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MIT2_094S11_lec5

MIT2_094S11_lec5 - 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 5- F.E. displacement formulation, cont’d Prof. K.J. Bathe MIT OpenCourseWare For the continuum Reading: Ch. 4 Differential formulation • Variational formulation (Principle of Virtual Displacements) • Next, we assumed infinitesimal small displacement, Hooke’s Law, linear analysis KU = R (5.1a) ( m ) = H ( m ) U u (5.1b) K = K ( m ) (5.1c) m R = R ( m ) (5.1d) B m ( m ) = B ( m ) U (5.1e) U T = U 1 U 2 U n , ( n = all d.o.f. of element assemblage) (5.1f) ··· K ( m ) = B ( m ) T C ( m ) B ( m ) dV ( m ) (5.1g) V ( m ) R B ( m ) = H ( m ) T f B ( m ) dV ( m ) (5.1h) V ( m ) Surface loads Recall that in the principle of virtual displacements, “surface” loads = U S f T f S f dS f (5.2) S f u S ( m ) = H S ( m ) U (5.3) H S ( m ) = H ( m ) (5.4) evaluated at the surface 19 MIT 2.094 5. F.E. displacement formulation, cont’d Substitute into (5.2) U T H S ( m ) T f S ( m ) dS ( m ) (5.5) S ( m ) for element...
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MIT2_094S11_lec5 - 2.094 — Finite Element Analysis of...

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