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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 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 ij t e ij d V t = R t (10.3) t e ij = 1 2 ( u i ) t x j + ( u 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 + t t + 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 + t F = t F + F (10.9) t + t U = t U + U (10.10) where only t F and t U are known....
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