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Unformatted text preview: 1.050 Engineering Mechanics I Lecture 28 Introduction: Energy bounds in linear elasticity (contd) 1 1.050 Content overview I. Dimensional analysis II. Stresses and strength III. Deformation and strain IV. Elasticity Lecture 23: Applications and examples Lecture 24: Beam elasticity Lecture 25: Applications and examples (beam elasticity) Lecture 26: contd and closure Lecture 27: Introduction: Energy bounds in linear elasticity (1D system) Lecture 28: Introduction: Energy bounds in linear elasticity (1D system), contd Lecture 29: Generalization to 3D, examples V. How things fail and how to avoid it Lectures 32 to 37 3 1.050 Content overview I. Dimensional analysis 1. On monsters, mice and mushrooms Lectures 1-3 2. Similarity relations: Important engineering tools Sept. II. Stresses and strength 3. Stresses and equilibrium Lectures 4-15 4. Strength models (how to design structures, foundations.. against mechanical failure) Sept./Oct. III. Deformation and strain 5. How strain gages work? 6. How to measure deformation in a 3D Lectures 16-19 structure/material? Oct. IV. Elasticity 7. Elasticity model link stresses and deformation Lectures 20-31 8. Variational methods in elasticity Oct./Nov. V. How things fail and how to avoid it 9. Elastic instabilities 10. Plasticity (permanent deformation) Lectures 32-37 11. Fracture mechanics Dec. 2 Outline and goals Use concept of concept of convexity to derive conditions that specify the solutions to elasticity problems Obtain two approaches: Approach 1: Based on minimizing the potential energy Approach 2: Based on minimizing the complementary energy Last part: Combine the two approaches: Upper/lower bound 4 1 5 Reminder: convexity of a function f ( x ) f | ( b a ) f ( b )...
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- Fall '08