Elliptical crack and punch problems solved by integral equation method for piezoelectric media |
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Authors: | T K Saha S Saha |
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Institution: | 1. Department of Mathematics, Surendranath College, 24/2 M.G. Road, Kolkata, 700009, India 2. Department of Mathematics, S.R.S. Vidyamahapitha, Kamarpukur, Hooghly, West Bengal, India
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Abstract: | The problem of an elliptical crack embedded in an unbounded transversely isotropic piezoelectric media with the crack-plane
parallel to the plane of isotropy of the media and subjected to remote normal mechanical as well as electric loading is considered
first. The problem has been successfully reduced to a pair of coupled integral equations that are suitable for the application
of an integral equation method developed earlier for three-dimensional problems of LEFM. Solution to the mechanical displacement
and electric potentials are obtained for prescribed uniform loadings and expressions for corresponding intensity factors and
crack opening displacement are deduced. The above method has further been applied to solve the problem of a rigid flat-ended
elliptical punch indenting a transversely isotropic piezoelectric half-space surface with the plane of isotropy parallel to
the surface. Solutions to mechanical stress and electric displacement are obtained for prescribed constant normal displacement
and constant electric potential interior to the elliptical region and expression for the total force required to maintain
a prescribed indentation is deduced. |
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