9._Stationary_Rpinciple_-_Hw_5

9._Stationary_Rpinciple_-_Hw_5 - AERSP 301 Energy Methods...

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AERSP 301 Energy Methods Energy Methods The Stationary Principle The Stationary Principle Jose Palacios Fall 2009
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Energy Methods & The Stationary Principle Energy Methods & The Stationary Principle Energy Methods (Lagrangian Methods) vs. Newtonian Methods (based on Force/Moment Equilibrium) Energy Methods: we define Strain Energy and External Work (also Kinetic Energy, for dynamic problems) What is the difference between rigid and elastic bodies? – No Strain in rigid body (idealization, no body is rigid) Strain in elastic body Is there strain energy associate with “rigid” bodies? … “elastic” structures? What is Kinetic Energy? How does a rigid body behave under the application of loads? Can it undergo translation? Rotation? Elastic deformation? How does the behavior of an elastic body under the application of loads differ?
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Energy Methods & The Stationary Principle Energy Methods & The Stationary Principle When a force is applied to an elastic body, work is done. That work is stored as energy (Strain Energy) Consider the following case: Work done by force, F, as u (instantaneous displacement) goes from 0 q.
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Stationary Principle Stationary Principle Stationary Principle, or Principle of Minimum Total Potential Energy The external work potential is defined as: The work done by a system in expanding against forces exerted from outside Define a scalar function π (q) – Total Potential Energy For the spring problem The Stationary Principle states that among all geometrically possible displacements, q, π (q) is a minimum for the actual q.
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Stationary Principle
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9._Stationary_Rpinciple_-_Hw_5 - AERSP 301 Energy Methods...

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