rayleigh_ritz_beam_uniform - Principle of Stationery...

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Principle of Stationery Potential Energy Among all admissible displaced configurations of a conservative system those that satisfy equations of equilibrium make the potential energy stationery with respect to small admissible variations of displacement. If the stationery condition is a relative minimum, the equilibrium state is stable. Example : For the beam shown, using an admissible displacement function ( )( ) x L x a x v = 1 , use the principle of stationery potential energy to find the maximum deflection of the beam. P x y,v Solution: The potential energy of the system is given by W - U = Π The strain energy in the beam is dV 2 1 U x x V = σ Since I My x = and correspondingly EI My x = , = V dV EI My I My 2 1 = V dV EI y M 2 2 2 2 1 Now given, 2 2 dx v d I E M =
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= V dV dx v d EI y I E U 2 2 2 2 2 2 2 2 1 V dV y dx v d E 2 2 2 2 2 1 = dx dA y dx
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rayleigh_ritz_beam_uniform - Principle of Stationery...

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