10 Composites

Pagina 1

Aerospace Structure – Exercises 11 1 Exercise #11 Composites Aerospace Structure – Exercises 11 2 EX. 1 Calculate the equivalent stiffness in bending for t he simply supported beam in the figure below, consi dering the given lamination sequence. Evaluate the displacement at L/2 and compare stiffn ess and weight with a beam in Aluminium with the sa me geometry. L = 100 mm b = 10 mm th = 0.8 mm (th UD = 0.1 mm ; th FB = 0.2 mm) q = 0.2 N/mm ρ = 1900 kg/m 3 Solution ( ) ( ) ( ) ( )                             −− −− =           ⇒                             − − =           xy yy xx xy yx xy y yx xy yyx yx xy xxy yx xy x xy yy xx xy yy xx xy yx yx y xy x xy yy xx G vv E vv Ev vv Ev vv E G EE v E v E γ ε ε τ σ σ τ σ σ γ ε ε 00 011 011 100 01 01 ( ) ( ) ( ) ( )                   −− −− = xy yx xy y yx xy yyx yx xy xxy yx xy x G vv E vv Ev vv Ev vv E 00 011 011 Q           = 4500 00 010060 3018 03018 150905 0UD Q           = 4500 00 0150905 3018 03018 10060 90 UD Q           = 4500 00 060150 3008 03008 60150 0FB Q Graphite UD 0° Graphite UD 90° Graphite FB 0° Ex [MPa] 150000 10000 60000 Ey [MPa] 10000 150000 60000 Gxy [MPa] 4500 4500 4500 v 0.3 0.02 0.05 Aerospace Structure – Exercises 11 3 ( ) ( ) ( )           = =−+−+−⋅=−= ∑ = − 192 00 02480 129 0129 4170 ) 0 . 02 . 0 () 2 . 03 . 0 () 3 . 04 . 0 (3 123 1 33 0 33 90 33 0 1 3 1 3 FB UD UD N i iii QQQZZQD mm NDth DDDE b x /97591 )( 12 22 3 2 12 22 11 =−= PLVC mm Lz qzqJEdz Lz qzqJEJE MM WW zMqLz qz M Tqz qL T L b x L b x L b x xx de xx yy 3 . 668 1 22 1 22 12 2 / 0 342 / 0 232 / 0 2 =      +−=      +−=′=Δ = − =′−= − =′+− = ∫∫ δδ If the beam is made with aluminum the calculations…