Question

In solid mechanics, what is the correct vector form of the equations of motion for a plane elasticity problem?

(a) D*σ+f=ρü

(b) D*σ+f=ρu̇

(c) D^2*σ+f=ρü

(d) D*σ+f=ρu

This question was addressed to me in my homework.

The doubt is from Plane Elasticity in chapter Plane Elasticity of Finite Element Method

Answer 1

Right answer is (a) D*σ+f=ρü

For explanation I would say: For plane elasticity problems, the equations of motion are one of the governing equations. The vector form of equations of motion is D*σ+f=ρü, where f denotes body force vector, σ is the stress vector, u is the displacement vector, D is a matrix of differential operator and ρ is the density.