Abstract
Meshfree method is a new numerical method whose solution domain only discredited into independent nodes. To model crack discontinuous interface in practical, the equivalent distance for the weight function arguments is adapted. Firstly, the paper analysis the feature of the function, which point out that the methods have their own disadvantages. And then the paper put forward new binary linear equation, which is used to the weight function arguments to dispose of the crack’s noncontiguous interface. The function can simulate the displacement field around crack tip or crack closure line and also avoid the value overflow phenomenon which the node and a computation superposition occurs in the present processing method. The method has provided new mentality and idea for the present meshfree method in crack analysis. Finally three typical crack theoretical models are established as example. The comparison with the analytical solution shows that the displacement value the crack and the stress intensity factors has a better precise based on the new method, and also verified the method is valid.DOI: http://dx.doi.org/10.5755/j01.mech.24.3.19009
Highlights
Most fracture mechanics problems in engineering are solved by numerical analysis method such as finite element method (FEM) or boundary element method [1,2], because only few simple and special fracture mechanics problems can be solved analytically.Mesh free method is a new numerical method that appeared in recent years
In order to simulate the diffraction effect including visibility method and transparency attenuation in crack problem, the equivalent distance as weight function argument need to be calculated, which is the main strategy of mesh free method to simulate the influence of crack
The new method can simulate the displacement field around crack tip or crack closure line and avoid the value overflow phenomenon which the node and a computation superposition occurs in the present processing method
Summary
Most fracture mechanics problems in engineering are solved by numerical analysis method such as finite element method (FEM) or boundary element method [1,2], because only few simple and special fracture mechanics problems can be solved analytically. As a new method in development, its rigorous mathematical derivation and computational efficiency is still behind the FEM When it used to deal with discontinuous interface problems such as crack, its base function, weight function argument and approximate function etc. There are mainly three criterions to simulate the discontinuity line in the mesh free method: visibility criterion, diffraction criterion and transparency attenuation criterion [4]. In order to simulate the diffraction effect including visibility method and transparency attenuation in crack problem, the equivalent distance as weight function argument need to be calculated, which is the main strategy of mesh free method to simulate the influence of crack. The comparison with the analytical solution shows that their stress intensity factors have a better precise based on the new function according to the diffraction criterion, which verified the method valid
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