# 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-&oint;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.

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-&oint;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

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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-&oint;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-&oint;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.

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