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Boundary Element Methods in Dynamic Analysis: Part II (1986-1996)
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1997
Year
Numerical AnalysisFinite Element MethodMethod Of Fundamental SolutionEngineeringCivil EngineeringNumerical SimulationMechanical EngineeringWave PropagationDynamic AnalysisFinite ElementsBoundary Element MethodsBoundary Element MethodStructural OptimizationComputational MechanicsStructural MechanicsBoundary LayerStructural EngineeringNumerical Method For Partial Differential Equation
This review continues a prior survey of boundary element methods for elastodynamics published in Applied Mechanics Reviews. The paper surveys boundary element techniques for elastodynamic problems from 1986 to 1996 and highlights gaps requiring future study. It describes integral formulations and advanced numerical treatments—including direct, indirect, T‑matrix, symmetric, dual‑reciprocity, and hybrid boundary‑finite element schemes—in both frequency and time domains for two‑, three‑dimensional and anti‑plane elastodynamic problems, and their application to wave propagation, structural dynamics, soil‑structure and fluid‑structure interaction, and various special subjects. The review cites 1,333 references.
A review of boundary element methods for the numerical solution of elastodynamic problems covering the period 1986-1996 is presented. It is a continuation of a review article on the same subject by the same author which appeared previously in Applied Mechanics Reviews (AMR 40(1) 1-23 (Jan 1987) Reprint No AMR015). Integral formulations and their advanced numerical treatment in both frequency and time domains from the direct boundary element method viewpoint are described. They cover two - and three - dimensional cases as well as the anti-plane case of linear elastodynamics under harmonic or transient disturbances. Indirect formulations, boundary methods, T-matrix methods, symmetric formulations, dual reciprocity boundary element methods and hybrid schemes combining boundary with finite elements are also described. All these boundary element methodologies are applied to: i) wave propagation analysis including wave propagation due to external loads, wave diffraction by surface or subsurface irregularities and cracks and crack propagation; ii) dynamic analysis of structures including beams, membranes, plates and shells as well as two - and three - dimensional structures; iii) soil-structure interaction including foundation analysis, piles and underground structures; iv) fluid-structure interaction including structures inside fluids or containing fluids and dam-reservoir systems; and v) the special subjects of viscoelasticity, inhomogeneity, anisotropy, poroelasticity-thermoelasticity, large deformations, contact analysis, inverse scattering and optimum design and control. Finally, areas where further research is needed are identified. There are 1333 references.