{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MIT2_094S11_lec10 - 2.094 Finite Element Analysis of Solids...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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 0 t x = x + u (10.7) Hence t F is known. Then we consider t t t t F = R (10.8) Consider the loads (applied external loads) to be deformation-independent, e.g. 41
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
MIT 2.094 10. F.E. large deformation/general nonlinear analysis Then we can write t t F = t F + F (10.9) t t U = t U + U (10.10) where only t F and t U are known. = t K Δ U , t K = tangent stiffness matrix at time t (10.11) F From (10.8), t K Δ U = t t R t F (10.12) We use this to
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}