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tute2_Elasticity_sol copy - CVEN4304 Structural...

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Unformatted text preview: CVEN4304: Structural Analysis & Finite Elements 1 THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF CIVIL AND ENVIRONMENTAL ENGINEERING CVEN4304: Structural Analysis & Finite Elements Tutorial Set 2 - Solution Elasticity Question 1 1. Equilibrium: (a) ∂σ xx ∂ x + ∂τ xy ∂ y = (b) ∂τ xy ∂ x + ∂σ yy ∂ y = Thus, (a) a 2 + a 9 = (b) a 8 + a 6 = or (a) a 2 =- a 9 (b) a 6 =- a 8 2. Outward normal { n } = braceleftBigg l m bracerightBigg Tractions: Φ x = l σ xx + m τ xy , Φ y = l τ xy + m σ yy (a) l = 1 , m = Φ x = a 1 + a 2 x + a 3 y , Φ y = a 7 + a 8 x + a 9 y (b) l = , m = 1 Φ x = a 7 + a 8 x + a 9 y , Φ y = a 4 + a 5 x + a 6 y (c) l = cos α , m = sin α Φ x = cos α ( a 1 + a 2 x + a 3 y ) + sin α ( a 7 + a 8 x + a 9 y ) , Φ y = cos α ( a 7 + a 8 x + a 9 y ) + sin α ( a 4 + a 5 x + a 9 y ) . CVEN4304: Structural Analysis & Finite Elements 2 Question 2 a54 a45 x y a45 { n } = braceleftBigg 1 bracerightBigg a27 { n } = braceleftBigg- 1 bracerightBigg a54 { n } = braceleftBigg 1 bracerightBigg a63 { n } = braceleftBigg- 1 bracerightBigg 1. side y = : l = , m =- 1 Φ x =- τ xy ( y = ) = 8 a 1 x 2 , Φ y =- σ yy ( y = ) = 2. side y = b : l = , m = + 1 Φ x = τ xy ( y = b ) =- 8 a 1 x 2 , Φ y = σ yy ( y = b ) =- 8 a 1 b 2 3. side x = : l =- 1 , m = Φ x...
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