Time-domain BEM for dynamic crack analysis

Time-domain boundary element method (BEM) for elastodynamic crack analysis is presented in this paper. Special attention is devoted to BEM based on traction boundary integral equations (BIEs) in time-domain. Both the hypersingular and the non-hypersingular traction BIEs are dealt with. A time-steppi...

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Bibliographic Details
Published inMathematics and computers in simulation Vol. 50; no. 1; pp. 351 - 362
Main Authors Zhang, Ch, Savaidis, A.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Amsterdam Elsevier B.V 01.11.1999
Elsevier
Subjects
Boundary element method
Boundary integral equations
Dynamic crack analysis
Exact sciences and technology
Fracture mechanics
Integral equations, integral transforms
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, boundary value problems
Sciences and techniques of general use
Dynamic crack analysis
Fracture mechanics
Boundary element method
Boundary integral equations
Shape function
Singularity
Equation of motion
Riemann convolution
Time domain analysis
Betti Reyleigh reciprocal theorem
Green function
Hooke law
Convolution
Crack analysis
Integral equation
Elastodynamics
Crack
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Summary:Time-domain boundary element method (BEM) for elastodynamic crack analysis is presented in this paper. Special attention is devoted to BEM based on traction boundary integral equations (BIEs) in time-domain. Both the hypersingular and the non-hypersingular traction BIEs are dealt with. A time-stepping scheme in conjunction with a collocation method is applied for solving the time-domain BIEs numerically. This scheme uses a linear shape-function in time which allows an analytic time-integration of the system matrix. Two different spatial shape-functions are used in the numerical solution procedure, namely, “crack-tip elements” behind crack-tips while constant elements away from crack-tips. The use of “crack-tip elements” takes the proper local behavior of the crack opening displacements (COD) at crack-tips into account, and it makes an accurate calculation of the dynamic stress intensity factors feasible. The hypersingular integrals arising in the hypersingular time-domain traction BEM can be easily evaluated numerically and analytically by a direct method. Numerical examples for the dynamic stress intensity factors are given to show that the time-domain traction BEM is very accurate and efficient for elastodynamic crack analysis.
ISSN:0378-4754
1872-7166
DOI:10.1016/S0378-4754(99)00077-4