Explicit solutions in isotropic planar elastostatics
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| Title: | Explicit solutions in isotropic planar elastostatics |
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| Authors: | Granath, Andreas, Åhag, Per, Perälä, Antti, Czyż, Rafał |
| Source: | Acta Mathematica Vietnamica. 50(2):285-301 |
| Subject Terms: | Cardioid, Complex variables, Conformal mapping, Eccentric annulus, Epitrochoid, Isotropic planar elastostatics, Notch problem, Plane elasticity |
| Description: | Addressing the intricate challenges in plane elasticity, especially with non-vanishing traction and complex geometries, requires innovative methods. This paper offers a novel approach, drawing inspiration from the Neumann problem for the inhomogeneous Cauchy-Riemann equations. Our method applies to domains conformally equivalent to a unit disk or an annulus, focusing on deriving explicit solutions for the displacement field rather than the stress tensor, which distinguishes it from most traditional approaches. We explore solutions for specific classical cases to demonstrate its efficacy, such as a cardioid domain, a ring domain with a shifted hole, and a gear-like structure. This work enhances the toolkit for researchers and practitioners tackling isotropic planar elastostatic challenges with a unified and flexible approach. |
| File Description: | electronic |
| Access URL: | https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-240990 https://doi.org/10.1007/s40306-025-00572-w |
| Database: | SwePub |
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Nájsť tento článok vo Web of Science | Abstract: | Addressing the intricate challenges in plane elasticity, especially with non-vanishing traction and complex geometries, requires innovative methods. This paper offers a novel approach, drawing inspiration from the Neumann problem for the inhomogeneous Cauchy-Riemann equations. Our method applies to domains conformally equivalent to a unit disk or an annulus, focusing on deriving explicit solutions for the displacement field rather than the stress tensor, which distinguishes it from most traditional approaches. We explore solutions for specific classical cases to demonstrate its efficacy, such as a cardioid domain, a ring domain with a shifted hole, and a gear-like structure. This work enhances the toolkit for researchers and practitioners tackling isotropic planar elastostatic challenges with a unified and flexible approach. |
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| ISSN: | 02514184 23154144 |
| DOI: | 10.1007/s40306-025-00572-w |