Abstract
By means of the theory of complex functions, dynamic propagation problems of mode III semi- infinite crack were researched. The problems studied can be facilely transformed into riemann-hilbert problems and the universal expression of analytical solutions of stress, displacement and dynamic stress intensity factor under the conditions of moving increasing loads Px/t and Pt2/x, respectively, are very facilely obtained using the measures of self-similar functions. In view of corresponding material properties, the mutative rule of dynamic stress intensity factor was illuminated very well.
Highlights
For an orthotropic anisotropic body, let the Cartesian co-ordinates be coincident with the axes of elastic symmetry
The problems studied can be facilely transformed into riemann-hilbert problems and the universal expression of analytical solutions of stress, displacement and dynamic stress intensity factor under the conditions of moving increasing loads Px/t and Pt2/x, respectively, are very facilely obtained using the measures of self-similar functions
Using the relative expression: f(x, y, t) = tn f(x/t, y/t), just n is an integer number; and the problem researched will be facilely translated into homogeneous functions of zeroth dimension, i.e., homogeneous functions
Summary
For an orthotropic anisotropic body, let the Cartesian co-ordinates be coincident with the axes of elastic symmetry. Utilizing relevant Representations of the anti-plane problem concerning elastodynamics equations of motion for an orthotropic anisotropic body, the general expressions can be rewritten in the following modality (Cherepanov, 1979; Nian-Chun et al, 2004; 2005; 2006; Atkinson, 1975; 1965):. When the crack moves at high speed, its dimension must relate to variables x and t, the crack edges subjected to loads have relation to variables x and t
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