A thin-walled cylindrical pressure vessel is made of composite materials, and is loaded by internal pressure,...

 

  
  

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A thin-walled cylindrical pressure vessel is made of composite materials, and is loaded by internal pressure, p, and an external torque, T, as shown in Figure 1. Diameter of the vessel is D = 100 cm. the laminate selection is [0/+45/902], the fibre and matrix properties are given in Tables 2 and 3. Each layer is with the same thickness, and the total thickness of the wall, h= 12.5 mm. and the loading case isp=1MPa; T=100.So kN.m; So > 0. Perform stress and failure analysis of the composite material system to find out the maximum value(s) of So for the first ply failure and the second ply failure. ih Figure 1. Thin-wall cylindrical pressure vessel under internal pressure and torque loading Table 2 elastic and strength properties of the fibres property symbol Longitudinal young's modulus Transverse young's modulus In-plane shear modulus Poisson's ratio Longitudinal tensile strength Fibre volume fraction E₁f Ezf G12f V12f oft Vf units GPa GPa GPa MPa fibre 150 16 8 0.32 1650 0.65 Table 3 elastic and strength properties of the matrix property symbol young's modulus shear modulus Poisson's ratio Tensile strength Compressive strength Shear strength Em Gm Vm น omt omc Tm units GPa GPa MPa MPa MPa fibre 3.4 1.3 0.31 68 210 110 1.Find the laminate stiffness matrices [A], [B] and [D]. 2.Calculate the unit forces acting on an element of the cylindrical shell, {N}r-y. N₁ = ₂h, Ny = ₂h, and Nry = Tryh; {M}r-y can be considered as zero in this case. {E}I-Y 3.Calculate the mid-plane strains in the laminate, 4.Calculate the curvatures in the laminate, {k}-y 5.Calculate the global strains, {}-y, at the surfaces of each lamina. 6.Calculate the global stresses, {0}-y,at the surfaces of each lamina. 7.Find the local stresses, {0}₁-2 ???, at the surfaces of each lamina. A thin-walled cylindrical pressure vessel is made of composite materials, and is loaded by internal pressure, p, and an external torque, T, as shown in Figure 1. Diameter of the vessel is D = 100 cm. the laminate selection is [0/+45/902], the fibre and matrix properties are given in Tables 2 and 3. Each layer is with the same thickness, and the total thickness of the wall, h= 12.5 mm. and the loading case isp=1MPa; T=100.So kN.m; So > 0. Perform stress and failure analysis of the composite material system to find out the maximum value(s) of So for the first ply failure and the second ply failure. ih Figure 1. Thin-wall cylindrical pressure vessel under internal pressure and torque loading Table 2 elastic and strength properties of the fibres property symbol Longitudinal young's modulus Transverse young's modulus In-plane shear modulus Poisson's ratio Longitudinal tensile strength Fibre volume fraction E₁f Ezf G12f V12f oft Vf units GPa GPa GPa MPa fibre 150 16 8 0.32 1650 0.65 Table 3 elastic and strength properties of the matrix property symbol young's modulus shear modulus Poisson's ratio Tensile strength Compressive strength Shear strength Em Gm Vm น omt omc Tm units GPa GPa MPa MPa MPa fibre 3.4 1.3 0.31 68 210 110 1.Find the laminate stiffness matrices [A], [B] and [D]. 2.Calculate the unit forces acting on an element of the cylindrical shell, {N}r-y. N₁ = ₂h, Ny = ₂h, and Nry = Tryh; {M}r-y can be considered as zero in this case. {E}I-Y 3.Calculate the mid-plane strains in the laminate, 4.Calculate the curvatures in the laminate, {k}-y 5.Calculate the global strains, {}-y, at the surfaces of each lamina. 6.Calculate the global stresses, {0}-y,at the surfaces of each lamina. 7.Find the local stresses, {0}₁-2 ???, at the surfaces of each lamina.

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