HW6-solution

HW6-solution - Aerospace Structural Composites I Homework 6...

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Aerospace Structural Composites I Homework 6 Anirban Chaudhuri 1. The unidirectional Boron/Epoxy layer of Example 6.2.1 (using E 1 = 204GPa, E 2 = 18.5GPa, G 12 = 5.59GPa, 12 = 0.23, t = 0.125mm) is to be loaded by combined axial and shear stresses with xy x r . Determine the strength of this layer based on the Tsai-Hill failure criterion as a function of the fiber orientation in the range 0 o 90 o , and plot the strength for r = 0.05 and r = 0.2 . Typical strength properties of Boron/Epoxy layers are X t = 1260MPa, X c = 2500MPa, Y t = 61MPa, Y c = 202MPa, and S = 67MPa. Solution: The stresses in the principal direction can be found by using the equation (1). 22 1 2 12 2 2 x y xy mn m n nm m n mn mn m n         …(1) where, m=cos and n=sin . We have y =0 and xy = r x . So the principal stresses are given below. 1 2 12 () (1 ) x x x mr n nr m mn r     …(2) Tsai-Hill criterion is given in equation (3) [Eq. 6.2.11 in book] 2 12 1 2 1 2 2 2 111 1 1 tt t XYX S     …(3) For the case of compressive loading the X t and Y t are replaced by X c and Y c respectively. The values found in equation (2) are substituted in equation (3) for both tensile and compressive loading case and the strengths are plotted for r = 0.05 and r = 0.2 . The strength ( x ) in each case is found by solving the equation (3) (after substituting the values) in MATLAB. The MATLAB code used for this purpose is given in Appendix I.

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