unit7_notes

# unit7_notes - 16.21 Techniques of Structural Analysis and...

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16.21 Techniques of Structural Analysis and Design Spring 2005 Section 2 - Energy and Variational Principles Unit #7 - Concepts of work and energy Ra´ul Radovitzky March 2, 2005 Work Figure 1: Work of a force on a moving particle 1

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± Work done by a force: dW = f d u = f i u i = f d u cos ( ² fu ) (1) · B B W AB = dW = f d u (2) · A A Work done by a moment: dW = M = M i θ i (3) · B B W AB = dW = M (4) · A A Extend deFnition to material bodies: total work is the addition of the work done on all particles: by forces distributed over the volume: W = f u dV · V by forces distributed over the surface: W = t u dS · S by concentrated forces: n W = f i u ( x i ) · i =1 Another classiFcation: Work done by external forces: we will assume that external forces don’t change during the motion or deformation, i.e., they are independent of the displacements. This will lead to the potential character of the external work and to the deFnition of the potential of the external forces
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## This note was uploaded on 11/07/2011 for the course AERO 16.21 taught by Professor Dffs during the Fall '10 term at MIT.

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unit7_notes - 16.21 Techniques of Structural Analysis and...

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