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EN
Analysis of cracked cruciform specimens under biaxial loading conditions is very important and closer to reality in the study of behavior of marine, naval, aeronautical and railway structures. The aim of this work is to examine the evolution of fracture parameters in a combined mixed mode of an aluminum alloy A6082-T6 cruciform specimen as a function of the biaxial loading with different ratios. To this end, the effects of main parameters, such as load ratio, crack length, crack orientation and non-proportional loading coefficient have been analyzed and discussed in order to highlight fracture toughness of the studied material. The results show that the finite element method is a useful tool for calculation of crack characteristics in the mechanics of biaxial fracture. According to the obtained results, a non-proportional evolution of the fracture parameters, namely, the SIFs KI and KII , T-stress, and the biaxiality parameter was observed. Indeed, the latter depends considerably on the crack length, the angle of crack orientation and the applied biaxial loading. Detailed concluding remarks are presented at the end of this work.
2
Content available remote Mode I crack problems by coupled fractal finite element and meshfree method
EN
This paper presents a coupling technique for integrating the fractal finite element method (FFEM) with element-free Galerkin method (EFGM) for analyzing homogeneous, isotropic, and two-dimensional linear-elastic cracked structures subjected to Mode I loading condition. FFEM is adopted for discretization of domain close to the crack tip and EFGM is adopted in the rest of the domain. In the transition region interface elements are employed. The shape functions within interface elements which comprise both the element-free Galerkin and the finite element shape functions, satisfy the consistency condition thus ensuring convergence of the proposed coupled FFEM-EFGM. The proposed method combines the best features of FFEM and EFGM, in the sense that no structured mesh or special enriched basis functions are necessary and no post-processing (employing any path-independent integrals) is needed to determine fracture parameters such as stress-intensity factors (SIFs) and T-stress. The numerical results show that SIFs and T-stress obtained using the proposed method, are in excellent agreement with the reference solutions for the structural and crack geometries considered in the present study. Also a parametric study is carried out to examine the effects of the integration order, the similarity ratio, the number of transformation terms, and the crack-length to width ratio, on the quality of the numerical solutions.
EN
A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2D), anisotropic and linear elastic solids with continuously varying material properties. Both quasi-static thermal and transient elastodynamic problems are considered. For time-dependent problems, the Laplace transform technique is utilized. The analyzed domain is divided into small subdomains of circular shapes. A unit step function is used as the test function in the local weak form. It leads to Local Integral Equations (LIE) involving a domain-integral only in the case of transient dynamic problems. The Moving Least Squares (MLS) method is adopted for approximating the physical quantities in the LIE. Efficient numerical methods are presented to compute the fracture parameters, namely, the stress intensity factors and the T-stress, for a crack in Functionally Graded Materials (FGM). The path-independent integral representations for stress intensity factors and T-stresses in continuously non-homogeneous FGM are presented.
PL
Przedstawiono bezsiatkową metodę analizy szczelin opartą na podejściu Petrova-Galerkina dla dwuwymiarowych liniowo-sprężystych i anizotropowych ośrodków o zmieniających się własnościach materiałowych. Rozważono zarówno kwazistatyczne problemy naprężeń cieplnych, jak i zagadnienia elastodynamiki, w których zastosowano aparat transformacji Laplace'a. Badany obszar podzielono na małe podobszary kołowe. Jako funkcję testową w lokalnej, słabej postaci zastosowano jednostkową funkcję schodkową, co prowadzi do lokalnych równań całkowych (LIE). Metodę ruchomych najmniejszych kwadratów (MLS) zastosowano do przybliżenia wielkości fizycznych w LIE. Przedstawiono efektywne metody numeryczne wyznaczania parametrów pękania, a w szczególności współczynników koncentracji naprężeń oraz naprężeń T dla szczelin w materiałach funkcjonalnie gradientowych (FGM). Przedstawiono niezależne od drogi całkowania reprezentacje tych parametrów w materiałach FGM o kontynualnie zmieniającej się niejednorodności.
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