written 7.0 years ago by | • modified 6.9 years ago |
E=200GPa, v=0.3, t=10mm
Now x1,y1=10,20
x2,y2=70,20
x3,y3=40,60
β1=y2−y3=20−60=−40
β2=y3−y1=60−20=40
β3=y1−y2=20−00=0
γ1=−(x2−x3)=−(70−40)=−30
γ2=−(x3−x1)=−(40−10)=−30
γ3=−(x1−x2)=−(10−70)=60
2A=|1x1y11x2y21x3y3|=|110201702014060|
=1(70∗60∗−40∗20)−10(60−20)+20(40−70)
=3400−400+(−600)
∴2A=2400mm2
[B]=12A[β10β20β300γ10γ20γ3γ1β1γ2β2γ3β3]
[B]=12400[−400400000−300−30060−30−40−3040600]
[B]=[−0.016700.01670000−0.01250−0.012500.025−0.0125−0.0167−0.01250.01670.0250]
[B]T=[−0.01670−0.01250−0.01250.01670.01670−0.01250−0.01250.0167000.02500.0250]
Plane-Stress condition,
[D]=E1−v2[1v0v10001−v2]
E=200GPa=2∗103N/mm2,v=0.3
[D]=2∗1031−0.32[10.300.310001−0.32]
[D]=1.99∗103[10.300.310000.35]
v=t∗A=10∗24002=12000mm2
Stiffness matrix [K] is given by,
[K]=[B]T[D][B]t∗A
[K]=1.99∗103∗1200∗[−0.01670−0.01250−0.01250.01670.01670−0.01250−0.01250.0167000.02500.0250]∗[10.300.310000.35]∗[−0.016700.01670000−0.01250−0.012500.025−0.0125−0.0167−0.01250.01670.0250]
[K]=106∗[0.8768000000.35710.66850000−0.58840.02750.8768000−0.02750.1557−0.35710.668500−0.2885−0.3846−0.28850.38460.57690−0.3297−0.82420.3797−0.824201.6464]