Haghighi the element matrices recall that the total

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Unformatted text preview: ns. Chapter 22 Page 17 K. Haghighi 2 - The work done by dist. loads acting on the surface of the body (e ) = (uP + vP + wP )dΓ Wp ∫x y z Γ where Px , Py , Pz are surface stress or pressure comp. to x, y, z. since ⎧u ⎫ ⎪⎪ (e ) ⎨ v ⎬ = [N] U ⎪w⎪ ⎩⎭ {} Chapter 22 Page 18 K. Haghighi therefore ⎧Px ⎫ ⌠ (e ) = ⎮ U(e ) T [N]T ⎪P ⎪ dΓ Wp ⎨ y⎬ ⎮ ⎪P ⎪ ⎮ ⎩ z⎭ ⌡ {} Γ 3 - The work done by body forces X, Y & Z is given by (e ) = (uX + vY + wZ )dV Wbf similarly ∫ V ⎧X ⎫ ⌠ (e ) = ⎮ U(e ) T [N]T ⎪ Y ⎪ dV Wbf ⎨⎬ ⎮ ⎪Z⎪ ⎮ ⎩⎭ ⌡ {} V Chapter 22 Page 19 K. Haghighi The Element Matrices: Recall that the total potential energy in a continu...
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