Question

If the equation ∫Ωche\((\frac{\partial w_1}{\partial x}\sigma_{xx}+\frac{\partial w_1}{\partial y}\)σxy-w1fx+ρw1\(\ddot{u_x})\)dxdy-∮Γchew1(σxxnx+σxyny)ds=0 represents the weak form of plane elasticity equations, then the weight functions w1 and w2 are the first variations of ux and uy, respectively.

(a) True

(b) False

I have been asked this question during an interview.

I need to ask this question from Plane Elasticity in portion Plane Elasticity of Finite Element Method

Answer 1

Right answer is (a) True

Easy explanation: The equations ∫Ωche\((\frac{\partial w_1}{\partial x}\sigma_{xx}+\frac{\partial w_1}{\partial y}\)σxy-w1fx+ρw1\(\ddot{u_x})\)dxdy-∮Γchew1(σxxnx+σxyny)ds=0 and ∫Ωche\((\frac{\partial w_2}{\partial x}\sigma_{xy}+\frac{\partial w_2}{\partial y}\)σyy-w2fy+ρw2\(\ddot{u_y})\)dxdy-∮Γchew2(σxynx+σyyny)ds=0 represents the weak forms of plane elasticity equations, where Ω is the area of cross-section of the domain, ┌ is a portion of element boundary, and the weight functions w1 and w2 are the first variations of ux and uy respectively.