tool. With regard to this, a shell structure composed of only a single element is taken into consideration represented geometrically exact in a curvilinear setting. The stress/strain are computed at the Gauss points using the framework of differential geometry and the results are validated against ones predicted by ANSYS as a commercial software. One should notice that, nowadays, this approach is not implemented in commercial software such as ANSYS due to its complications. Rather, such software prefers to use the so-called solid degenerated shell elements. Using such approach, one can circumvent dealing directly with objects such as Christoffel symbols which naturally emerge as soon as the derivative are taken in a curvilinear coordinate system.
UR - http://www.scopus.com/inward/record.url?scp=85153827217&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-87312-7_45
DO - 10.1007/978-3-030-87312-7_45
M3 - Contribution to book/anthology
AN - SCOPUS:85153827217
SN - 9783030873110
SP - 463
EP - 474
BT - Current Trends and Open Problems in Computational Mechanics
PB - Springer International Publishing AG
ER -