Question

In the weak form of the principle of virtual displacements, 0=\(\int_{V_e}\)(σijδεij+ρüiδui)dV-\(\int_{V_e}\)fiδuidV-∮set̂iδuids , applied to plane finite elastic element,which term corresponds to virtual strain energy stored in the body?

(a) \(\int_{V_e}\)(σijδεij)dV

(b) ∮set̂ iδuids

(c) \(\int_{V_e}\)(ρü iδui)dV

(d) \(\int_{V_e}\)fiδuidV

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The above asked question is from Plane Elasticity topic in division Plane Elasticity of Finite Element Method

Answer 1

Correct option is (a) \(\int_{V_e}\)(σijδεij)dV

To elaborate: There are four terms in the vector form of the principle of virtual displacements applied to plane finite elastic element, 0=\(\int_{V_e}\)(σijδεij+ρüiδui)dV-\(\int_{V_e}\)fiδuidV-∮set̂iδuids. The first term in the equation corresponds to the virtual strain energy stored in the body.The second term deals with 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.