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MIT2_094S11_lec6

# MIT2_094S11_lec6 - 2.094 — Finite Element Analysis of...

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Unformatted text preview: 2.094 — Finite Element Analysis of Solids and Fluids Fall ‘08 Lecture 6- Finite element formulation, example, convergence Prof. K.J. Bathe MIT OpenCourseWare 6.1 Example Reading: Ex. 4.6 in the text t = 0 . 1 , E,ν plane stress (6.1) KU = R ; R = R B + R s + R c + R r = K ( m ) ; K ( m ) = B ( m ) T C ( m ) B ( m ) d V ( m ) (6.2) K V ( m ) m R B = R ( m ) ( m ) ; R = H ( m ) T f B ( m ) d V ( m ) (6.3) B B V ( m ) m 6.1.1 F.E. model u 1 u 2 u 3 u 4 v 1 v 2 v 3 v 4 ⎡ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ⎤ u 1 × × × × × ← (6.4) K el. (2) = ⎢ ⎢ ⎢ ⎣ . . . ⎥ ⎥ ⎥ ⎦ . . . 23 MIT 2.094 6. Finite element formulation, example, convergence In practice, ⎞ ⎛ B T CB dV ; = B ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ u 1 . . . u 4 v 1 . . . v 4 ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ K (6.5) = el V where K is 8x8 and B is 3x8. Assume we have K (8x8) for el. (2) U 1 U 2 U 3 U 4 U 5 U 11 U 18 ··· ··· ⎡ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ × × × × × × × × × . . ....
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MIT2_094S11_lec6 - 2.094 — Finite Element Analysis of...

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