VERSION HISTORY
LIRA-FEM
Accounting for orthotropy
New check and limitation on the specified parameters for orthotropy stiffness. The stiffness should be positive:
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for plate FEs ν12 ≥ 0, ν21 ≥ 0, ν12*ν21 < 1;
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for solids ν12 ≥ 0, ν21 ≥ 0, ν13 ≥ 0, ν31 ≥ 0, ν23 ≥ 0, ν32 ≥ 0,
ν12*ν21 + ν23*(ν12*ν31 + ν32) + ν13*(ν21*ν32 + ν31) < 1
Conditions that the matrix of physical constants for orthotropy is positively definite:
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for plate FEs E1*E2 > (0.5*(E1*ν12+E2*ν21))^2;
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for solids
E1*E2*(1-ν23*ν32)*(1-ν13*ν31) > (0.5*(E1*(ν12+ν13*ν32)+E2*(ν21+ν31*ν23)))^2
E1*E3*(1-ν23*ν32)*(1-ν12*ν32) > (0.5*(E1*(ν13+ν12*ν23)+E3*(ν31+ν21*ν32)))^2
E2*E3*(1-ν13*ν31)*(1-ν12*ν32) > (0.5*(E2*(ν23+ν13*ν21)+E3*(ν32+ν12*ν31)))^2