performance_index - Cantilever Beam, end load: δ =...

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Cantilever Beam, end load: δ = [FL 3 ]/[3EI] [constraint] Rectangular section, A = bt; I = bt 3 /12; m = bLt ρ [objective function] , δ = [4FL 3 /[Ebt 3 ] [a] b and L fixed, t free t 3 = [4FL 3 ]/[Eb δ ] t 3 = m 3 /[b 3 L 3 ρ 3 ] m 3 = [4Fb 2 L 6 ρ 3 ]/[E δ ] m = [4F/ δ ] 1/2 [b 1/2 L] 2 [ ρ /E 1/3 ] M 1 = E 1/3 / ρ log[M 1 ] = [1/3]log[E] - log[ ρ ]; log[E] = 3log[M 1 ] + 3log[ ρ ] M 1 has a numerical value of [100*10 9 N*m -2 ] 1/3 /1.0 Mg*m -3 = M 1 = 4640 N 1/3 *m 7/3 /Mg Example F = 100N, b = 0.3m, d = 0.05m, L = 2m m = 7.73x10 -3 Mg = 7.73 kg for flexible low density foam [ r = ~ 0.02 Mg/m 3 ], t = 64 cm!
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[b] L fixed, b and t free [1] single constraint, limited deflection, d [i] b coupling b = m/tL ρ = [4FL 3 /[E δ t 3 ] m = [4FL 4 ρ ]/[E δ t 2 ] = [4F/ δ max ][L 4 /t 2 ][ ρ /E]; M 2 = E/ r [ii] t coupling t 3 = [4FL 3 ]/[Eb δ ] = m 3 /[ ρ 3 L 3 b 3 ] m = [4F/ δ ] 1/3 [L 2 b 2/3 ][ ρ 3 /E]; M 3 = E 1/3 / r [2] dual constraints - d and s f use the two constraint equations to determine values for free variables b and t F max = 4[I/y m
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performance_index - Cantilever Beam, end load: δ =...

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