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Course Goals

(You will be surveyed to assess the effectiveness of the course in meeting these goals at the end of the course)

1. Understand the mathematical and physical foundations of the continuum mechanics of solids, including deformation and stress measures; constitutive relations; failure criteria; have the ability to pose and solve boundary value problems involving deformable solids; and understand the basis for numerical methods in solid mechanics.

  2. Be proficient in the use of a modern finite element analysis program (ABAQUS/CAE) for analyzing stress, deformation and failure in components, assemblies and structures.

  3.  Possess the ability to apply the principles of solid mechanics to solve engineering problems and to design systems or components to meet desired needs; including (a) to idealize a system or component for the purposes of stress analysis; (b) to use appropriate numerical and analytical techniques to model the system (c) to interpret and draw appropriate conclusions from the results and (d) present results and conclusions clearly in written and oral presentations.


Course Outline  Fall 2012

1. Introduction

1.1 Scope of the course

1.2 Basic concepts of solid mechanics

1.3 Introduction to computational resources

2. Mathematical background

2.1 Vector algebra

2.2 Index notations

2.3 Matrices and tensors

2.4 Vector and tensor calculus

3. Stress in a solid

3.1 Body forces, surface forces and traction vector at a point on the surface

3.2 Stress tensor at a point

3.3 Principal stresses at a point

3.4 Balance of momentum and equilibrium equations

4. Strain in a solid

4.1 Displacement field in a deformed solid

4.2 Strain tensor  in a Solid

4.3 Principal strains at a point

4.4 Compatibility conditions on a strain field

4.5 Principal strains at a point

5. Mechanical Behavior of Solids

5.1 Role of experiments in solid mechanics

5.2 Elastic material behavior

5.3 Plastic material behavior

5.4 Visco-elastic material behavior

6. Boundary value problems for linear elastic solids

6.1 Field equations for plane strain deformation

6.2 Thick walled pressure vessel

6.3 Field equations for plane stress deformation

6.3 Plate with hole in tension, stress concentration

7. Variational methods for elastic solids

7.1 Principle of virtual work

7.2 Variational statement of governing equations

7.3 Work and energy theorems in solid mechanics

7.4 Derivations of field equations for thin plate in bending

8.  The finite element method for numerical analyses

8.1 Finite elements

8.2 Element interpolation functions

8.4 Element strains, stresses and strain energy density

8.5 Element Stiffness Matrix

8.6 Global Stiffness Matrix

8.7 Boundary Loading

9. Boundary value problems for elastic-plastic materials

9.1 Tension-torsion of thin walled tubes

9.2 Plastic limit load

9.3 Approximate methods in metal forming

10. Failure modes in solid mechanics

10.1 Fracture

10.2 Fatigue

10.3 Buckling

10.4 Large deflections

10.5 Plastic collapse