Haghighi note that 1 et d t d t t e tt

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Unformatted text preview: ed Hooke’s Law (e ) = 1 {ε}T [D]{ε}dV Λ ∫ 2V 1 since [D]T = [D] , sym. Now writing strains in terms of total strains and then relating them to nodal displacements, {ε} = {e} − {ε T } Chapter 22 Page 13 K. Haghighi Subst. in 1 ( ) (e ) = 1 {e}T − {ε }T [D]({e} − {ε })dV Λ ∫ T T 2V expand to get (e ) = 1 {e}T [D]{e}dV − 1 {e}T [D]{ε }dV Λ ∫ ∫ T 2V 2V 1 1 T − ∫{ε T } [D]{e}dV + ∫{ε T }T [D]{ε T }dV 2V 2V Chapter 22 Page 14 K. Haghighi Note that: 1) {e}T ([D]{ε T }) = = ([D]{ε T })T {e} TT {ε T } [D] {e} T {ε T } [D]{e} = ∴ 2nd & 3rd integrals are identical! 2) Last integral is indep. of {U} and may therefore be omitted. Ch...
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This document was uploaded on 01/29/2014.

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