GENETIC ALGORITHMS IN SIMULATING OPTIMAL STACKING SEQUENCE OF A COMPOSITE LAMINATE PLATE WITH CONSTANT THICKNESS

P.-F. Pai, S. Deng, C.-C. Lai, and P.-S. Wu

References

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  19. [19] S.A. Brah & J.L. Hunsucker, Branch and bound algorithmfor the flow shop with multiple processors, European JournalOperational Research, 51, 1991, 88–99.Appendix A¯S(k) =¯S(k)11¯S(k)12¯S(k)13 0 0 ¯S(k)16¯S(k)12¯S(k)22¯S(k)23 0 0 ¯S(k)26¯S(k)13¯S(k)23¯S(k)33 0 0 ¯S(k)360 0 0 ¯S(k)44¯S(k)45 00 0 0 ¯S(k)45¯S(k)55 0¯S(k)16¯S(k)26¯S(k)36 0 0 ¯S(k)66(A1)¯S(k): the compliance tensor of the k-th ply (A2)¯S(k)11 = S(k)11 m4+ (2S(k)12 + S(k)66 )m2n2+ S(k)22 n4(A3)¯S(k)12 = (S(k)11 + S(k)22 − S(k)66 )m2n2+ S(k)12 (m4+ n4) (A4)¯S(k)13 = S(k)13 m2+ S(k)23 n2(A5)¯S(k)22 = S(k)11 n4+ (2S(k)12 + S(k)66 )m2n2+ S(k)22 m4(A6)¯S(k)23 = S(k)13 n2+ S(k)23 m2(A7)¯S(k)33 = S(k)33 (A8)¯S(k)16 = (2S(k)11 − 2S(k)12 − S(k)66 )nm3− (2S(k)22 − 2S(k)12 − S(k)66 )mn3(A9)¯S(k)26 = (2S(k)11 − 2S12 − S66)n3m− (2S22 − 2S12 − S66)m3n (A10)¯S(k)36 = 2(S(k)13 − S(k)23 )mn (A11)¯S(k)44 = S(k)44 m2+ S(k)55 n2(A12)¯S(k)45 = (S(k)55 − S(k)44 )mn (A13)¯S(k)55 = S(k)44 n2+ S(k)55 m2(A14)¯S(k)66 = 4(S(k)11 − 2S(k)12 + S(k)22 )m2n2+ S(k)66 (m2− n2)2(A15)where:S(k)ij : the interlaminar strain of the k-th plyi, j: directionsm: cos θn: sin θAppendix Bf1 =12nk=1[˜σ(k)22 ]2¯S(k)22 −[ ¯S(k)12 ]2¯S(k)11(B1)f2 =1120nk=1{3[˜σ(k)22 ]2+ 15˜σ(k)22 B(k)4 + 20˜σ(k)22 B(k)5+ 20[B(k)4 ]2+ 60B(k)4 B(k)5 + 60[B(k)5 ]2}ׯS(k)22 −[ ¯S(k)13 ]2¯S(k)11(B2)f3 =16nk=1{[˜σ(k)22 ]2+ 3˜σ(k)22 B(k)4 + 3[B(k)4 ]2} ¯S(k)44 (B3)f4 =16nk=1{[˜σ(k)12 ]2+ 3˜σ(k)12 B(k)2 + 3[B(k)2 ]2} ¯S(k)55 (B4)f5 =32nk=1[˜σ(k)12 ]2¯S(k)66 −[ ¯S(k)16 ]¯S(k)11(B5)f6 =12nk=1˜σ(k)22 [˜σ(k)11¯S(k)11 + ˜σ(k)22¯S(k)12 + ˜σ(k)12¯S(k)16 ] (B6)f7 =12nk=1˜σ(k)12 [˜σ(k)11¯S(k)11 + ˜σ(k)22¯S(k)12 + ˜σ(k)12¯S(k)16 ] (B7)f8 =16nk=1{[˜σ(k)22 ]2+ 3˜σ(k)22 B(k)4 + 6˜σ(k)22 B(k)4 }ׯS(k)22 −¯S(k)12¯S(k)13¯S(k)11(B8)f9 = ˜σ(k)22 ˜σ(k)12¯S(k)26 −¯S(k)12¯S(k)16¯S(k)11(B9)f10 =16nk=1˜σ(k)12 [˜σ(k)22 + 3B(k)4 + 6B(k)5 ]¯S(k)36 −¯S(k)13¯S(k)16¯S(k)11(B10)f11 =16nk=1[2˜σ(k)22 ˜σ(k)12 + 3˜σ(k)22 B(k)2 + 3˜σ(k)12 B(k)4+ 6B(k)2 B(k)4 ] ¯S(k)45 (B11)67 doi:10.1016/0377-2217(91)90148-O

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