Consider an infinite solid, which contains a semi-infinite crack on the (x1,x3) plane. Suppose that the...

  

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Consider an infinite solid, which contains a semi-infinite crack on the (x1,x3) plane. Suppose that the solid deforms in plane strain and is subjected to bounded stress at infinity. The stress field near the tip of the crack can be derived from the Airy function 3/2 (cos3@/2+3 cos / 2) 32x KII 3/2 (sin 30/2 + sin 8/2) 2x a) Derive the stress equations in terms of polar coordinates using the definitions: Orr = 1 ap + 1 06 r r 202 000 86 r b) Check if the Airy stress functions satisfy the Biharmonic condition: Tre 10 2 1 (-8 (-) + - 0) r r Or (106) r r p=0 Consider an infinite solid, which contains a semi-infinite crack on the (x1,x3) plane. Suppose that the solid deforms in plane strain and is subjected to bounded stress at infinity. The stress field near the tip of the crack can be derived from the Airy function 3/2 (cos3@/2+3 cos / 2) 32x KII 3/2 (sin 30/2 + sin 8/2) 2x a) Derive the stress equations in terms of polar coordinates using the definitions: Orr = 1 ap + 1 06 r r 202 000 86 r b) Check if the Airy stress functions satisfy the Biharmonic condition: Tre 10 2 1 (-8 (-) + - 0) r r Or (106) r r p=0 Consider an infinite solid, which contains a semi-infinite crack on the (x1,x3) plane. Suppose that the solid deforms in plane strain and is subjected to bounded stress at infinity. The stress field near the tip of the crack can be derived from the Airy function 3/2 (cos3@/2+3 cos / 2) 32x KII 3/2 (sin 30/2 + sin 8/2) 2x a) Derive the stress equations in terms of polar coordinates using the definitions: Orr = 1 ap + 1 06 r r 202 000 86 r b) Check if the Airy stress functions satisfy the Biharmonic condition: Tre 10 2 1 (-8 (-) + - 0) r r Or (106) r r p=0

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In order to derive the stress equations in terms of polar coordinates using the given definitions we need to take the derivatives of the Airy stress f... View the full answer