On Representing Strain Gradient Elastic Solutions of Boundary Value Problems by Encompassing the Classical Elastic Solution
The present work aims to primarily provide a general representation of the solution of the simplified elastostatics version of Mindlin’s Form II first-strain gradient elastic theory, which converges to the solution of the corresponding classical elastic boundary value problem as the intrinsic gradie...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/7/1152 |
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| author | Antonios Charalambopoulos Theodore Gortsas Demosthenes Polyzos |
| author_facet | Antonios Charalambopoulos Theodore Gortsas Demosthenes Polyzos |
| author_sort | Antonios Charalambopoulos |
| collection | DOAJ |
| description | The present work aims to primarily provide a general representation of the solution of the simplified elastostatics version of Mindlin’s Form II first-strain gradient elastic theory, which converges to the solution of the corresponding classical elastic boundary value problem as the intrinsic gradient parameters become zero. Through functional theory considerations, a solution representation of the one-intrinsic-parameter strain gradient elastostatic equation that comprises the classical elastic solution of the corresponding boundary value problem is rigorously provided for the first time. Next, that solution representation is employed to give an answer to contradictions arising by two well-known first-strain gradient elastic models proposed in the literature to describe the strain gradient elastostatic bending behavior of Bernoulli–Euler beams. |
| first_indexed | 2024-03-09T11:38:31Z |
| format | Article |
| id | doaj.art-b9ac586e834b4af7aded3d10beb527a6 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T11:38:31Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b9ac586e834b4af7aded3d10beb527a62023-11-30T23:37:54ZengMDPI AGMathematics2227-73902022-04-01107115210.3390/math10071152On Representing Strain Gradient Elastic Solutions of Boundary Value Problems by Encompassing the Classical Elastic SolutionAntonios Charalambopoulos0Theodore Gortsas1Demosthenes Polyzos2School of Applied Mathematics and Physical Sciences, National Technical University of Athens, 15780 Athens, GreeceDepartment of Mechanical Engineering and Aeronautics, University of Patras, 26504 Patras, GreeceDepartment of Mechanical Engineering and Aeronautics, University of Patras, 26504 Patras, GreeceThe present work aims to primarily provide a general representation of the solution of the simplified elastostatics version of Mindlin’s Form II first-strain gradient elastic theory, which converges to the solution of the corresponding classical elastic boundary value problem as the intrinsic gradient parameters become zero. Through functional theory considerations, a solution representation of the one-intrinsic-parameter strain gradient elastostatic equation that comprises the classical elastic solution of the corresponding boundary value problem is rigorously provided for the first time. Next, that solution representation is employed to give an answer to contradictions arising by two well-known first-strain gradient elastic models proposed in the literature to describe the strain gradient elastostatic bending behavior of Bernoulli–Euler beams.https://www.mdpi.com/2227-7390/10/7/1152strain gradient elastic theorygeneral solution representationBernoulli–Euler beammaterial with microstructure |
| spellingShingle | Antonios Charalambopoulos Theodore Gortsas Demosthenes Polyzos On Representing Strain Gradient Elastic Solutions of Boundary Value Problems by Encompassing the Classical Elastic Solution Mathematics strain gradient elastic theory general solution representation Bernoulli–Euler beam material with microstructure |
| title | On Representing Strain Gradient Elastic Solutions of Boundary Value Problems by Encompassing the Classical Elastic Solution |
| title_full | On Representing Strain Gradient Elastic Solutions of Boundary Value Problems by Encompassing the Classical Elastic Solution |
| title_fullStr | On Representing Strain Gradient Elastic Solutions of Boundary Value Problems by Encompassing the Classical Elastic Solution |
| title_full_unstemmed | On Representing Strain Gradient Elastic Solutions of Boundary Value Problems by Encompassing the Classical Elastic Solution |
| title_short | On Representing Strain Gradient Elastic Solutions of Boundary Value Problems by Encompassing the Classical Elastic Solution |
| title_sort | on representing strain gradient elastic solutions of boundary value problems by encompassing the classical elastic solution |
| topic | strain gradient elastic theory general solution representation Bernoulli–Euler beam material with microstructure |
| url | https://www.mdpi.com/2227-7390/10/7/1152 |
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