# Teaching

Since 2015, Prof. Holmes has led **DICE** (**D**igital **I**nspiration, **Communication**, and **E**ducation), a program that hopes to improve understanding, communication, and accessibility for mechanics students. We have digitized lecture notes, created lecture videos, started a Structural Mechanics Newsletter, engaged academics and the general public on Twitter/X, created graduate-level short courses, and published open source code.

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.

### 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:

- Stress
- Strain
- Axial Load
- Torsion
- Beam Bending: Normal Stress
- Beam Bending: Transverse Shear Stress
- Combined Loading
- Stress Transformation
- Beam Deflection
- Beam Buckling

### 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 2023

**Structural Mechanics Newsletter**

- Slap Shots, Exploding Watermelons, and Strandbeests
- Solar Sails, Soft Robots, and Building Things with Rocks and Strings

In years past, this course progresses through the following topics:

- Lecture 1 – Strain Energy [notes] [video]
- Lecture 2 – Stretching and Bending [notes] [video]
- Lecture 3 – Review Paper Discussion [notes] [video]
- Lecture 4 – Elastogravity, Elastocapillarity, and Castigliano’s Theorems [notes] [video]
- Lecture 5 – Stability, Buckling of a Hinged Column [notes] [video]
- Lecture 6 – Snapping Truss [notes] [video]
- Introduction to Mathematica: [MMA Notebook]
- Snapping Truss: [MMA Notebook]
- Lecture 7 – Principle of Least Action and Variational Calculus [notes] [video]
- Lecture 8 – Principle of Minimum Potential Energy [notes] [video]
- Lecture 9 – Approximate Solutions by Trigonometric Series [notes] [video]
- Lecture 10 – Ritz Method [notes] [video]
- Lecture 11 – Weak Forms [notes] [video]
- Lecture 12 – Equilibrium Equations [notes] [video]
- Lecture 13 – Stress Transformation 2D [notes] [video]
- Lecture 14 – Stress Transformation 3D [notes] [video]
- Lecture 15 – Strain [notes] [video]
- Lecture 16 – Constitutive Relations [notes] [video]
- Lecture 17 – Axisymmetric Problems [notes] [video]
- Lecture 18 – Thick-Walled Pressure Vessels [notes] [video]
- Lecture 19 – Spinning Disks [notes] [video]
- Lecture 20 – Direct Stiffness Method I [notes] [video]
- Lecture 21 – Direct Stiffness Method II [notes] [video]

### ME712: 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: Fall 2023

Notes: Lecture Notes — *Updated:* 10/5/2020

YouTube Channel: Lectures

Mathematica: Download Student Version — BU Student

The course progresses through the following topics:

- Lecture 1 – Dimensional Analysis and Projectiles [notes] [video]
- Lecture 2 – Similarity Variables and Diffusion [notes] [video] [Mathematica]
- Problem Set 1: [PDF]
- Reading 1: [A new wrinkle on liquid sheets]
- Lecture 3 – Buckingham Pi Theorem and Fatigue [notes] [video]
- Lecture 4 – Discussing Problem Set 1 [notes] [video]
- Lecture 5 – Bubbles and Wrinkles! [notes] [video] [Slides]
- Lecture 6 – How to Nondimensionalize an Equation [notes] [video]
- Problem Set 2: [PDF]
- Lecture 7 – Perturbation Methods (Regular) [notes] [video]
- Lecture 8 – Discussing Problem Set 2 [notes] [video]
- Lecture 9 – Perturbation Methods (Regular) – Projectiles [notes] [video]
- Lecture 10 – Perturbation Methods (Regular) – Projectiles (cont.) [notes] [video]
- Lecture 11 – Perturbation Methods (Regular) – System of Equations [video]
- Thermokinetics [MMA]
- Lecture 12 – Perturbation Methods (Singular) [video]
- Singular Perturbation [MMA]
- Lecture 13 – Boundary Layers [video]
- Singular Perturbation of an ODE [MMA]
- Lecture 14 – Multiple Boundary Layers [BREAKOUT ROOMS]
- Lecture 15 – Multiple Boundary Layers and Two-Timing [video]
- Lecture 16 – Problem Set 3 [video]
- Lecture 17 – Variational Calculus and Principle of Least Action [video]
- Lecture 18 – Euler-Lagrange Equations; Planar Geodesics [video]
- Lecture 19 – Deriving the
*elastica*from a Variational Principle [video] - Lecture 20 – Constrained Minimization: Lagrange Multipliers and Penalty Functions [video]
- Lecture 21 – Dynamical Systems and Linear Stability Analysis [video]
- Lecture 22 – Stability and Bifurcations [video]
- Lecture 23 – Tensor Analysis and Differential Geometry [video]
- Lecture 24 – Gaussian Curvature; Calculus on Curved Surfaces [video]

### 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).

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.