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?
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.
Stationary Principle

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

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