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lec37_review - 1.050 Engineering Mechanics I Review session...

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1.050 Engineering Mechanics I Review session 1 1.050 – Content overview I. Dimensional analysis 1. On monsters, mice and mushrooms 2. Similarity relations: Important engineering tools II. Stresses and strength 3. Stresses and equilibrium 4. Strength models (how to design structures, foundations.. against mechanical failure) III. Deformation and strain 5. How strain gages work? 6. How to measure deformation in a 3D structure/material? IV. Elasticity 7. Elasticity model – link stresses and deformation 8. Variational methods in elasticity V. How things fail – and how to avoid it 9. Elastic instabilities 10. Fracture mechanics 11. Plasticity (permanent deformation) Lectures 1-3 Sept. Lectures 4-15 Sept./Oct. Lectures 16-19 Oct. Lectures 20-32 Oct./Nov. Lectures 33-37 Dec. 2 1
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Notes regarding final exam Please contact me or stop by at any time for any questions The final will be comprehensive and cover all material discussed in 1.050 . Note that the last two p-sets will be important for the final. To get an idea about the style of the final, work out old finals and the practice final There will be 2-3 problems with several questions each (e.g. beam problem/ truss problem, continuum problem) We will post old final exams from 2005 and 2006 today We will post an additional, new practice final exam on or around Wednesday next week Another list of variables and concepts will be posted next week Stay calm, read carefully, and practice time management 3 Stress, strain and elasticity - concepts 4 2
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5 Overview: 3D linear elasticity 0 div = + g r ρ σ ) ( x r σ Stress tensor Basis : Physical laws (Newton’s laws) BCs on boundary of domain n n T d T d r r r r = σ ) ( : : n n T r r r = σ ) ( ji ij σ σ = ) ( x r ε Strain tensor Basis : Geometry BCs on boundary of domain ξ ξ ξ r r r = d d : Linear deformation theory 1 Grad << ξ r ( ) ( ) T ξ ξ ε r r grad grad 2 1 + = Statically admissible (S.A.) Kinematically admissible (K.A.) Elasticity ε σ : c = kl ijkl ij c ε σ = ε ε σ G G K v 2 1 3 2 + = Basis
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