MIT2_092F09_exam2 - 2.092/2.093 FINITE ELEMENT ANALYSIS OF...

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2.092/2.093± F INITE E LEMENT A NALYSIS OF S OLIDS AND F LUIDS F ALL 2009± Quiz #2 Instructor: Prof. K. J. Bathe TA: Seounghyun Ham Problem 1 (10 points): A planar (two-dimensional) analysis of a fluid-structure system is to be performed. The simple model shown below is considered. 4 u i v i x y More elements Fig. 1 Thickness t = 1.0± Element 1 solid± 2 More elements 4 Element 2 fluid 1 of 3
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Infinitesimally small motions are assumed to take place. The solid is in plane strain conditions with C known, τ ε xx xx τ yy =C ε yy τ γ xy xy and mass density ρ s . The fluid is inviscid with bulk modulus β , u v + p = βε v ; ε v = x y and mass density ρ f . Here u and v are displacements for the fluid and acoustic motions are considered. (a) Establish the expressions for the “stiffness elements” for the degrees of freedom u i and v i .
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