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Theoretical Formulation, Exact Solutions, and Computational Analysis of Snap-Through Buckling of Shallow Arches.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Theoretical Formulation, Exact Solutions, and Computational Analysis of Snap-Through Buckling of Shallow Arches./
作者:	Dunham, Samuel David.
面頁冊數:	1 online resource (177 pages)
附註:	Source: Masters Abstracts International, Volume: 84-03.
Contained By:	Masters Abstracts International84-03.
標題:	Civil engineering. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29260224click for full text (PQDT)
ISBN:	9798841746706

Theoretical Formulation, Exact Solutions, and Computational Analysis of Snap-Through Buckling of Shallow Arches.
Dunham, Samuel David.

Theoretical Formulation, Exact Solutions, and Computational Analysis of Snap-Through Buckling of Shallow Arches. - 1 online resource (177 pages)

Source: Masters Abstracts International, Volume: 84-03.

Thesis (M.S.)--Tennessee Technological University, 2022.

Includes bibliographical references

Structural and mechanical components that exhibit snap-through buckling are becoming increasingly utilized across a wide range of industry due to their energy absorption capabilities. Additionally, snap-through buckling is still considered a type of structural instability and could cause catastrophic damage if an arch were to buckle under load. Therefore, the need to understand its complex behavior is of the utmost importance. Snap-through buckling problems can undergo large deformations compared to the thickness of the arch and will exhibit geometrically non-linear behavior. Numerical solutions and experiments are often used to describe snap-buckling, but such analyses cannot provide insight on the underlying relationships among the many variables in the problem. Thus, there are three primary objectives of this thesis. First, to derive the governing equations for snap-through buckling of shallow arches. Second, to present two exact solutions and explore the physics of snap-through buckling. Third, to perform a computational analysis across different arch profiles and loading types that are common in engineering applications. These objectives, together, will well equip future researchers by providing a basis for numerical modeling and providing insight on the underlying physics of the problem.The governing equations for snap-through buckling of shallow arches are derived and then two special cases are then solved exactly. The first case is a sinusoidal shallow arch with a sinusoidal distributed loading. While this case is impractical, it can be reduced to a single non-dimensional differential equation. First, the so-called equilibrium behavior will be explored, which is all combinations of load and displacement in which the arch is in equilibrium. Then, the governing non-dimensional differential equation is solved numerically. A similar approach is taken for a case that considers geometric imperfections of the arch. Furthermore, these cases were chosen due to their readiness as a means of verification for the finite element modelling methodology.In a computational analysis, two additional arch profiles are chosen due to their use in applications and other types of loadings are considered. These additional profiles and load types provide eleven more cases, and their non-dimensional equilibrium and dynamic behavior is explored. The results showed that across each arch profile, the equilibrium behavior was different. However, within one arch profile each loading case's equilibrium behavior were similar in shape, but not magnitude, when the proposed non-dimensionalizing factors were used. This implies that the assumption for the original configuration and the loading are critical for understanding the behavior of a system. These cases are intended to serve as a basis to design problems, and to showcase the modeling technique.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798841746706Subjects--Topical Terms:

860360
Civil engineering.
Subjects--Index Terms:

BucklingIndex Terms--Genre/Form:

542853
Electronic books.

Theoretical Formulation, Exact Solutions, and Computational Analysis of Snap-Through Buckling of Shallow Arches.
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504 $a Includes bibliographical references
520 $a Structural and mechanical components that exhibit snap-through buckling are becoming increasingly utilized across a wide range of industry due to their energy absorption capabilities. Additionally, snap-through buckling is still considered a type of structural instability and could cause catastrophic damage if an arch were to buckle under load. Therefore, the need to understand its complex behavior is of the utmost importance. Snap-through buckling problems can undergo large deformations compared to the thickness of the arch and will exhibit geometrically non-linear behavior. Numerical solutions and experiments are often used to describe snap-buckling, but such analyses cannot provide insight on the underlying relationships among the many variables in the problem. Thus, there are three primary objectives of this thesis. First, to derive the governing equations for snap-through buckling of shallow arches. Second, to present two exact solutions and explore the physics of snap-through buckling. Third, to perform a computational analysis across different arch profiles and loading types that are common in engineering applications. These objectives, together, will well equip future researchers by providing a basis for numerical modeling and providing insight on the underlying physics of the problem.The governing equations for snap-through buckling of shallow arches are derived and then two special cases are then solved exactly. The first case is a sinusoidal shallow arch with a sinusoidal distributed loading. While this case is impractical, it can be reduced to a single non-dimensional differential equation. First, the so-called equilibrium behavior will be explored, which is all combinations of load and displacement in which the arch is in equilibrium. Then, the governing non-dimensional differential equation is solved numerically. A similar approach is taken for a case that considers geometric imperfections of the arch. Furthermore, these cases were chosen due to their readiness as a means of verification for the finite element modelling methodology.In a computational analysis, two additional arch profiles are chosen due to their use in applications and other types of loadings are considered. These additional profiles and load types provide eleven more cases, and their non-dimensional equilibrium and dynamic behavior is explored. The results showed that across each arch profile, the equilibrium behavior was different. However, within one arch profile each loading case's equilibrium behavior were similar in shape, but not magnitude, when the proposed non-dimensionalizing factors were used. This implies that the assumption for the original configuration and the loading are critical for understanding the behavior of a system. These cases are intended to serve as a basis to design problems, and to showcase the modeling technique.
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650 4 $a Engineering. $3 586835
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653 $a Buckling
653 $a Geometrical nonlinearity
653 $a Snap through
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