# In the weak form of the principle of virtual displacements applied to a plane elastic finite element, what does the term $\int_{V_e}$(ρü iδui)dV correspond to?

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In the weak form of the principle of virtual displacements applied to a plane elastic finite element, what does the term $\int_{V_e}$(ρü iδui)dV correspond to?

(a) Virtual strain energy

(b) Kinetic energy

(c) Virtual work done by the body force

(d) Virtual work done by the surface traction

I got this question in class test.

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

## 1 Answer

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Correct choice is (b) Kinetic energy

For explanation I would say: Thefour terms in the vector form of the principle of virtual displacements are present in the equation, 0=$\int_{V_e}$(σijδεij+ρüiδui)dV-$\int_{V_e}$fiδuidV-∮set̂iδuids. The given term corresponds to the kinetic energy stored in the body, the third term represents the virtual work done by the body force, and the fourth term represents the virtual work done by the surface traction.

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