Galerkin Method

In Galerkin method, we choose

for .

(3.76)

Note that the constraints on arising out of the admissibility conditions of are as follows. The first admissibility condition requires that the functions must be zero at , (that is, at the point of application of the Dirichlet boundary condition on ). Note that this constraint is identical to the condition (3.71). The second condition implies that should be unconstrained at . The third condition requires that the derivative must be finite over the whole interval (0, L ).

Substituting the expression (3.76) for in equation (3.74), we get

for

(3.77)

Now, define the following :

,	(3.78)
	(3.79)

Then, equation (3.77) becomes

(3.80)

In matrix form, this can be written as :

(3.81)

Note that, we get the same set of algebraic equations as in the Ritz method (equations 3.13-3.16). Therefore, as in the Ritz method, the stiffness matrix is symmetric and positive definite.