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Underplane strain condition, what is the value of εyy if the problem is characterized by the displacement field ux=2x+3y, uy=5y^2, and uz=0?

(a) 10y

(b) 5y

(c) 3

(d) 0

I have been asked this question in homework.

Enquiry is from Plane Elasticity topic in portion Plane Elasticity of Finite Element Method

1 Answer

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Best answer
Correct answer is (a) 10y

The explanation is: The plane strain problems are characterized by the displacement field ux=ux(x,y), uy=uy(x,y) and uz=0, where (ux, uy, uz) denote the components of the displacement vector u in the (x, y, z) coordinatesystem. The displacement field results in the following strain field:

\(\epsilon_{xz}=\epsilon_{yz}=\epsilon_{zz}=0, \epsilon_{xx}=\frac{\partial u_x}{\partial x}, 2\epsilon_{xy}=\frac{\partial u_x}{\partial y}+\frac{\partial u_y}{\partial x}\) and \(\epsilon_{yy}=\frac{\partial u_y}{\partial y}\)

Thus, \(\epsilon_{yy}=\frac{\partial 5y^2}{\partial y}\)

=5*\(\frac{\partial y^2}{\partial y}\)



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