Buckling of geometrically confined shells Lucia Stein-Montalvo, Paul Costa, Matteo Pezzulla...
ME305: Mechanics of Materials
This course covers concepts of stress, strain, and deformation. We will introduce constitutive relationships that couple stress to strain by the material’s properties. We show how normal and shear stresses can emerge by axial loaded, torsional loaded, bending, and pressure, and we demonstrate how the stresses are combined during more complex loadings. We will show how stress can by transformed to identify the magnitudes and directions of principal stresses. Finally, we will introduce the concept of structural stability to describe the buckling of beams under compressive loading.
The goals of this course are:
- To identify and calculate stresses in various engineering structures.
- To determine how mechanical structures deform in response to external loads.
- To understand how stress and strain combine to enable problems with complex loads to be solved.
Syllabus: Fall 2017
The course progresses through the following topics:
- Axial Load
- Beam Bending: Normal Stress
- Beam Bending: Transverse Shear Stress
- Combined Loading
- Stress Transformation
- Beam Deflection
- Beam Buckling
This material is based upon work supported by the National Science Foundation under Grant No. 1454153. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
ME309: Structural Mechanics
This course covers the application of solid mechanics to structures using concepts from elementary elasticity, energy principles, and introductions to matrix and finite element methods.
The goals of this course are:
- To apply solid mechanics and elementary elasticity to structures.
- To formulate analytical solutions to simple structures using equilibrium methods and energy principles.
- To use numerical methods to predict deformation, stability, and failure of complex structures.
Syllabus: Spring 2018
Mathematica Notebook: Solid Mechanics
MATLAB: Truss (2D)
MATLAB: Truss Element (2D)
MATLAB: Frame (2D)
MATLAB: Frame Element (2D)
ME700: Applied Mathematics in Mechanics
This course introduces students to methods of applied mathematics relevant to theoretical and applied mechanics. We will discuss dimensional analysis, scaling, perturbation methods, variational calculus, and differential geometry.
Syllabus: Spring 2019
Mathematica Notebook: Method of Dominant Balance
Mathematica Notebook: Perturbation: Projectiles
Mathematica Notebook: Perturbation: Thermokinetics
Short Course: Swelling of Elastic Materials
This short course covers Darcy’s law, linear poroelasticity, and the swelling of elastomers. It was presented in two parts at the Complex Motion in Fluids Summer School in Krogerup, Denmark (Aug. 9th – 15th, 2015).
Short Course: Elastic Instabilities for Form and Function
This short course covers the mechanics of thin structures and their elastic stability. It was presented in three parts at the Universita di Roma, Sapienza in Rome, Italy (May 23rd – 27th, 2015).
Short Course: Confined Fluid Flow – Microfluidics and Capillarity
This short course covers fundamentals of low Reynolds number fluid flow and its exploitation within microfluidic devices and confined geometries. It was presented in three parts at the Universita di Roma, Sapienza in Rome, Italy (May 23rd – 27th, 2015).
Notes: Theoretical and Applied Mechanics
I am compiling various notes relevant to the study of theoretical and applied mechanics. The notes will not be exhaustive, and are meant to aid in my understanding of the material, or aid in my teaching of the material. Hopefully you find them useful.
This material is based upon work supported by the National Science Foundation under Grant No. 1505125. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.