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Lecture 3 : Potential Energy

Lecture 3 : Potential Energy. Hans Welleman. Potential Energy. E p. F g =mg. mgh 1. mgh 1.  h. mgh 2. mgh 2. F g =mg. h. plane of reference. h. no kinetic energy (statics). Total Energy. Sum of all energy in a system is constant Sum of all Potential energy = C Potential energy:

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Lecture 3 : Potential Energy

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  1. Lecture 3 :Potential Energy Hans Welleman

  2. Potential Energy Ep Fg=mg mgh1 mgh1 h mgh2 mgh2 Fg=mg h plane of reference h no kinetic energy (statics) Work and Energy methods

  3. Total Energy • Sum of all energy in a system is constant • Sum of all Potential energy = C • Potential energy: • Loads (energy with respect to reference, reduces) • Strain energie (Ev, increases) Work and Energy methods

  4. Stable Equilibrium V x pertubation Equilibrium Stationary Energy Function (hor. tangent) Work and Energy methods

  5. F force F F u F u displ. Situation 0 Situation 1 Situation 2 spring characteristics Potential Energy due to LoadsLoad Potential Work and Energy methods

  6. Stationary Energy Function at a Minimum Energy level • Extreme = derivative with respect to a governing variable ( u ) must be zero • Extreme is a minimum = 2nd deriv > 0 principle of minimum potential energy Work and Energy methods

  7. Application • Approximate displacement field • Demand Stationary Potential Energy: derivative(s) of V with respect to all governing variables ai must be zero. Work and Energy methods

  8. F x w(x) l z, w Example : Beam Work and Energy methods

  9. Solution Work and Energy methods

  10. Minimalise approximation Work and Energy methods

  11. k k k F a 4a 2a Example : Rigid Block Work and Energy methods

  12. k k k u2 u3 u1 F 4a 2a Displacement field u (assumption) Work and Energy methods

  13. Result exact solution Work and Energy methods

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