Boundary Element Methods for the Dynamic Analysis of Elastic, Viscoelastic, and Piezoelectric Solids

2004 ◽  
Author(s):  
L. Gaul ◽  
M. K��gl ◽  
F. Moser ◽  
M. Schanz
Keyword(s):  
Dynamic Analysis ◽  
Boundary Element ◽  
Boundary Element Methods ◽  
Piezoelectric Solids

Boundary Element Methods in Dynamic Analysis

1987 ◽  
Vol 40 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Dimitri E. Beskos
Keyword(s):  
Dynamic Analysis ◽  
Numerical Solution ◽  
Boundary Element ◽  
Vibration Isolation ◽  
Plane Motion ◽  
Boundary Element Methods ◽  
Material Behavior ◽  
Brief Assessment ◽  
Time Domains ◽  
Plates And Shells

A review of boundary element methods for the numerical solution of dynamic problems of linear elasticity is presented. The integral formulation and the corresponding numerical solution of three- and two-dimensional elastodynamics from the direct boundary element method viewpoint and in both the frequency and time domains are described. The special case of the anti-plane motion governed by the scalar wave equation is also considered. In all the cases both harmonic and transient dynamic disturbances are taken into account. Special features of material behavior such as viscoelasticity, inhomogeneity, anisotropy, and poroelasticity are briefly discussed. Some other nonconventional boundary element methods as well as the hybrid scheme that results from the combination of boundary and finite elements are also reviewed. All these boundary element methodologies are applied to: soil-structure interaction problems that include the dynamic analysis of underground and above-ground structures, foundations, piles, and vibration isolation devices; problems of crack propagation and wave diffraction by cracks; and problems dealing with the dynamics of beams, plates, and shells. Finally, a brief assessment of the progress achieved so far in dynamic analysis is made and areas where further research is needed are identified.

Boundary Element Methods in Dynamic Analysis: Part II (1986-1996)

1997 ◽  
Vol 50 (3) ◽  
pp. 149-197 ◽  
Author(s):  
Dimitri E. Beskos
Keyword(s):  
Wave Propagation ◽  
Dynamic Analysis ◽  
Boundary Element ◽  
Three Dimensional ◽  
Boundary Element Methods ◽  
Underground Structures ◽  
Hybrid Schemes ◽  
Structure Interaction ◽  
Time Domains ◽  
Plates And Shells

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.

Weighted Finite Difference and Boundary Element Methods Applied to Groundwater Pollution Problems

1991 ◽  
Vol 23 (1-3) ◽  
pp. 517-524
Author(s):  
M. Kanoh ◽  
T. Kuroki ◽  
K. Fujino ◽  
T. Ueda
Keyword(s):  
Boundary Element Method ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Element ◽  
Difference Method ◽  
Groundwater Pollution ◽  
Small Region ◽  
Boundary Element Methods ◽  
Computational Time ◽  
Element Method

The purpose of the paper is to apply two methods to groundwater pollution in porous media. The methods are the weighted finite difference method and the boundary element method, which were proposed or developed by Kanoh et al. (1986,1988) for advective diffusion problems. Numerical modeling of groundwater pollution is also investigated in this paper. By subdividing the domain into subdomains, the nonlinearity is localized to a small region. Computational time for groundwater pollution problems can be saved by the boundary element method; accurate numerical results can be obtained by the weighted finite difference method. The computational solutions to the problem of seawater intrusion into coastal aquifers are compared with experimental results.

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