MIT2_094S11_lec10

MIT2_094S11_lec10 - 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 10- F.E. large deformation/general nonlinear analysis Prof. K.J. Bathe MIT OpenCourseWare We developed t V t τ ij t e ij d V t = R t Reading: Ch. 6 (10.1) e t ij = 1 2 ∂u i ∂ x t j + ∂u j ∂ x t i (10.2) t V t τ ij δ t e ij d V t = R t (10.3) δ t e ij = 1 2 ∂ ( δu i ) ∂ t x j + ∂ ( δu j ) ∂ t x i ( ≡ t e ij ) (10.4) In FEA: t F = t R (10.5) In linear analysis t F = K t U KU = R (10.6) ⇒ In general nonlinear analysis, we need to iterate. Assume the solution is known “at time t ” t t x = x + u (10.7) Hence t F is known. Then we consider t +Δ t t +Δ t F = R (10.8) Consider the loads (applied external loads) to be deformation-independent, e.g. 41 • MIT 2.094 10. F.E. large deformation/general nonlinear analysis Then we can write t +Δ t F = t F + F (10.9) t +Δ t U = t U + U (10.10) where only t F and t U are known....
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This note was uploaded on 12/29/2011 for the course ENGINEERIN 2.094 taught by Professor Prof.klaus-jürgenbathe during the Spring '11 term at MIT.

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MIT2_094S11_lec10 - 2.094 — Finite Element Analysis of...

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