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.

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.

Response of Submerged Structures by the Finite Element-Cum-Boundary Element Method

2001 ◽  
Author(s):  
C. W. S. To ◽  
M. A. O’Grady
Keyword(s):  
Finite Element ◽  
Boundary Element ◽  
Fluid Structure Interaction ◽  
Three Dimensional ◽  
Problem Size ◽  
Hybrid Strain ◽  
Fluid Structure ◽  
Structure Interaction ◽  
High Convergence Rate ◽  
Shell Finite Element

Abstract A double asymptotic approximation based finite element-cum-boundary element approach for fluid-structure interaction problems is being proposed. In particular a staggered solution scheme has been applied to the analysis of various coupled fluid-structure systems. A stabilization scheme by reformulation, proposed by DeRuntz et al. was employed to circumvent the instability problem. In addition, the singularity in the excitation term was eliminated through a variable transformation as suggested by Everstine. Another feature of the present work is its incorporation of the hybrid strain based lower order triangular shell finite element developed by To and Liu. The eigenvalue solution exhibits high convergence rate for the particular shell finite element employed. The responses calculated exhibit the effectiveness of the proposed approach with application of the aforementioned shell finite element in dealing with three dimensional fluid-structure interaction problems. The reduction in problem size that this approach affords allows these complex interaction problems to be dealt with in a desktop engineering workstation environment, as opposed to the mainframe and supercomputer arenas where they have been implemented in the past.

Efficient Computations of Fully-Nonlinear Wave Interactions With Floating Structures

2010 ◽  
Author(s):  
Hongmei Yan ◽  
Yuming Liu
Keyword(s):  
Boundary Element ◽  
High Efficiency ◽  
Three Dimensional ◽  
Nonlinear Effects ◽  
Computational Effort ◽  
Boundary Element Methods ◽  
Computational Method ◽  
Wave Interactions ◽  
Time Step ◽  
Fully Nonlinear

We consider the problem of fully nonlinear three-dimensional wave interactions with floating bodies with or without a forward speed. A highly efficient time-domain computational method is developed in the context of potential flow formulation using the pre-corrected Fast Fourier Transform (PFFT) algorithm based on a high-order boundary element method. The method reduces the computational effort in solving the boundary-value problem at each time step to O(NlnN) from O(N2∼3) of the classical boundary element methods, where N is the total number of unknowns. The high efficiency of this method allows accurate computations of fully-nonlinear hydrodynamic loads, wave runups, and motions of surface vessels and marine structures in rough seas. We apply this method to study the hydrodynamics of floating objects with a focus on the understanding of fully nonlinear effects in the presence of extreme waves and large-amplitude body motions.

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