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Volume 2, Issue 2
An Intrinsic Formulation of the Von Kármán Equations

Philippe G. Ciarlet & Cristinel Mardare

DOI: 10.4208/cmaa.2023-0002

Commun. Math. Anal. Appl., 2 (2023), pp. 221-244.

Published online: 2023-06

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  • Abstract

To begin with, we identify the intrinsic equations of a von Kármán nonlinearly elastic plate, which allow to directly compute the stresses inside the plate without having to first compute the displacement field, by contrast with the classical displacement approach. Then we establish that these intrinsic equations possess weak solutions, which are the bending moments and stress resultants of the middle surface of the plate.

  • Keywords

Nonlinear elasticity, nonlinearly elastic plates, von Kármán equations, intrinsic elasticity, stress tensor field.

  • AMS Subject Headings

74K20, 74B20, 35J66, 53A04

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMAA-2-221, author = {Ciarlet , Philippe G. and Mardare , Cristinel}, title = {An Intrinsic Formulation of the Von Kármán Equations}, journal = {Communications in Mathematical Analysis and Applications}, year = {2023}, volume = {2}, number = {2}, pages = {221--244}, abstract = {

To begin with, we identify the intrinsic equations of a von Kármán nonlinearly elastic plate, which allow to directly compute the stresses inside the plate without having to first compute the displacement field, by contrast with the classical displacement approach. Then we establish that these intrinsic equations possess weak solutions, which are the bending moments and stress resultants of the middle surface of the plate.

}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2023-0002}, url = {http://global-sci.org/intro/article_detail/cmaa/21785.html} }
TY - JOUR T1 - An Intrinsic Formulation of the Von Kármán Equations AU - Ciarlet , Philippe G. AU - Mardare , Cristinel JO - Communications in Mathematical Analysis and Applications VL - 2 SP - 221 EP - 244 PY - 2023 DA - 2023/06 SN - 2 DO - http://doi.org/10.4208/cmaa.2023-0002 UR - https://global-sci.org/intro/article_detail/cmaa/21785.html KW - Nonlinear elasticity, nonlinearly elastic plates, von Kármán equations, intrinsic elasticity, stress tensor field. AB -

To begin with, we identify the intrinsic equations of a von Kármán nonlinearly elastic plate, which allow to directly compute the stresses inside the plate without having to first compute the displacement field, by contrast with the classical displacement approach. Then we establish that these intrinsic equations possess weak solutions, which are the bending moments and stress resultants of the middle surface of the plate.

Philippe G. Ciarlet & Cristinel Mardare. (2023). An Intrinsic Formulation of the Von Kármán Equations. Communications in Mathematical Analysis and Applications. 2 (2). 221-244. doi:10.4208/cmaa.2023-0002
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