MIT2_094S11_quiz2

MIT2_094S11_quiz2 - 2.094 FINITE ELEMENT ANALYSIS OF SOLIDS...

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2.094 F INITE E LEMENT A NALYSIS OF S OLIDS AND F LUIDS S PRING 2008 Quiz #2 Instructor: Prof. K. J. Bathe Date: 05/08/2008 Problem 1 (10 points) A computer program is used to perform a plane strain analysis. A total Lagrangian formulation is employed with the given elastic material law. Consider the 4-node element shown at time “t”. For this time: a) Calculate the deformation gradient. b) Calculate the second Piola-Kirchhoff stresses. c) Give the equation to calculate the Cauchy stresses. Do not actually do the arithmetic. 0 10 0 01 0 001 / 2 t SE 0 t ε ⎡⎤ = ⎢⎥ ⎣⎦ ; Poisson’s ratio = 0 Page 1 of 2
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Problem 2 (10 points) A two-dimensional steady-state planar fluid flow analysis solving the Navier-Stokes equations assuming incompressible, very low Reynolds number flow is to be performed. The governing equations in the principle of virtual velocities are: () , ii j i j V ji V j vv d V e d V v ρτ + =ℜ ∫∫ , 0 V pd V v = ( ) ,, 2 ij ij i j j i ij ij pv p ve τ δμ δ μ = =− + + +
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This note was uploaded on 02/24/2012 for the course MECHANICAL 2.094 taught by Professor Klaus-jürgenbathe during the Spring '11 term at MIT.

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MIT2_094S11_quiz2 - 2.094 FINITE ELEMENT ANALYSIS OF SOLIDS...

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