MIT2_092F09_lec12 - 2.092/2.093 Finite Element Analysis of...

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2.092/2.093 Finite Element Analysis of Solids & Fluids I Fall ‘09 Lecture 12 - FEA of Heat Transfer/Incompressible Fluid Flow Prof. K. J. Bathe MIT OpenCourseWare Reminder: Quiz #1, Oct. 29. Closed book, 4 pages of notes. Reading assigment: Section 7.4.2 We recall the principle of virtual temperatures. θ ¯ T dV = θ ¯ T q B dV + θ ¯ T q S dS V V S q θ ( m ) = H ( m ) θ ; θ ¯ ( m ) = H ( m ) θ ¯ θ ( m ) = B ( m ) θ ; θ ¯ ( m ) = B ( m ) θ ¯ Σ K ( m ) θ = Σ Q B ( m ) + Q S ( m ) m m K ( m ) = B ( m ) T k ( m ) B ( m ) dV ( m ) V ( m ) Q ( m ) = H ( m ) T q B ( m ) dV ( m ) B V ( m ) Q ( S m ) = H S ( m ) T q S ( m ) dS ( m ) (a) ( m ) S q In (a), we may have to integrate over two or more surfaces. Example H = 1 4 1 + x 2 (1 + y ) 1 4 1 x 2 (1 + y ) 1 4 1 x 2 (1 y ) B = h 1 ,x h 2 ,x h 3 ,x h 4 ,x h 1 ,y h 2 ,y h 3 ,y h 4 ,y H S (1) = H S y =+1 = 1 2 1 + x 2 1 2 1 x 2 0 1 4 1 + x 2 (1 y ) 0 1
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Lecture 12 FEA of Heat Transfer/Incompressible Fluid Flow 2.092/2.093,
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