Plate theories: A‐priori fulfillment of the local conditions by the consistent‐approximation approach
Abstract: Classical plates theories, like Kirchhoff's plate theory [1], are based on kinematical a‐priori assumptions. Avoiding these assumptions, we derive from the three‐dimensional theory of linear elasticity by means of Taylor‐series expansions the quasi two‐dimensional problem. This problem consists of infinitely many partial‐differential equations (PDEs) written in infinitely many displacement coefficients. With the consistent approximation approach we arrive at solvable hierarchical plate theories. By using the modular structure of the displacements coefficients (modularity), we obtain from these generic‐plate theories the complete‐plate theories, whose results fulfill the strong form of the local equilibrium conditions and the Neumann boundary conditions on the upper and lower face of the plate (local conditions) a‐priori. Furthermore, we show that every variable of the complete‐plate theories can be calculated.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Plate theories: A‐priori fulfillment of the local conditions by the consistent‐approximation approach ; volume:21 ; number:1 ; year:2021 ; extent:2
Proceedings in applied mathematics and mechanics ; 21, Heft 1 (2021) (gesamt 2)
- Creator
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Meyer-Coors, Michael
Kienzler, Reinhold
Schneider, Patrick
- DOI
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10.1002/pamm.202100136
- URN
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urn:nbn:de:101:1-2021121514221257801405
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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15.08.2025, 7:33 AM CEST
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Meyer-Coors, Michael
- Kienzler, Reinhold
- Schneider, Patrick
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