An Intuitive Derivation of Beam Models of Arbitrary Order
This article presents a new beam model that employs a recursive derivation procedure that enables the user to set the order of the governing differential equations as an input parameter, without the need for ad hoc assumptions or methodologies. This article employs a novel system of kinematic variab...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Applied Mechanics |
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| Online Access: | https://www.mdpi.com/2673-3161/4/1/8 |
| _version_ | 1797613822800822272 |
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| author | Hart Honickman |
| author_facet | Hart Honickman |
| author_sort | Hart Honickman |
| collection | DOAJ |
| description | This article presents a new beam model that employs a recursive derivation procedure that enables the user to set the order of the governing differential equations as an input parameter, without the need for ad hoc assumptions or methodologies. This article employs a novel system of kinematic variables, section constants, and section functions that facilitate the development of higher-order beam models that retain a clear philosophical link to classical beam models such as Euler–Bernoulli beam theory and Timoshenko beam theory. The present beam model is a type of equivalent single layer beam model, wherein section constants are used to model the global stiffness characteristics of the beam, and section functions are used to recover sectional fields of displacements, strains, and stresses. The present beam model is solved for several example beams, and the results are compared to the results of finite element analyses. It is shown that the present beam model can accurately predict the deformed shapes and stress fields of each of the example beams. This article also reveals an interesting peculiarity of the elastic potential energy that pertains to any unidimensional beam model that is governed by differential equations that are of finite order. |
| first_indexed | 2024-03-11T07:00:05Z |
| format | Article |
| id | doaj.art-f8ab4c5e977e4234b3f5b32e97545c3d |
| institution | Directory Open Access Journal |
| issn | 2673-3161 |
| language | English |
| last_indexed | 2024-03-11T07:00:05Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Mechanics |
| spelling | doaj.art-f8ab4c5e977e4234b3f5b32e97545c3d2023-11-17T09:20:15ZengMDPI AGApplied Mechanics2673-31612023-01-014110914010.3390/applmech4010008An Intuitive Derivation of Beam Models of Arbitrary OrderHart Honickman0Shinc Inc., 505 Glenlake Avenue, Toronto, ON M6P 1G9, CanadaThis article presents a new beam model that employs a recursive derivation procedure that enables the user to set the order of the governing differential equations as an input parameter, without the need for ad hoc assumptions or methodologies. This article employs a novel system of kinematic variables, section constants, and section functions that facilitate the development of higher-order beam models that retain a clear philosophical link to classical beam models such as Euler–Bernoulli beam theory and Timoshenko beam theory. The present beam model is a type of equivalent single layer beam model, wherein section constants are used to model the global stiffness characteristics of the beam, and section functions are used to recover sectional fields of displacements, strains, and stresses. The present beam model is solved for several example beams, and the results are compared to the results of finite element analyses. It is shown that the present beam model can accurately predict the deformed shapes and stress fields of each of the example beams. This article also reveals an interesting peculiarity of the elastic potential energy that pertains to any unidimensional beam model that is governed by differential equations that are of finite order.https://www.mdpi.com/2673-3161/4/1/8beamhigher-orderseriesshearwarpingshear deformation theory |
| spellingShingle | Hart Honickman An Intuitive Derivation of Beam Models of Arbitrary Order Applied Mechanics beam higher-order series shear warping shear deformation theory |
| title | An Intuitive Derivation of Beam Models of Arbitrary Order |
| title_full | An Intuitive Derivation of Beam Models of Arbitrary Order |
| title_fullStr | An Intuitive Derivation of Beam Models of Arbitrary Order |
| title_full_unstemmed | An Intuitive Derivation of Beam Models of Arbitrary Order |
| title_short | An Intuitive Derivation of Beam Models of Arbitrary Order |
| title_sort | intuitive derivation of beam models of arbitrary order |
| topic | beam higher-order series shear warping shear deformation theory |
| url | https://www.mdpi.com/2673-3161/4/1/8 |
| work_keys_str_mv | AT harthonickman anintuitivederivationofbeammodelsofarbitraryorder AT harthonickman intuitivederivationofbeammodelsofarbitraryorder |