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MEEM 5150 Advanced Mechanics of Materials Instructor:Dr. Qingli Dai 910 MEEM Bldg. Phone: 487 2620 Email: qingdai@mtu.edu Course website:Class Schedule: T- Th 1:00-2:30 PM Office hour: T 2:30-4 PM, Th 2:30-3 PM, or make an appointment Textbook: There is no required textbook for this course.

Notes with most of the slides used in the lectures are available at this website. Note that these slides only cover the theoretical aspects of the course: the applications are typically solved in class on the blackboard. ( Recommended textbook) P. Boresi, and R. Schmidt, Advanced Mechanics of Materials, Sixth Edition ( Other suggested textbooks) - K.

Hjelmstad, Fundamentals of Structural Mechanics - M. Sadd, Elasticity: Theory, Applications and Numerics - R. Young, Advanced Mechanics of Materials Grading outline: Homework – 30%, Term Project – 15%, Examinations – 50% (midterm-25%, final -25%), Classwork – 5% Course Objectives:- Introduce the fundamental concepts of mechanics of materials - Review the basic solid mechanics concepts - Discuss one and two dimensional structures - Energy methods and stability - Fracture and Fatigue - Numerical techniques Course Outline: 1. Math preliminaries a. Index Notation and Cartesian Tensors b. Coordinate Transformation c. Principal Values and Directions d.

Algebra and Calculus of Cartesian Tensors 2. Stress and Equilibrium a.

Principal stress and stress transformation b. Octahedral, mean, and deviatoric stress c. Mohr’s circle in two and three dimensions d. Equilibrium equation 3. Deformation: Displacements and Strains a.

Lagrangian strain tensor and physical strain components b. Strain-displacement relations c. Principal strain and strain transformation d. Strain compatibility equations 4.

Constitutive Behavior a. Stain energy and complimentary strain energy b. Isotropic elasticity and Hooke’s law c. Thermoelasticity d. Orthotropic materials e.

Plastic behavior (yield criteria) 5. Energy Methods a. Castigliano’s first theorem b. Linear load-deflection relations c. Deflection of statically determinate structures (Dummy unit load method) 6.

Beam Theories a. Beam Bending 1. Symmetrical bending – Bernoulli’s beam theory 2. Nonsymmetrical bending 3. Shear center b.

Beam Torsion 1. Torsion of a beam with circular cross section 2. Saint- Venant’s semi-inverse method 3. Linear elastic solution of non-circular cross section (ellipse and equilateral triangle) 7.

Plate Theories & Applications a. Stress resultant in a flat plate b. Strain-displacement relations for plates (considering rotation) c. Equilibrium equations for small displacement theory d. Download anti filter for windows.

Stress-strain-temperature relations for isotropic plates e. Solutions of a rectangular plate with different supports 8. Fracture and Fatigue a. Stress concentration factors for elliptical holes b. Failure criteria, stress intensity factors and stress around the crack tip c. Stationary blunt and sharp cracks d. Fracture toughness and crack extension force e.