3-10 - 184 Finite Element Analysis and Design 10 The...

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184 Finite Element Analysis and Design 10. The boundary value problem for a clamped-clamped beam can be written as 4 4 ( ) 0, 0 1 (0) (1) (0) 0 : boundary condtions dw p x x dx dw dw ww dx dx When a uniformly distributed load is applied; i.e., 0 () p x p , calculate the approximate beam deflection wx using the Galerkin method. Hint: Assume the approximate deflection as   2 2 ( ) ( ) 1 w x c x cx x . Solution: There is only one trial function whose second derivative becomes 2 ( ) 2 12 12 x x x  Then, the coefficient matrix and the vector on the RHS become
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