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FEA lectures - MIT OpenCourseWare http://ocw.mit.edu 2.094...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 2.094 Finite Element Analysis of Solids and Fluids Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . 2.094 Finite Element Analysis of Solids and Fluids Fall 08 MIT OpenCourseWare Contents 1 Large displacement analysis of solids/structures 3 1.1 Project Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Large Displacement analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Mathematical model/problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.2 Requirements to be fulfilled by solution at time t . . . . . . . . . . . . . . . . . . . 5 1.2.3 Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.4 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Finite element formulation of solids and structures 7 2.1 Principle of Virtual Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3 Finite element formulation for solids and structures 10 4 Finite element formulation for solids and structures 14 5 F.E. displacement formulation, contd 19 6 Finite element formulation, example, convergence 23 6.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 6.1.1 F.E. model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 6.1.2 Higher-order elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 7 Isoparametric elements 28 8 Convergence of displacement-based FEM 33 9 u / p formulation 37 10 F.E. large deformation/general nonlinear analysis 41 11 Deformation, strain and stress tensors 45 12 Total Lagrangian formulation 49 1 MIT 2.094 Contents 13 Total Lagrangian formulation, contd 53 14 Total Lagrangian formulation, contd 57 15 Field problems 61 15.1 Heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 15.1.1 Differential formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 15.1.2 Principle of virtual temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 15.2 Inviscid, incompressible, irrotational ow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 16 F.E. analysis of Navier-Stokes uids 65 17 Incompressible uid ow and heat transfer, contd 71 17.1 Abstract body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 17.2 Actual 2D problem (channel ow) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 17.3 Basic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 17.4 Model problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .....
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This note was uploaded on 05/18/2011 for the course MAE 269A taught by Professor Ju during the Spring '11 term at UCLA.

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FEA lectures - MIT OpenCourseWare http://ocw.mit.edu 2.094...

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