Unformatted text preview: Problem 4 Consider an elastic body B , with boundary ∂ B = ∂ B u ∪ ∂ B t , displacements u = ¯ u specified on ∂ B u , conservative tractions t applied on ∂ B t , and conservative body forces f applied throughout B . As discussed in class, the total potential energy of the body is Π[ u ] = Z B wdV + Z B GdV + Z ∂ B gdS, where w is the strain energy density and f i =-∂G ∂u i and t i =-∂g ∂u i . Complete the derivation outlined in class, to show that stationarity of Π requires that equilibium of the body and the appropriate traction and displacement conditions on the boundary be satisfied. 1...
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- Fall '04
- Energy, Trigraph, Calculus of variations, Euler–Lagrange equation, Joseph Louis Lagrange