On a uniformly-valid asymptotic plate theory
| Autor: | David J. Steigmann, Fan-Fan Wang, Hui-Hui Dai |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Surface (mathematics)
Physics::Instrumentation and Detectors Applied Mathematics Mechanical Engineering Mathematical analysis 02 engineering and technology Weak formulation 021001 nanoscience & nanotechnology Finite element method Physics::Fluid Dynamics 020303 mechanical engineering & transports 0203 mechanical engineering Mechanics of Materials Plate theory A priori and a posteriori 0210 nano-technology Series expansion Nonlinear elasticity Mathematics |
| Zdroj: | International Journal of Non-Linear Mechanics. 112:117-125 |
| ISSN: | 0020-7462 |
| DOI: | 10.1016/j.ijnonlinmec.2019.02.011 |
| Popis: | A uniformly-valid plate theory, independent of the magnitudes of applied loads, is derived based on the two-dimensional plate theory obtained from series expansions about the bottom surface of a plate. For five different magnitudes of surface loads, it is shown by using asymptotic expansions that this unified plate theory recovers five well-known plate models in the literature to leading-order. This demonstrates its uniform validity. More generally, it provides a uniformly-valid plate model provided that two asymptotic conditions are satisfied, which can be checked as a posteriori. The weak formulation of the uniformly-valid plate equations is furnished, which can be used for finite element implementation. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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