Meyer-Coors, Michael ; Kienzler, Reinhold ; Schneider, Patrick (2024)
Modularity of the displacement coefficients and complete plate theories in the framework of the consistent-approximation approach.
In: Continuum Mechanics and Thermodynamics, 2021, 33 (4)
doi: 10.26083/tuprints-00023441
Artikel, Zweitveröffentlichung, Verlagsversion
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Kurzbeschreibung (Abstract)
Starting from the three-dimensional theory of linear elasticity, we arrive at the exact plate problem by the use of Taylor series expansions. Applying the consistent-approximation approach to this problem leads to hierarchic generic plate theories. Mathematically, these plate theories are systems of partial-differential equations (PDEs), which contain the coefficients of the series expansions of the displacements (displacement coefficients) as variables. With the pseudo-reduction method, the PDE systems can be reduced to one main PDE, which is entirely written in the main variable, and several reduction PDEs, each written in the main variable and several non-main variables. So, after solving the main PDE, the reduction PDEs can be solved by insertion of the main variable. As a great disadvantage of the generic plate theories, there are fewer reduction PDEs than non-main variables so that not all of the latter can be determined independently. Within this paper, a modular structure of the displacement coefficients is found and proved. Based on it, we define so-called complete plate theories which enable us to determine all non-main variables independently. Also, a scheme to assemble Nth-order complete plate theories with equations from the generic plate theories is found. As it turns out, the governing PDEs from the complete plate theories fulfill the local boundary conditions and the local form of the equilibrium equations a priori. Furthermore, these results are compared with those of the classical theories and recently published papers on the consistent-approximation approach.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2024 |
| Autor(en): | Meyer-Coors, Michael ; Kienzler, Reinhold ; Schneider, Patrick |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | Modularity of the displacement coefficients and complete plate theories in the framework of the consistent-approximation approach |
| Sprache: | Englisch |
| Publikationsjahr: | 18 März 2024 |
| Ort: | Darmstadt |
| Publikationsdatum der Erstveröffentlichung: | Juli 2021 |
| Ort der Erstveröffentlichung: | Berlin ; Heidelberg |
| Verlag: | Springer |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Continuum Mechanics and Thermodynamics |
| Jahrgang/Volume einer Zeitschrift: | 33 |
| (Heft-)Nummer: | 4 |
| DOI: | 10.26083/tuprints-00023441 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/23441 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichung DeepGreen |
| Kurzbeschreibung (Abstract): | Starting from the three-dimensional theory of linear elasticity, we arrive at the exact plate problem by the use of Taylor series expansions. Applying the consistent-approximation approach to this problem leads to hierarchic generic plate theories. Mathematically, these plate theories are systems of partial-differential equations (PDEs), which contain the coefficients of the series expansions of the displacements (displacement coefficients) as variables. With the pseudo-reduction method, the PDE systems can be reduced to one main PDE, which is entirely written in the main variable, and several reduction PDEs, each written in the main variable and several non-main variables. So, after solving the main PDE, the reduction PDEs can be solved by insertion of the main variable. As a great disadvantage of the generic plate theories, there are fewer reduction PDEs than non-main variables so that not all of the latter can be determined independently. Within this paper, a modular structure of the displacement coefficients is found and proved. Based on it, we define so-called complete plate theories which enable us to determine all non-main variables independently. Also, a scheme to assemble Nth-order complete plate theories with equations from the generic plate theories is found. As it turns out, the governing PDEs from the complete plate theories fulfill the local boundary conditions and the local form of the equilibrium equations a priori. Furthermore, these results are compared with those of the classical theories and recently published papers on the consistent-approximation approach. |
| Freie Schlagworte: | Linear elasticity, Consistent-approximation approach, Pseudo-reduction method, Modularity of displacement coefficients, Complete plate theory, Local boundary conditions, Local form of the equilibrium equations |
| Status: | Verlagsversion |
| URN: | urn:nbn:de:tuda-tuprints-234417 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften und Maschinenbau |
| Fachbereich(e)/-gebiet(e): | 16 Fachbereich Maschinenbau 16 Fachbereich Maschinenbau > Institut für Leichtbau und Strukturmechanik (LSM) |
| Hinterlegungsdatum: | 18 Mär 2024 13:43 |
| Letzte Änderung: | 19 Mär 2024 07:27 |
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| Suche nach Titel in: | TUfind oder in Google |
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- Modularity of the displacement coefficients and complete plate theories in the framework of the consistent-approximation approach. (deposited 18 Mär 2024 13:43) [Gegenwärtig angezeigt]
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