# What can one conclude about the displacement components ux and uy in the finite element model of the plane elasticity equations?

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What can one conclude about the displacement components ux and uy in the finite element model of the plane elasticity equations?

(a) They are primary variables and must be carried as primary nodal degrees of freedom

(b) They are secondary variables and must be carried as primary nodal degrees of freedom

(c) They are primary variables and must be carried as secondary nodal degrees of freedom

(d) They are secondary variables and must be carried as secondary nodal degrees of freedom

The question was posed to me in an interview for job.

This interesting question is from Plane Elasticity in section Plane Elasticity of Finite Element Method

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The correct option is (b) They are secondary variables and must be carried as primary nodal degrees of freedom

For explanation I would say: An examination of the weak form, 0=∫Ωehe$[\frac{\partial w_1}{\partial x}(c_{11}\frac{\partial u_x}{\partial x}+c_{12}\frac{\partial u_y}{\partial y}) + c_{66}\frac{\partial w_1}{\partial y} (\frac{\partial u_x}{\partial y} + \frac{\partial u_y}{\partial x})$+ρw1ux]dxdy-∫Ωehew1fxdxdy-∮┌dhew1txds reveals the following:

(i) ux and uy are the primary variables, which must be carried as the primary nodal degrees of freedom.

(ii) only first derivatives of ux and uywith respect to x and y, respectively, appear.

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