scholarly journals Dynamic Crack Analysis in Isotropic/Orthotropic Media via Extended Isogeometric Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Tiantang Yu ◽  
Yongling Lai ◽  
Shuohui Yin
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Isogeometric Analysis ◽  
Dynamic Stress ◽  
Time Integration ◽  
Integration Scheme ◽  
Dynamic Crack ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Orthotropic Media

The extended isogeometric analysis (X-IGA) is the combination of the extended finite element method (X-FEM) and the isogeometric analysis (IGA), so the X-IGA possesses the advantages of both methods. In this paper, the X-IGA is extended to investigate the dynamic stress intensity factors of cracked isotropic/orthotropic media under impact loading. For this purpose, a corresponding dynamic X-IGA model is developed, the Newmark time integration scheme is used to achieve a dynamic response, and the dynamic stress intensity factors are evaluated through the contour interaction integral technique. Numerical simulations show that the X-IGA results agree with other available reference solutions, and accurate results can be obtained by using the X-IGA with a relatively coarse mesh.

scholarly journals Dynamic crack propagation between two bonded orthotropic plates

2004 ◽  
Vol 2004 (1) ◽  
pp. 55-68 ◽  
Author(s):  
M. S. Matbuly
Keyword(s):  
Stress Intensity ◽  
Crack Propagation ◽  
Stress Intensity Factors ◽  
Dynamic Stress ◽  
Fourier Transforms ◽  
Dynamic Crack ◽  
Cauchy Type ◽  
Intensity Factors ◽  
Orthotropic Plates ◽  
Dynamic Stress Intensity Factors

The problem of crack propagation along the interface of two bonded dissimilar orthotropic plates is considered. Using Galilean transformation, the problem is reduced to a quasistatic one. Then, using Fourier transforms and asymptotic analysis, the problem is reduced to a pair of singular integral equations with Cauchy-type singularity. These equations are solved using Gauss-Chebyshev quadrature formulae. The dynamic stress intensity factors are obtained in closed form expressions. Furthermore, a parametric study is introduced to investigate the effect of crack growth rate and geometric and elastic characteristics of the plates on values of dynamic stress intensity factors.

Elastodynamic Fracture Analysis of Multiple Cracks by Laplace Finite Element Alternating Method

1999 ◽  
Vol 67 (3) ◽  
pp. 606-615 ◽  
Author(s):  
W.-H. Chen ◽  
C.-L. Chang ◽  
C.-H. Tsai
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Laplace Transform ◽  
Stress Intensity Factors ◽  
Dynamic Stress ◽  
Multiple Cracks ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Alternating Method ◽  
The Laplace Transform

The Laplace finite element alternating method, which combines the Laplace transform technique and the finite element alternating method, is developed to deal with the elastodynamic analysis of a finite plate with multiple cracks. By the Laplace transform technique, the complicated elastodynamic fracture problem is first transformed into an equivalent static fracture problem in the Laplace transform domain and then solved by the finite element alternating method developed. To do this, an analytical solution by Tsai and Ma for an infinite plate with a semi-infinite crack subjected to exponentially distributed loadings on crack surfaces in the Laplace transform domain is adopted. Finally, the real-time response can be computed by a numerical Laplace inversion algorithm. The technique established is applicable to the calculation of dynamic stress intensity factors of a finite plate with arbitrarily distributed edge cracks or symmetrically distributed central cracks. Only a simple finite element mesh with very limited number of regular elements is necessary. Since the solutions are independent of the size of time increment taken, the dynamic stress intensity factors at any specific instant can even be computed by a single time-step instead of step-by-step computations. The interaction among the cracks and finite geometrical boundaries on the dynamic stress intensity factors is also discussed in detail. [S0021-8936(00)02103-6]

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