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Article: Matrix Green’s function solution of closed-form singularity for functionally graded and transversely isotropic materials under circular ring force vector
| Title | Matrix Green’s function solution of closed-form singularity for functionally graded and transversely isotropic materials under circular ring force vector |
|---|---|
| Authors | |
| Keywords | Circular ring force vector Closed-form singular solution Elasticity Functionally graded materials Green's function Transversely isotropy |
| Issue Date | 1-Jan-2023 |
| Publisher | Elsevier |
| Citation | Engineering Analysis with Boundary Elements, 2023, v. 146, p. 569-597 How to Cite? |
| Abstract | The paper develops the Green's function solution in matrix form for functionally graded and transversely isotropic material (FGTIM) due to the loading of a circular ring force vector. The force vector is concentrated along a horizontal circular ring and acts at any location in the interior of the FGTIM material occupying either a fullspace or a halfspace. Without loss of generality, the variations of the FGTIM's five elastic parameters are expressed as five arbitrary step functions with the depth as the independent variable. The two-dimensional Fourier integral transforms in the cylindrical coordinate system are used for the mathematical formulation and derivation in matrix form. The Green's function solution of the displacement and stress fields is explicitly expressed in the matrix form in terms of classical improper Hankel transform integrals of the orders of 0 to 3. The kernel functions of the Hankel transform integrals are explicitly expressed in the forms of backward transfer matrix. Their mathematical properties are analyzed analytically and numerically. The singular terms associated with the improper Hankel transform integrals are analytically isolated and expressed in the exact closed-form in terms of the complete elliptic integrals of the first, second and third kind. Such closed-form singular terms can be expressed as the matrix Green's function solution for the corresponding bi-material due to the same circular ring force vector. Numerical results show that the computation of the matrix Green's function solution can be achieved with high accuracy and efficiency and the heterogeneity and anisotropy can have significant effects on the elastic fields in the FGTIM induced by the circular ring force vector. |
| Persistent Identifier | http://hdl.handle.net/10722/340387 |
| ISSN | 2021 Impact Factor: 3.250 2020 SCImago Journal Rankings: 0.925 |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Xiao, S | - |
| dc.contributor.author | Yue, ZQ | - |
| dc.date.accessioned | 2024-03-11T10:43:46Z | - |
| dc.date.available | 2024-03-11T10:43:46Z | - |
| dc.date.issued | 2023-01-01 | - |
| dc.identifier.citation | Engineering Analysis with Boundary Elements, 2023, v. 146, p. 569-597 | - |
| dc.identifier.issn | 0955-7997 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/340387 | - |
| dc.description.abstract | <p>The paper develops the Green's function solution in matrix form for functionally graded and transversely isotropic material (FGTIM) due to the loading of a circular ring force vector. The force vector is concentrated along a horizontal circular ring and acts at any location in the interior of the FGTIM material occupying either a fullspace or a halfspace. Without loss of generality, the variations of the FGTIM's five elastic parameters are expressed as five arbitrary step functions with the depth as the independent variable. The two-dimensional Fourier integral transforms in the <a href="https://www.sciencedirect.com/topics/engineering/cylindrical-coordinate-system" title="Learn more about cylindrical coordinate system from ScienceDirect's AI-generated Topic Pages">cylindrical coordinate system</a> are used for the mathematical formulation and derivation in matrix form. The Green's function solution of the displacement and stress fields is explicitly expressed in the matrix form in terms of classical improper Hankel transform integrals of the orders of 0 to 3. The <a href="https://www.sciencedirect.com/topics/computer-science/kernel-function" title="Learn more about kernel functions from ScienceDirect's AI-generated Topic Pages">kernel functions</a> of the Hankel transform integrals are explicitly expressed in the forms of backward <a href="https://www.sciencedirect.com/topics/mathematics/transfer-matrix" title="Learn more about transfer matrix from ScienceDirect's AI-generated Topic Pages">transfer matrix</a>. Their <a href="https://www.sciencedirect.com/topics/engineering/mathematical-property" title="Learn more about mathematical properties from ScienceDirect's AI-generated Topic Pages">mathematical properties</a> are analyzed analytically and numerically. The singular terms associated with the improper Hankel transform integrals are analytically isolated and expressed in the exact closed-form in terms of the <a href="https://www.sciencedirect.com/topics/engineering/complete-elliptic-integral" title="Learn more about complete elliptic integrals from ScienceDirect's AI-generated Topic Pages">complete elliptic integrals</a> of the first, second and third kind. Such closed-form singular terms can be expressed as the matrix Green's function solution for the corresponding bi-material due to the same circular ring force vector. Numerical results show that the computation of the matrix Green's function solution can be achieved with high accuracy and efficiency and the heterogeneity and anisotropy can have significant effects on the elastic fields in the FGTIM induced by the circular ring force vector.</p> | - |
| dc.language | eng | - |
| dc.publisher | Elsevier | - |
| dc.relation.ispartof | Engineering Analysis with Boundary Elements | - |
| dc.subject | Circular ring force vector | - |
| dc.subject | Closed-form singular solution | - |
| dc.subject | Elasticity | - |
| dc.subject | Functionally graded materials | - |
| dc.subject | Green's function | - |
| dc.subject | Transversely isotropy | - |
| dc.title | Matrix Green’s function solution of closed-form singularity for functionally graded and transversely isotropic materials under circular ring force vector | - |
| dc.type | Article | - |
| dc.identifier.doi | 10.1016/j.enganabound.2022.10.018 | - |
| dc.identifier.scopus | eid_2-s2.0-85141746682 | - |
| dc.identifier.volume | 146 | - |
| dc.identifier.spage | 569 | - |
| dc.identifier.epage | 597 | - |
| dc.identifier.eissn | 1873-197X | - |
| dc.identifier.issnl | 0955-7997 | - |