(a) Draw sketches and derive the reduction of the stiffness matrix for an anisotropic material to...

 

 

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(a) Draw sketches and derive the reduction of the stiffness matrix for an anisotropic material to that of an orthotropic material according to the material symmetry. The stiffness for an anisotropic material is [C1 C2 C3 C4 C15 C16 C12 C22 C23 C24 C25 C25 C13 C23 C3 C34 C35 C36 C14 C24 C34 C44 C45 C46 C15 C25 C35 C45 C55 C56 C16 C25 C36 C46 C56 C66 and the stiffness for an orthotropic material is [C C12 C13 I 0 0 C12 C2 C3 0 0 C13 C3 C33 0 0 0 0 0 0 C44 0 0 0 0 0 0 C55 0 0 0 0 0 0 C66 [14 marks] b) A unidirectional carbon/epoxy lamina with fibre direction at 30 to the reference x-axis is loaded under pure shear stress, as shown in Figure 2. It was found that the value of the maximum positive shear stress was four times the value of the maximum negative shear stress that can be applied on this lamina, 47max The material properties are: = =100=1672 1600 MPa, t2>0. = Using the maximum stress failure theory, determine the value of 0-30 Figure 2 (a) Draw sketches and derive the reduction of the stiffness matrix for an anisotropic material to that of an orthotropic material according to the material symmetry. The stiffness for an anisotropic material is [C1 C2 C3 C4 C15 C16 C12 C22 C23 C24 C25 C25 C13 C23 C3 C34 C35 C36 C14 C24 C34 C44 C45 C46 C15 C25 C35 C45 C55 C56 C16 C25 C36 C46 C56 C66 and the stiffness for an orthotropic material is [C C12 C13 I 0 0 C12 C2 C3 0 0 C13 C3 C33 0 0 0 0 0 0 C44 0 0 0 0 0 0 C55 0 0 0 0 0 0 C66 [14 marks] b) A unidirectional carbon/epoxy lamina with fibre direction at 30 to the reference x-axis is loaded under pure shear stress, as shown in Figure 2. It was found that the value of the maximum positive shear stress was four times the value of the maximum negative shear stress that can be applied on this lamina, 47max The material properties are: = =100=1672 1600 MPa, t2>0. = Using the maximum stress failure theory, determine the value of 0-30 Figure 2