Fractal finite element method based shape sensitivity analysis of mixed-mode fracture

2008 ◽  
Vol 44 (15) ◽  
pp. 875-888 ◽  
Author(s):  
R.M. Reddy ◽  
B.N. Rao
Keyword(s):  
Finite Element Method ◽  
Sensitivity Analysis ◽  
Finite Element ◽  
Mixed Mode ◽  
Mixed Mode Fracture ◽  
Shape Sensitivity ◽  
Shape Sensitivity Analysis ◽  
Mode Fracture ◽  
Element Method

Complex-Variable Finite-Element Method for Mixed Mode Fracture and Interface Cracks

AIAA Journal ◽  
2018 ◽  
Vol 56 (11) ◽  
pp. 4632-4637
Author(s):  
Daniel Ramirez Tamayo ◽  
Arturo Montoya ◽  
Harry Millwater
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Complex Variable ◽  
Mixed Mode ◽  
Mixed Mode Fracture ◽  
Interface Cracks ◽  
Mode Fracture ◽  
Element Method

Probabilistic Fracture Mechanics Using Fractal Finite Element Method

2008 ◽  
Author(s):  
R. M. Reddy ◽  
B. N. Rao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Mixed Mode ◽  
Fracture Parameter ◽  
Shape Sensitivity ◽  
Probabilistic Fracture Mechanics ◽  
Reliability Method ◽  
Cracked Structures ◽  
Element Method

This paper presents probabilistic fracture-mechanics analysis of linear-elastic cracked structures subjected to mixed-mode (modes I and II) loading conditions using fractal finite element method (FFEM). The method involves FFEM for calculating fracture response characteristics; statistical models of uncertainties in load, material properties, and crack geometry; and the first-order reliability method for predicting probabilistic fracture response and reliability of cracked structures. The sensitivity of fracture parameters with respect to crack size, required for probabilistic analysis, is calculated using continuum shape sensitivity analysis. Numerical examples based on mode-I and mixed-mode problems are presented to illustrate the proposed method. The results show that the predicted failure probability based on the proposed formulation of the sensitivity of fracture parameter is accurate in comparison with the Monte Carlo simulation results. Since all gradients are calculated analytically, reliability analysis of cracks can be performed efficiently using FFEM.

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