lec29 - 1.050 – Content overview 1.050 Engineering...

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Unformatted text preview: 1.050 – Content overview 1.050 Engineering Mechanics I Lecture 29 Energy bounds in 1D systems Examples and applications 1.050 – Content overview I. Dimensional analysis II. Stresses and strength III. Deformation and strain 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. Plasticity (permanent deformation) 1 11. Fracture mechanics Lectures 1-3 Sept. Lectures 4-15 Sept./Oct. Lectures 16-19 Oct. Lectures 20-31 Oct./Nov. Lectures 32-37 Dec. 2 Example system: 1D truss structure Rigid boundary 1 3 2 IV. Elasticity … Lecture 23: Applications and examples N 1 N 3 N 2 Lecture 24: Beam elasticity Lecture 25: Applications and examples (beam elasticity) Lecture 26: … cont’d and closure Lecture 27: Introduction: Energy bounds in linear elasticity (1D system) Lecture 28: Introduction: Energy bounds in linear elasticity (1D system), cont’d Rigid bar δ 1 δ 2 δ 3 Lecture 29: 1D examples Lecture 30: Generalization to 3D P … V. How things fail – and how to avoid it Lectures 32 to 37 ξ 3 4 1 1 Minimum potential energy approach Conditions for Consider two kinematically admissible (K.A.) kinematically admissible displacement fields (K.A.): Deformation must be compatible w/ (1) rigid bar Approximation δ 1 ‘ = δ 2 ‘ = δ 3 ‘ = ξ ‘ to solution (K.A.) N 1 (2) δ 1 δ 2 3 2 N 3 N 1 δ 2 P δ 3 δ 2 = δ 1 + 2 ( ξ − δ 1 ) Actual solution 3 ξ Prescribed force δ 3 = δ 1 + 4 ( ξ − δ 1...
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lec29 - 1.050 – Content overview 1.050 Engineering...

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