Question

For a plane elasticity problem, which term in the weak form of the principle of virtual displacements is affected by a change in the applied surface traction forces?

(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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My enquiry is from Plane Elasticity topic in portion Plane Elasticity of Finite Element Method

Answer 1

Correct option is (b) ∮set̂ iδuids

To elaborate: The vector form of the principle of virtual displacements applied to the plane finite elastic element consists of four terms. Two terms correspond to energy stored in the body. The term, ∮set̂ iδuids represents the virtual work done by the surface traction forces, and thus, it is affected by a change in the applied surface traction forces.