2.(10 points)What are requirements for shape function?The quadratic mP(x.yayis incomplete but symmetric.st fo representing the fied variable a four-node rectangular element having 1 degree of freedom per node?Explain. Solution:Shape functions must meet:(1)Completeness:(2)Compatibility. It's wrong,because it cannot represent rigid motion and constant strain status compatibility,that is be like this:P(x,y)=a+bx+cy+dxy.2. (10 points) What are requirements for shape function? The quadratic polynomial P(x,y)=a0+a1x 2 +a2xy+a3y 2 is incomplete but symmetric. Is this function suitable for representing the field variable in a four-node rectangular element having 1 degree of freedom per node? Explain. Solution: Shape functions must meet: (1) Completeness; (2) Compatibility. It’s wrong, because it cannot represent rigid motion and constant strain status (for structural analysis), and cannot guarantee the compatibility, that is continuity of field variables along the common boundary. The right one should be like this: P(x,y)=a+bx+cy+dxy