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approximate assume axis Barenblatt boundary conditions boundary value problem calculated circular hole coefficients cohesive forces components of stress conformal mapping consider conventional units coordinates corresponding cosh crack is given crack of length crack surface curve cylinder deduce defined denotes determining the stress displacement field displacement vector distribution of stress dual integral equations easily shown elastic equilibrium equations of elastic expression Figure formula Fredholm integral equation Griffith crack half-space harmonic function Hilbert problem hoop stress infinity internal pressure Lowengrub method notch obtain penny-shaped crack plane strain plane stress points polynomial pressure p0 problem of determining radius relation Section semi-infinite shearing stress shown in Fig sinh Sneddon solid solution strain energy stress components stress distribution stress field stress intensity factor substitute from equation symmetry tension tractions two-dimensional unit of length variation velocity vicinity