Hi guys, I'm recently using FlexPDE to find the resonant frequencies of a torsional oscillator, but it does not match the analytic solution. It uses a Finite Element Method to find solutions.(adsbygoogle = window.adsbygoogle || []).push({});

Is there something wrong with the equations I'm using?

C11 = G*(1-nu)

C12 = G*nu

C13 = G*nu

C22 = G*(1-nu)

C23 = G*nu

C33 = G*(1-nu)

C44 = G*(1-2*nu)/2

Strains

ex = dx(U)

ey = dy(V)

ez = dz(W)

gxy = dy(U) + dx(V)

gyz = dz(V) + dy(W)

gzx = dx(W) + dz(U)

VARIABLES

U { X displacement }

V { Y displacement }

W { Z displacement }

Stresses

Sx = C11*ex + C12*ey + C13*ez

Sy = C12*ex + C22*ey + C23*ez

Sz = C13*ex + C23*ey + C33*ez

Txy = C44*gxy

Tyz = C44*gyz

Tzx = C44*gzx

EQUATIONS

U: dx(Sx) + dy(Txy) + dz(Tzx) + lambda*rho*U = 0 { the U-displacement equation }

V: dx(Txy) + dy(Sy) + dz(Tyz) + lambda*rho*V = 0 { the V-displacement equation }

W: dx(Tzx) + dy(Tyz) + dz(Sz) + lambda*rho*W = 0 { the W-displacement equation }

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# [FlexPDE] Not sure if displacement equations are right

Can you offer guidance or do you also need help?

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