## Lectures on transform methods |

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### Contents

The Stress Intensity Factor for a Griffith Crack in an Elastic | 1 |

The Stress Intensity Factor for a PennyShaped Crack in an Elastic | 17 |

Inversion Formulae for Integral Transform Pairs of General Kinds | 28 |

2 other sections not shown

### Common terms and phrases

Abel transforms alternative form Applying the operator Bessel function boundary conditions boundary value problems calculate components cos(vt)dt cosh deduce immediately defined by equation derived displacement vector elastic equilibrium equation 2.8 equation 3.1 equation 5-5 equations of elastic equivalent Fourier cosine transform Fourier sine transform Fourier Transforms function f(x function u(p,$,z Gegenbauer polynomial Griffith crack Hankel transform harmonic hence hypergeometric function hypergeometric series I. N. Sneddon infinite wedge integral equation integral transform pairs inversion formula inversion theorem Kontorovich-Lebedev transform last equation Lebedev Lj(x magnitude F act Mellin transform obtain the equation odd function order zero penny-shaped crack point forces Poisson's ratio positive integer Proc relation Replacing s_ result satisfies the boundary satisfies the condition Similarly sinh solution f(x solution of Problem stress intensity factor substitute from equation theory of elasticity Tn(x transform of f(x transform of order Transforms whose kernels write written