Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A Review
A review of mathematical models for elastic plates with buckling and contact phenomena is provided. The state of the art in this domain is presented. Buckling effects are discussed on an example of a system of nonlinear partial differential equations, describing large deflections of the plate. Unila...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/4/566 |
| _version_ | 1797570819956670464 |
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| author | Aliki D. Muradova Georgios E. Stavroulakis |
| author_facet | Aliki D. Muradova Georgios E. Stavroulakis |
| author_sort | Aliki D. Muradova |
| collection | DOAJ |
| description | A review of mathematical models for elastic plates with buckling and contact phenomena is provided. The state of the art in this domain is presented. Buckling effects are discussed on an example of a system of nonlinear partial differential equations, describing large deflections of the plate. Unilateral contact problems with buckling, including models for plates, resting on elastic foundations, and contact models for delaminated composite plates, are formulated. Dynamic nonlinear equations for elastic plates, which possess buckling and contact effects are also presented. Most commonly used boundary and initial conditions are set up. The advantages and disadvantages of analytical, semi-analytical, and numerical techniques for the buckling and contact problems are discussed. The corresponding references are given. |
| first_indexed | 2024-03-10T20:30:49Z |
| format | Article |
| id | doaj.art-3e949b3f34b5472d9fa9ea87e3a120c1 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T20:30:49Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-3e949b3f34b5472d9fa9ea87e3a120c12023-11-19T21:22:22ZengMDPI AGMathematics2227-73902020-04-018456610.3390/math8040566Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A ReviewAliki D. Muradova0Georgios E. Stavroulakis1School of Production Engineering and Management, Institute of Computational Mechanics and Optimization, Technical University of Crete, 73100 Chania, GreeceSchool of Production Engineering and Management, Institute of Computational Mechanics and Optimization, Technical University of Crete, 73100 Chania, GreeceA review of mathematical models for elastic plates with buckling and contact phenomena is provided. The state of the art in this domain is presented. Buckling effects are discussed on an example of a system of nonlinear partial differential equations, describing large deflections of the plate. Unilateral contact problems with buckling, including models for plates, resting on elastic foundations, and contact models for delaminated composite plates, are formulated. Dynamic nonlinear equations for elastic plates, which possess buckling and contact effects are also presented. Most commonly used boundary and initial conditions are set up. The advantages and disadvantages of analytical, semi-analytical, and numerical techniques for the buckling and contact problems are discussed. The corresponding references are given.https://www.mdpi.com/2227-7390/8/4/566elastic plate modelpartial differential equationboundary conditionsinitial conditionsbuckling phenomenoncontact effects |
| spellingShingle | Aliki D. Muradova Georgios E. Stavroulakis Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A Review Mathematics elastic plate model partial differential equation boundary conditions initial conditions buckling phenomenon contact effects |
| title | Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A Review |
| title_full | Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A Review |
| title_fullStr | Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A Review |
| title_full_unstemmed | Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A Review |
| title_short | Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A Review |
| title_sort | mathematical models with buckling and contact phenomena for elastic plates a review |
| topic | elastic plate model partial differential equation boundary conditions initial conditions buckling phenomenon contact effects |
| url | https://www.mdpi.com/2227-7390/8/4/566 |
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