Haghighi so by comparison we get e bt dbdv

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Unformatted text preview: ous 3 - D elastic sys. is n T (e ) Π= ∑Π − {U} {P} e =1 where Π (e ) = Λ(e ) − Wbf (e ) − Wp (e ) (e ), W (e ) & W (e ) gives Subst. for Λ bf p Chapter 22 Page 20 K. Haghighi {} 2 {} (e ) = 1 U(e ) T ⎛ [B]T [D][B]dV ⎞ U(e ) ⎟ ⎜∫ Π ⎜ ⎟ ⎝V ⎠ ⎛ ⎧X ⎫ ⎜ (e ) T⎜ [B]T [D]{ε }dV T⎪ ⎪ −U + ∫ [N] ⎨ Y ⎬ dV T ⎜∫ V ⎪Z⎪ ⎜V ⎜ ⎩⎭ ⎝ ⎞ ⎧Px ⎫ ⎟ 1 ⎪⎪⎟ + ∫ [N]T ⎨Py ⎬ dΓ⎟ Γ ⎪P ⎪ ⎟ ⎩ z⎭ ⎟ ⎠ {} Chapter 22 Page 21 K. Haghighi Note that in these prob., minimization of the potential energy means that ∂Π = [K ]{U} − {F} − {P} = 0 ∂{U} comes from Π (e ) = Λ(e )...
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