184 Finite Element Analysis and Design 10. The boundary value problem for a clamped-clamped beam can be written as 44( )0,01(0)(1)(0)0 : boundary condtionsdwp xxdxdwdwwwdxdxWhen a uniformly distributed load is applied; i.e., 0()p xp, calculate the approximate beam deflection wxusing the Galerkin method. Hint: Assume the approximate deflection as 22( )( )1w xc xcxx. Solution: There is only one trial function whose second derivative becomes 2( )21212xxxThen, the coefficient matrix and the vector on the RHS become
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