Abstract
We first show how the classical Marguerre–von Kármán equations modeling the deformation of a nonlinearly elastic shallow shell can be recast as equations whose sole unknowns are the bending moments and stress resultants inside the middle surface of the shell. Thus, these equations allow to compute the stresses inside the shell without having to compute first the displacement field. We then show that the boundary value problem formed by these new equations is well posed by establishing an existence theorem. © The Author(s) 2023.
| Original language | English |
|---|---|
| Pages (from-to) | 386-400 |
| Journal | Mathematics and Mechanics of Solids |
| Volume | 29 |
| Issue number | 2 |
| Online published | 5 Aug 2023 |
| DOIs | |
| Publication status | Published - Feb 2024 |
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The work described in this paper was substantially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China [Project No. 9042860, CityU 11303319].
Research Keywords
- existence theory
- intrinsic equations
- Marguerre–von Kármán equations
- nonlinear elasticity
- shallow shells
RGC Funding Information
- RGC-funded
Fingerprint
Dive into the research topics of 'Intrinsic Marguerre–von Kármán equations'. Together they form a unique fingerprint.Projects
- 1 Finished
-
GRF: Intrinsic Theory of Nonlinearly Elastic Plates and Shallow Shells
MARDARE, C. (Principal Investigator / Project Coordinator) & CIARLET, P. G. (Co-Investigator)
1/01/20 → 12/08/24
Project: Research
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