descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2018 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Applied Mathematics, volume 78, pages 1,256-1,282 (issn: 0036-1399, eissn: 1095-712X,

Authors: Poblet-Puig, Jordi; Shanin, Andrey;

doi: 10.1137/17m1118257

handle: 2117/116425

A Boundary Algebraic Formulation for Plane Strain Elastodynamic Scattering

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Abstract

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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Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs, Difference equations, Wave scattering in solid mechanics, Classificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problems, boundary integral method, Numerical methods for integral equations, Numerical solution of discretized equations for boundary value problems involving PDEs, Difference equations, Partial--Numerical solutions, Classificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problems, :65 Numerical analysis::65N Partial differential equations, boundary value problems [Classificació AMS], :Matemàtiques i estadística::Anàlisi numèrica [Àrees temàtiques de la UPC], Strength of materials, Resistència de materials, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica, :Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics [Àrees temàtiques de la UPC], scattering, Classificació AMS::74 Mechanics of deformable solids::74S Numerical methods, Other numerical methods in solid mechanics, elastodynamics, Equacions diferencials parcials--solucions numèriques, Partial--Numerical solutions, Classical linear elasticity, :74 Mechanics of deformable solids::74S Numerical methods [Classificació AMS], Boundary element methods applied to problems in solid mechanics

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