Consider the cantilever beam problem shown previously in Exercise 8.2 with no axial force (N =0). Assume

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Consider the cantilever beam problem shown previously in Exercise 8.2 with no axial force (N =0). Assume a plane stress anisotropic model given by Hooke’s law (11.5.1) and governed by the Airy stress function equation (11.5.6). Show that the stress function:

3P [cxy- 4c3 xy S16 -+ 3 6511 - (26x - y)] 3P 0x = -2-3x - 2018 (G-2). ox xy+ 3P S16 2c3 S113 satisfies the

Next show that these stresses satisfy the problem boundary conditions in the usual sense with
exact pointwise specification on y =± c, and only resultant force conditions on the end's x = 0
and x = L. What happens to this solution if we let the material become orthotropic?

Data from exercise 8.2

Show that the Airy function:

3P 4c (xy- xy N + 3c solves the following cantilever beam problem, as shown in the following figure. As usual

Equation 11.5.1

ex = S110x + S120y + S165xy ey = S120x + S220y + S26Txy 2exy S160x+S260y + S665xy

Equation 11.5.6

ato $22x - 2526 ax ay at $ xJy +(2S12 +S66). a 24 = +Su- 0 xy dy4 2516

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