A size-dependent 3D solution of functionally graded shallow nanoshells
An unavailable semi-analytical non-local 3D solution for functionally graded nanoshells with constant radii of curvature is presented. The small length scale effect is included in Eringen’s nonlocal elasticity theory. The constitutive and equilibrium equations are written in terms of curvilinear ort...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2023-11-01
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| Series: | Curved and Layered Structures |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/cls-2022-0215 |
| _version_ | 1797303149886701568 |
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| author | Monge Joao Carlos Mantari Jose Luis Llosa Melchor Nicolas Hinostroza Miguel Angel |
| author_facet | Monge Joao Carlos Mantari Jose Luis Llosa Melchor Nicolas Hinostroza Miguel Angel |
| author_sort | Monge Joao Carlos |
| collection | DOAJ |
| description | An unavailable semi-analytical non-local 3D solution for functionally graded nanoshells with constant radii of curvature is presented. The small length scale effect is included in Eringen’s nonlocal elasticity theory. The constitutive and equilibrium equations are written in terms of curvilinear orthogonal coordinates systems which are only valid for spherical and cylindrical shells, and rectangular plates. The stresses and displacements are assumed in terms of the Navier method which is applicable for simply supported structures. The derivatives in terms of thickness are approximated by the differential quadrature method (DQM). The thickness domain is discretized by the Chebyshev–Gauss–Lobatto grid distribution. Lagrange interpolation polynomials are considered as the basis function for DQM. The correct free surface boundary condition for out-of-plane stresses is considered. Several problems of isotropic and functionally graded shells subjected to different types of loads are analyzed. The results are compared with other three-dimensional solutions and higher-order theories. It is important to emphasize that the radii of curvature are crucial at nanoscale, so it should be considered in the design of nanodevices. |
| first_indexed | 2024-03-07T23:48:47Z |
| format | Article |
| id | doaj.art-0ea195674b884c2490253d68316611b7 |
| institution | Directory Open Access Journal |
| issn | 2353-7396 |
| language | English |
| last_indexed | 2024-03-07T23:48:47Z |
| publishDate | 2023-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Curved and Layered Structures |
| spelling | doaj.art-0ea195674b884c2490253d68316611b72024-02-19T09:01:28ZengDe GruyterCurved and Layered Structures2353-73962023-11-0110119621910.1515/cls-2022-0215A size-dependent 3D solution of functionally graded shallow nanoshellsMonge Joao Carlos0Mantari Jose Luis1Llosa Melchor Nicolas2Hinostroza Miguel Angel3Faculty of Physics, National University of San Marcos, Av. Carlos German Amezaga375, Cercado de Lima, Lima, PeruDepartment of Science, Universidad de Ingenieria y Tecnologia - UTEC, Jr. Medrano Silva165, Barranco, Lima, PeruFaculty of Physics, National University of San Marcos, Av. Carlos German Amezaga375, Cercado de Lima, Lima, PeruPostgraduate School, National University of Engineering, Av. Túpac Amaru210, Rimac, Lima, PeruAn unavailable semi-analytical non-local 3D solution for functionally graded nanoshells with constant radii of curvature is presented. The small length scale effect is included in Eringen’s nonlocal elasticity theory. The constitutive and equilibrium equations are written in terms of curvilinear orthogonal coordinates systems which are only valid for spherical and cylindrical shells, and rectangular plates. The stresses and displacements are assumed in terms of the Navier method which is applicable for simply supported structures. The derivatives in terms of thickness are approximated by the differential quadrature method (DQM). The thickness domain is discretized by the Chebyshev–Gauss–Lobatto grid distribution. Lagrange interpolation polynomials are considered as the basis function for DQM. The correct free surface boundary condition for out-of-plane stresses is considered. Several problems of isotropic and functionally graded shells subjected to different types of loads are analyzed. The results are compared with other three-dimensional solutions and higher-order theories. It is important to emphasize that the radii of curvature are crucial at nanoscale, so it should be considered in the design of nanodevices.https://doi.org/10.1515/cls-2022-0215nanoshellfunctionally graded materialeringen’s nonlocal elasticity theoryequilibrium equations |
| spellingShingle | Monge Joao Carlos Mantari Jose Luis Llosa Melchor Nicolas Hinostroza Miguel Angel A size-dependent 3D solution of functionally graded shallow nanoshells Curved and Layered Structures nanoshell functionally graded material eringen’s nonlocal elasticity theory equilibrium equations |
| title | A size-dependent 3D solution of functionally graded shallow nanoshells |
| title_full | A size-dependent 3D solution of functionally graded shallow nanoshells |
| title_fullStr | A size-dependent 3D solution of functionally graded shallow nanoshells |
| title_full_unstemmed | A size-dependent 3D solution of functionally graded shallow nanoshells |
| title_short | A size-dependent 3D solution of functionally graded shallow nanoshells |
| title_sort | size dependent 3d solution of functionally graded shallow nanoshells |
| topic | nanoshell functionally graded material eringen’s nonlocal elasticity theory equilibrium equations |
| url | https://doi.org/10.1515/cls-2022-0215 |
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