Evaluation of fracture parameters for crack problems in fgm by a meshless method

Sladek, J.; Sladek, V.; Zhang, C.; Tan, C.-L.

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Tytuł artykułu

Evaluation of fracture parameters for crack problems in fgm by a meshless method

Autorzy

Sladek J. , Sladek V. , Zhang C. , Tan C.-L.

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Wyznaczanie parametrów pękania dla szczelin w materiałach funkcjonalnie gradientowych metodą bezsiatkową

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Abstrakty

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.

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.

Słowa kluczowe

stress intensity factors T-stress meshless methods hermoelasticity nonhomogenity orthotropic materials

parametry pękania analiza szczelin naprężenia T materiały funkcjonalnie gradientowe

Wydawca

Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej

Czasopismo

Journal of Theoretical and Applied Mechanics

Rocznik

2006

Tom

Vol. 44 nr 3

Strony

603--636

Opis fizyczny

Bibliogr. 63 poz., rys.

Twórcy

autor

Sladek J.

autor

Sladek V.

autor

Zhang C.

autor

Tan C.-L.

Institute of Construction and Architecture, Slovak Academy of Sciences, Bratislava, Slovakia, usarslad@savba.sk

Bibliografia

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