Mechanics of Deformable Structures: Part 2
Gain essential skills in strength of materials and structural analysis. Learn how to analyze multi-axial states of stress and strain, apply objective failure criteria, and predict linear elastic structural behavior using energy methods.
Course Information
About this Course
In this online course from the MIT Department of Mechanical Engineering, you will develop the foundational knowledge to predict and prevent structural failure. You’ll get an introduction to energy methods, which form one basis for numerical techniques (like the Finite Element Method) to solve complex mechanics problems.
Learn how to model the multi-axial stress-strain response of isotropic linear elastic materials under combined loads, including axial, torsional, and bending forces. Discover how to apply objective failure criteria to measure loading severity and prevent structural failure. Finally, learn how to use energy methods to efficiently predict the structural response of statically determinate and indeterminate structures.
This is the third course in a 3-part series which explores how mechanical engineers can use analytical methods and calculations to predict structural behavior. The three courses in the series are:
Part 1 – 2.01x: Elements of Structures. (Elastic response of Structural Elements: bars, shafts, beams).
Part 2 – 2.02.1x Mechanics of Deformable Structures: Part 1. (Assemblages of Elastic, Elastic-Plastic, and Viscoelastic Structural Elements).
Part 3 – 2.02.2x Mechanics of Deformable Structures: Part 2. (Multi-axial Loading and Deformation. Energy Methods).
Based on the first subject in solid mechanics for MIT Mechanical Engineering students, these undergraduate-level courses will teach you to rely on the notions of equilibrium, geometric compatibility, and constitutive material response to ensure that your structures will perform their specified mechanical functions without failing.
What you'll learn
- Hooke’s law for isotropic linear elastic materials and homogeneous problems in linear elasticity. Pressure vessels. Superposition of loading conditions.
- Traction on a face. Stress transformation. Principal stress components. Stress and strain invariants. Tresca and Mises yield criteria.
- Elastic strain energy. Castigliano methods. Potential energy formulations. Approximate solutions and the Rayleigh Ritz method
Prerequisites
- Multivariable Calculus (Derivatives, Integrals (1D, 2D))
- Physics: Classical Mechanics (Vectors, Forces, Torques, Newton's Laws)
- 2.01x (axial loading, torsion, bending in linear elastic structures)
Meet your instructors
David Parks
Professor, Mechanical Engineering
Professor David Parks graduated in Engineering Mechanics from the University of Illinois at Urbana-Champaign and obtained his M.S. and Ph.D. degrees at Brown University. He was Assistant Professor in the Department of Engineering and Applied Science at Yale University for two and a half years before moving to MIT, where he is currently Professor of Mechanical Engineering. His primary interests focus on the development of accurate and tractable models of the mechanical behavior of engineering materials that are based on essential features of the material structures and mechanisms of deformation and failure in a range of materials including metals, polymers, ceramics, and composites. Recent research has centered on the mechanical behavior of graphene under extreme loading, and on solid state roll-bonding of polymer laminae via plastic deformation.
