Int. J. Appl. Comput. Math (2019) 5:165
https://doi.org/10.1007/s40819-019-0752-6
ORIGINAL PAPER
P-Wave Interaction in a Cracked Orthotropic Strip
Sanatan Jana
1
· S. C. Mandal
1
© Springer Nature India Private Limited 2019
Abstract
In this paper diffraction of P-Waves in an infinite orthotropic strip containing two coplanar
Griffith cracks is analyzed. Using Fourier transform the problem is reduced to a system
of dual integral equation. Abel’s transform technique is used to further reduce the system
of dual integral equation to a Fredholm integral equation of second kind and finally the
integral equation is solved numerically to find the Stress Intensity Factor (SIF). Graphical
representation has been made to show the effect of material orthotropy.
Keywords Griffith crack · Orthotropic strip · Symmetric position · P-wave · Stress intensity
factor
Introduction
Recently the study of nature of elastic waves in presence of cracks has gained momentum in
many engineering applications like designing metal and polymer forming process, machining
etc. These research problems have great importance and versatility in potential applications
in the fields of seismology and geophysics. Analytic study of cracks and inclusion are very
important to civil, aerospace, nuclear and mechanical engineering. Specially in civil engineer-
ing for designing of load bearing components of vehicles, power generation, the reduction
of cracks are the important and challenging issue. There are a number of researchers dealing
with problems involving one or more cracks in infinite anisotropic medium. It is prominent
in literature that stress has a square root singularity at the tip of the crack. A non dimensional
quantity SIF is calculated to find the nature of stress at the tip of the crack. Erdogan and Gupta
[1], Dhaliwal et al. [2] studied the problems of interfacial Griffith crack in bonded isotropic
elastic materials. Ohyoshi [3] solved to quantify the impact of orthotropy on singular stresses
for a finite crack by considering the diffraction of P and SV waves by a finite crack located on
a symmetric surface of orthotropy. Delale and Erdogan [4] considered corresponding static
problem of internal and edge cracks in an orthotropic strip. Chen and Sih [5] solved the elas-
todynamic crack problems. Problems with Griffith cracks in orthotropic elastic material were
B Sanatan Jana
sanatanmath@gmail.com
S. C. Mandal
scmandal.ju@gmail.com
1
Department of Mathematics, Jadavpur University, Kolkata 700032, India
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