I have a question regarding the shape functions. Why the shape function is kept orthogonal to residue in Galerkin method? Looking forward to hearing from you all.
Because the weight functions are equal to the shape functions (Wi=Ni) as you have Integral(Wi*R(q)dV)=0 and the reason is that they were initially defined by the derivative of the polynomial displacement q with respect to the constants ai (ex: q(x)=Sum(Ni(x)*qi)=Sum(ai*x¨^(i))). It is not necessary to use the definition of orthogonal functions but you need to know the differential equation of your problem in order to get the corresponding FE problem when using Galerkine's method.
Galerkine for Finite Elements
Hello Mudassir,
Because the weight functions are equal to the shape functions (Wi=Ni) as you have Integral(Wi*R(q)dV)=0 and the reason is that they were initially defined by the derivative of the polynomial displacement q with respect to the constants ai (ex: q(x)=Sum(Ni(x)*qi)=Sum(ai*x¨^(i))). It is not necessary to use the definition of orthogonal functions but you need to know the differential equation of your problem in order to get the corresponding FE problem when using Galerkine's method.