1 11 2 22 2 3 0 13 0 11 11 11 11 0 11 0 2 0 13 12 12 12 0 14 0 14 0 32 0 32 ( ) sin , 2 ( ) cos , 1 ( ) [( 40 5 96 48 48 5 20 ( 1) 40 )sin ( 96 48 48 40 40 )cos 2 2 3 (20 20 )sin (20 2 w B w B w E hC E hB A A A E h B E h E h C A A A E hC E h C hE B hE B θ θ θ θ θ β κμ κμ κ β μ μ θ θ μ κμ κμ κ μ θ μ = = = − + − − − + + + + − − − − + + + + 0 31 0 31 0 21 24 22 21 4 42 41 0 3 20 )cos ] 2 5 ( ) 48 ( 1) ( ) sin2 cos2 2 ...... hE B hE B hE C C B A w B B E h θ μ β μ κ θ θ θ ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ + ⎪ ⎪ + − − + ⎪ = + + ⎪ ⎪ ⎪⎩ (10) where: ijA ， ij B ， ij C are the undetermined coefficients. Substituting Eq. (7)-(10) into Eq.(5), the generalized displacement fields of FGMs spherical shell are obtained. 5. Conclusion For a functionally graded spherical shell with Reissner effect, the higher order crack tip fields which are similar to the Williams’ solutions of crack problems in homogenous materials are obtained. As the in-homogeneity parameter 0→β , the solutions degenerate to the corresponding fields of isotropic homogeneous spherical shell with Reissner’s effect. Obviously, these results provide the theoretical basis for experimental investigation and engineering application. Acknowledgements The research is supported by the National Natural Science Foundation of China (No.11172332., No. 90305023) References [1] Y.Z. Li, C.T. Liu, Analysis of Reissner plate bending fracture problem. Acta Mechanica Sinica, 4 (1983) 366–374. [2] E. Reissner, The effect of transverse shear deformation on the bending of elastic plates. ASCE.J.Appl.Mech, (1945) 69–78. [3] F.Delale, Erdagan, Effect of transverse shear and material orthotropy in a cracked spherical
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