Elastodynamics by BEM: a new direct formulation

A new direct BE formulation is proposed for the solution of elastodynamic problems. An analytical regularization procedure is devised via an integration‐by‐parts technique without introducing any hypothesis about either the discretization of the boundary geometry or the space–time interpolation of the elastic fields involved. The only requirement is for continuity in the displacement field. The regularization of the integral equations for static elasticity using the same approach, already available in the literature, is presented as a particular case of the general procedure introduced herein. The numerical implementation of this technique is discussed and two‐dimensional examples are presented. Copyright © 1999 John Wiley & Sons, Ltd.     

A 2‐D time‐domain boundary element method with damping

A new material damping model which is convenient for use in the time‐domain boundary element method (TDBEM) is presented and implemented in a proposed procedure. Since only fundamental solutions for linear elastic material are employed, the procedure has high efficiency and is easy to be integrated into current TDBEM codes. Analytical and numerical results for benchmark problems demonstrate that the accuracy of the proposed method is high. Copyright © 2001 John Wiley & Sons, Ltd.     

基于加速度时域信息的结构损伤识别方法研究

研究了基于加速度时域信息构造残差量的结构损伤识别方法。针对该方法实施过程中可能产生的识别方程组病态问题,以及随之产生的求解结果对测量噪声敏感等问题,采用截断奇异值分解技术(TSVD)求解识别方程组。以IASC?ASCE的基准结构为算例,采用本文的方法,识别出两种情况的损伤位置,损伤程度的识别误差分别为3.8%、6.0%,验证了所研究的基于加速度时域信息的结构损伤识别方法是有效的。     

An efficient stabilized boundary element formulation for 2D time-domain acoustics and elastodynamics

The present paper describes a procedure that improves efficiency, stability and reduces artificial energy dissipation of the standard time-domain direct boundary element method (BEM) for acoustics and elastodynamics. Basically, the developed procedure modifies the boundary element convolution-related vector, being very easy to implement into existing codes. A stabilization parameter is introduced into the recent-in-time convolution operations and the operations related to the distant-in-time convolution contributions are approximated by matrix interpolations. As it is shown in the numerical examples presented at the end of the text, the proposed formulation substantially reduces the BEM computational cost, as well as its numerical instabilities.     

Time discontinuous Galerkin methods with energy decaying correction for non‐linear elastodynamics

In this paper a new time discontinuous Galerkin (TDG) formulation for non‐linear elastodynamics is presented. The new formulation embeds an energy correction which ensures truly energy decaying, thus allowing to achieve unconditional stability that, as shown in the paper, is not guaranteed by the classical TDG formulation. The resulting method is simple and easily implementable into existing finite element codes. Moreover, it inherits the desirable higher‐order accuracy and high‐frequency dissipation properties of the classical formulation. Numerical results illustrate the very good performance of the proposed formulation. Copyright © 2010 John Wiley & Sons, Ltd.     

A hypersingular time‐domain BEM for 2D dynamic crack analysis in anisotropic solids

A hypersingular time‐domain boundary element method (BEM) for transient elastodynamic crack analysis in two‐dimensional (2D), homogeneous, anisotropic, and linear elastic solids is presented in this paper. Stationary cracks in both infinite and finite anisotropic solids under impact loading are investigated. On the external boundary of the cracked solid the classical displacement boundary integral equations (BIEs) are used, while the hypersingular traction BIEs are applied to the crack‐faces. The temporal discretization is performed by a collocation method, while a Galerkin method is implemented for the spatial discretization. Both temporal and spatial integrations are carried out analytically. Special analytical techniques are developed to directly compute strongly singular and hypersingular integrals. Only the line integrals over an unit circle arising in the elastodynamic fundamental solutions need to be computed numerically by standard Gaussian quadrature. An explicit time‐stepping scheme is obtained to compute the unknown boundary data including the crack‐opening‐displacements (CODs). Special crack‐tip elements are adopted to ensure a direct and an accurate computation of the elastodynamic stress intensity factors from the CODs. Several numerical examples are given to show the accuracy and the efficiency of the present hypersingular time‐domain BEM. Copyright © 2008 John Wiley & Sons, Ltd.     

Comparative study of time and frequency domain BEM approaches in frictional contact problem for antiplane crack under harmonic loading

Two different boundary element methods (BEM) for crack analysis in two dimensional (2-D) antiplane, homogeneous, isotropic and linear elastic solids by considering frictional contact of the crack edges are presented. Hypersingular boundary integral equations (BIE) in time-domain (TD) and frequency domain (FD), with corresponding elastodynamic fundamental solutions are applied for this purpose. For evaluation of the hypersingular integrals involved in BIEs a special regularization process that converts the hypersingular integrals to regular integrals is applied. Simple regular formulas for their calculation are presented. For the problems solution while considering frictional contact of the crack edges a special iterative algorithm of Udzava's type is elaborated and used. Numerical results for crack opening, frictional contact forces and dynamic stress intensity factors (SIFs) are presented and discussed for a finite III-mode crack in an infinite domain subjected to a harmonic crack-face loading and considering crack edges frictional contact interaction using the TD and FD approaches.