A boundary algebraic formulation for plane strain elastodynamic scattering
Solving of elastodynamic problems arises in many scientific fields such as wave propagation in the ground, non-destructive testing, vibration design of buildings, or vibroacoustics in general. An integral formulation based on boundary algebraic equations is presented here. This formulation leads to...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/116425 |
| Acceso en línea: | https://hdl.handle.net/2117/116425 |
| Access Level: | acceso abierto |
| Palabra clave: | Difference equations, Partial--Numerical solutions Strength of materials elastodynamics scattering boundary integral method Equacions diferencials parcials--solucions numèriques Resistència de materials Classificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problems Classificació AMS::74 Mechanics of deformable solids::74S Numerical methods Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica |
| Sumario: | Solving of elastodynamic problems arises in many scientific fields such as wave propagation in the ground, non-destructive testing, vibration design of buildings, or vibroacoustics in general. An integral formulation based on boundary algebraic equations is presented here. This formulation leads to a numerical method with a discretised boundary. An important advantage of the method over the standard boundary element method (BEM) is that no contour (2D) or surface (3D) integral needs to be computed. This feature is helpful in order to obtain a discrete version of the combined field integral equations (designed to damp numerically the fictitious eigenfrequencies) without difficulties caused by the evaluation of hypersingular integrals. The key aspects are: (i) the approach deals with discrete equations from the very beginning; (ii) discrete (instead of continuous) tensor Green's functions are considered (the methodology to evaluate them is demonstrated); (iii) the boundary must be described by means of a regular square grid. In order to overcome the drawback of this third condition the boundary integral is coupled, if needed, with a thin layer of finite elements. This improves the description of curved geometries and reduces numerical errors. The properties of the method are demonstrated by means of numerical examples: the scattering of waves by objects and holes in an unbounded elastic medium, and an interior elastic problem. |
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