A super‐element for crack analysis in the time domain

Abstract

SUMMARYA super-element for the dynamic analysis of two-dimensional crack problems is developed based on the scaled boundary finite-element method. The boundary of the super-element containing a crack tip is discretized with line elements. The governing partial differential equations formulated in the scaled boundary co-ordinates are transformed to ordinary differential equations in the frequency domain by applying the Galerkin's weighted residual technique. The displacements in the radial direction from the crack tip to a point on the boundary are solved analytically without any a priori assumption. The scaled boundary finite-element formulation leads to symmetric static stiffness and mass matrices. The super-element can be coupled seamlessly with standard finite elements. The transient response is evaluated directly in the time domain using a standard time-integration scheme. The stress field, including the singularity around the crack tip, is expressed semi-analytically. The stress intensity factors are evaluated without directly addressing singular functions, as the limit in their definitions is performed analytically.

Integral transform approach for dynamic fracture calculation and crack growth modelling

“…4). The same isotropic problem with a little various material properties was simulated by Song [2] applying the time-domain SBFEM and a finer mesh with 23 super-elements, and over 200 nodes. This expresses one of the disadvantages of time-domain methods, that means a mass matrix has to be applied in timeintegration.…”

“…This expresses one of the disadvantages of time-domain methods, that means a mass matrix has to be applied in timeintegration. Since the mass matrix used in [2] is the low-frequency expansion of the dynamic stiffness matrix, it may just symbolize the inertial results at low frequencies. The higher frequency constituents have to be an example of fine meshes with small dimensions.…”

“…The properties in the principal material axes stand for: Young´s modulus E 1 = 82 GPa, E 2 = R · E 1 , shear modulus G 12 = 29 GPa, Poisson's ratio υ 12 = 0.4006 and the mass density ρ = 2450 kg/m 3 . The same problem was solved by Song applying the time-domain SBFEM [2] and Albuquerque et al using the BEM [7]. Two events of R = 0.5 and 2.0 are studied.…”

“…As regards how the time processes of DSIFs are calculated, the methods given can be arranged into time-domain ways based on the direct time integration, and integral transform methods inclusive of the Laplace transform and the Fourier one (that means, the frequency-domain method in virtue of frequency analysis, and the discrete or fast Fourier transform (FFT). Superb literature surveys of these methods were presented by Ariza and Dominguez [1], and Song [2].…”

Hydrodynamic Pressure Evaluation of Reservoir Subjected to Ground Excitation Based on SBFEM

“…Therefore, it can handle well bounded domain problems with cracks and stress singularities and unbounded domain problems including infinite soil or unbounded acoustic fluid medium. In analyzing crack and stress singularities problems, the SBFEM placed the scaling center on the crack tip and only discretized the boundary of bounded domain using supper elements except the straight traction free crack faces, which permitted a rigorous representation of the stress singularities around the crack tip (Song, 2004;Song & Wolf, 2002;Yang & Deeks, 2007). The response of unbounded domain problems was obtained by using the SBFEM alone or coupling FEM and the SBFEM.…”