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# ha2 - 16.20 Handed Out Lecture 9 Due Lecture 12 HOME...

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16.20 Handed Out: Lecture 9 Due: Lecture 12 HOME ASSIGNMENT #2 Warm-Up Exercises 1. The three-dimensional (3-D) stress-strain equations are written as: σ mn = E mnpq ε pq These can be reduced for the plane stress case (i.e. σ 33 = σ 13 = σ 23 = 0) to a two-dimensional (2-D) representation: σ αβ = E * αβσγ ε σγ where the asterisk indicates that this is a 2-D elasticity tensor for plane stress whose components do not have a one-to-one correspondence with the 3-D elasticity tensor, E mnpq . For an orthotropic material find the relations between E * αβσγ and E mnpq . 2. Repeat the previous problem for an isotropic material. Practice Problems 3. A unidirectional graphite/epoxy composite material is loaded in the plane of its fibers. This material is transversely isotropic ( ν 12 = ν 13 ; E 22 = E 33 ) and has the following four elastic constants: E 11 = 130 GPa E 22 = 10.5 GPa ν 12 = 0.28 G 12 = 6.0 GPa The part is thin compared to its in-plane dimensions. Determine all the non-

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ha2 - 16.20 Handed Out Lecture 9 Due Lecture 12 HOME...

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