Energy_03_Complementary_Strain_Energy - Section 5.3 5.3...

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Section 5.3 Solid Mechanics Part I Kelly 194 5.3 Complementary Energy The linear elastic solid was considered in the previous section, with the characteristic straight force-deflection curve for axial deformations, Fig. 5.2.2. Here, consider the more general case of a bar of non-linear elastic material, of length L , fixed at one end and subjected to a steadily increasing force P . The work dW done in extending the bar a small amount Δ d is Δ = Pd dW (5.3.1) Force is now no longer proportional to extension Δ , Fig. 5.3.1. However, the total work done during the complete extension up to a final force P and final extension Δ is once again the total area beneath the force-extension curve. The work done is equal to the stored elastic strain energy which must now be expressed as an integral, Δ = Δ d P U 0 (5.3.2) The strain energy can be calculated if the precise force-deflection relationship is known. Figure 5.3.1: force-displacement curve for a non-linear material 5.3.1 Complementary Energy
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This note was uploaded on 01/20/2012 for the course ENGINEERIN 1 taught by Professor Staff during the Fall '11 term at Auckland.

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Energy_03_Complementary_Strain_Energy - Section 5.3 5.3...

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