Analytical solution for the problem of pure bending of orthotropic micropolar plate
When analysing the problem of pure bending of a plate, it can be noticed that, for cylindrical bending, a spatial problem collapses into a plane-strain problem. For such a boundary-value problem of the Cosserats' continuum, three engineering parameters are required: Young’s modulus, Poisson’s r...
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| Format: | Article |
| Language: | English |
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University of Rijeka, Faculty of Civil Engineering
2024-12-01
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| Series: | Zbornik Radova |
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| Online Access: | https://zr.gradri.uniri.hr/index.php/zr/article/view/248 |
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| author | Damjan Jurković Gordan Jelenić Sara Grbčić Erdelj |
| author_facet | Damjan Jurković Gordan Jelenić Sara Grbčić Erdelj |
| author_sort | Damjan Jurković |
| collection | DOAJ |
| description | When analysing the problem of pure bending of a plate, it can be noticed that, for cylindrical bending, a spatial problem collapses into a plane-strain problem. For such a boundary-value problem of the Cosserats' continuum, three engineering parameters are required: Young’s modulus, Poisson’s ratio and the characteristic length for bending. Here we consider an orthotropic form of such a problem, whereby two Young’s moduli, four Poison’s ratios and one characteristic length for bending are found to be sufficient to propose a mathematical model of this problem. General equations of the isotropic micropolar continuum are introduced, and the analytical solution for the pure bending of an isotropic micropolar plate is generalized to the case of orthotropic microstructure. By defining the ratio of a distributed force and a distributed moment boundary conditions required for the pure-bending state, a closed-form solution to this problem is obtained in terms of displacement, strains and stress functions. It is shown that the derived results reduce to the isotropic ones if a material isotropy is assumed.
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| format | Article |
| id | doaj-art-3489e76b3f3443aaa41a7291b7761d00 |
| institution | Kabale University |
| issn | 0350-8552 2584-6159 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | University of Rijeka, Faculty of Civil Engineering |
| record_format | Article |
| series | Zbornik Radova |
| spelling | doaj-art-3489e76b3f3443aaa41a7291b7761d002025-01-28T12:07:51ZengUniversity of Rijeka, Faculty of Civil EngineeringZbornik Radova0350-85522584-61592024-12-0127110.32762/zr.27.1.8Analytical solution for the problem of pure bending of orthotropic micropolar plateDamjan Jurković0Gordan Jelenić1Sara Grbčić Erdelj2University of Rijeka, Faculty of Civil EngineeringUniversity of Rijeka, Faculty of Civil EngineeringUniversity of Rijeka, Faculty of Civil EngineeringWhen analysing the problem of pure bending of a plate, it can be noticed that, for cylindrical bending, a spatial problem collapses into a plane-strain problem. For such a boundary-value problem of the Cosserats' continuum, three engineering parameters are required: Young’s modulus, Poisson’s ratio and the characteristic length for bending. Here we consider an orthotropic form of such a problem, whereby two Young’s moduli, four Poison’s ratios and one characteristic length for bending are found to be sufficient to propose a mathematical model of this problem. General equations of the isotropic micropolar continuum are introduced, and the analytical solution for the pure bending of an isotropic micropolar plate is generalized to the case of orthotropic microstructure. By defining the ratio of a distributed force and a distributed moment boundary conditions required for the pure-bending state, a closed-form solution to this problem is obtained in terms of displacement, strains and stress functions. It is shown that the derived results reduce to the isotropic ones if a material isotropy is assumed. https://zr.gradri.uniri.hr/index.php/zr/article/view/248orthotropic micropolar continuumanalytical solution of pure bendingcharacteristic length for bending |
| spellingShingle | Damjan Jurković Gordan Jelenić Sara Grbčić Erdelj Analytical solution for the problem of pure bending of orthotropic micropolar plate Zbornik Radova orthotropic micropolar continuum analytical solution of pure bending characteristic length for bending |
| title | Analytical solution for the problem of pure bending of orthotropic micropolar plate |
| title_full | Analytical solution for the problem of pure bending of orthotropic micropolar plate |
| title_fullStr | Analytical solution for the problem of pure bending of orthotropic micropolar plate |
| title_full_unstemmed | Analytical solution for the problem of pure bending of orthotropic micropolar plate |
| title_short | Analytical solution for the problem of pure bending of orthotropic micropolar plate |
| title_sort | analytical solution for the problem of pure bending of orthotropic micropolar plate |
| topic | orthotropic micropolar continuum analytical solution of pure bending characteristic length for bending |
| url | https://zr.gradri.uniri.hr/index.php/zr/article/view/248 |
| work_keys_str_mv | AT damjanjurkovic analyticalsolutionfortheproblemofpurebendingoforthotropicmicropolarplate AT gordanjelenic analyticalsolutionfortheproblemofpurebendingoforthotropicmicropolarplate AT saragrbcicerdelj analyticalsolutionfortheproblemofpurebendingoforthotropicmicropolarplate |