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MIT2_092F09_exam1

# MIT2_092F09_exam1 - ∂ ∂ ⎠ ⎣ τ 1-ν y y x xy ⎦...

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Instructor: Prof. K. J. Bathe TA: Seounghyun Ham 2.092/2.093± F INITE E LEMENT A NALYSIS OF S OLIDS AND F LUIDS F ALL 2009± Quiz #1 Problem 1 (10 points): Consider the solution of the problem shown below. A rod is spinning in steady-state at ω rad/sec. The rod is idealized as two one-dimensional elements. Assume linear analysis. ω rad/sec Cross-± 100 sectional area=1 60 η Young’s modulus E Mass density ρ 2 η A( η )= 4 - 20 U 1 =0 U 2 U 3 x for element 1 x for element 2 a) Establish the finite element displacement interpolation functions, for each element. b) Give the element stiffness matrices and load vectors, but do not perform any integration. 1 of 2±

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τ x 1 ν 0 ⎥⎡ ε x E xx τ yy ⎢ ⎥ = ν 1 0 2 ⎥⎢ ε yy ; ε u v u v 1- xx = ; ε yy = ; γ ν + = ⎥⎢ x γ
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Unformatted text preview: ∂ ∂ ⎠ ⎣ τ 1-ν y y x xy ⎦ ⎣ ⎢ 0 ⎥ xy ⎦ ⎣ 2 ⎦ 1 2 3 4 6 u 1 v 1 4 x,u y,v f x B f y B Problem 2 (10 points): Consider the two-dimensional plane stress element shown below. 4 node element Thickness t Young’s modulus E Poisson’s ratio ν f B = ( 4+x ) x f B =0 y a)± Establish all displacement interpolation functions. b)± Give the K matrix and the load vector R B of the element. Give all required expressions but do not perform any integration. Give all answers but write as little as possible ! 2 of 2 MIT OpenCourseWare http://ocw.mit.edu 2.092 / 2.093 Finite Element Analysis of Solids and Fluids I Fall 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms ....
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