| EPSRC Reference: |
EP/H028587/1 |
| Title: |
RIGOROUS DERIVATION OF MODERATE AND HIGH-CONTRAST NONLINEAR COMPOSITE PLATE THEORIES |
| Principal Investigator: |
Cherdantsev, Dr M |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Sch of Mathematics |
| Organisation: |
Cardiff University |
| Scheme: |
Postdoc Research Fellowship |
| Starts: |
01 November 2010 |
Ends: |
31 October 2013 |
Value (£): |
207,141
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| EPSRC Research Topic Classifications: |
| Continuum Mechanics |
Non-linear Systems Mathematics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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| Panel History: |
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Summary on Grant Application Form |
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There are several results obtained quite recently that are concerned with the derivation of 2D models (i.e. plates, shells) from the equations of the full 3D elasticity. The related treatment usually starts by introducing a small parameter which represents the plate thickness, and seeks a procedure for passing to the limit as the parameter tends to zero. In the setting of linearised elasticity the related 2D limit theory, which is sometimes referred to as the ``Kirchhoff-Love theory'', has been extensively studied starting since 1970's. However, the rigorous nonlinear, frame-indifferent, plate theories have only been addressed recently in the membrane-limit context and also in the flexural and von Karman regimes.The above rigorous approaches to nonlinear plate theories can be termed classical in the sense that they work under the assumption of uniform coercivity of the underlying stored-energy function. It would be practically important, however, to try to understand what additional effects emerge when the material of which a thin body is made allows for significantly larger strains in some parts of it than in others. Another feature that limits the applicability of these recent results is that they only apply to homogeneous plates, while the vast majority of the materials used nowadays in industry are ``composites'', whose mathematical 3D theory has been fairly well developed, at least in the classical periodic context. The present project will address these two shortcomings of the existing theories. In the wider mathematical context this will serve three major objectives: 1) To make the mathematical theory of plates more complete by providing a rigorous derivation of a wider class of models, including some that are more realistic; 2) To bridge the gap between the homogenisation theory and the existing nonlinear plate theories; 3) To make an advance on ``non-classical'' effects, such as the in-plane non-locality in the overall response, for realistic plates. In the applied context, it will generate new developments in the design of composites, and a more recent class of metamaterials , which are difficult to obtain experimentally by trial and error.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.cf.ac.uk |