Haghighi where ue col vector of elem nodal disps n

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Unformatted text preview: [D] = [Ι ] Chapter 22 Page 7 K. Haghighi The strain-displacement Relations: generally for each. disp. comp. @ a point we have u = f (x , y , z ) v = g(x, y, z ) w = h(x, y, z ) Using FEM, disp. are approx. as: ⎧u ⎫ ⎪⎪ v⎬ = [N]3×n U(e ) n×1 ⎨ ⎪w⎪ ⎩ ⎭3×1 {} Chapter 22 Page 8 K. Haghighi where {U(e )}= col. vector of elem. nodal disp’s n = f (elem. type) Displacements & strains are related according to a ∂u ∂v e xx = , e yy = , ∂x ∂y ∂w e zz = ∂z ∂u ∂w ∂v ∂w ∂u ∂v + , e xz = + , e yz = + e xy = ∂y ∂x ∂z ∂x ∂z ∂y Chapter 22 Page 9 K. Haghighi No...
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