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Fall 2006

ES 240 Project: Analysis of a Fin Design for use in a Micromechanical Fish

I am preforming my research at the Microrobotics Laboratory. Here I am will be designing systems for a micromechanical fish. One of the researchers in the lab has been prototpying a design for the fin mechanism. For this project, I plan to analyze and optimize her design using ABAQUS. The need for this is clear: due to the size and inertia restrictions of working on the millimeter scale, it is important to not overdesign the systems. We will be working near the limits of the materials.

Megan McCain's picture

ES 240 Project: Stretching Cardiac Myocytes

In the ventricle of the heart, the cells (myocytes) are not isotropically arranged. Myocytes are cylindrically shaped and align edge to edge, and then form a large sheet of parallel rows of aligned cells. This "sheet" is wrapped around itself to form the thick wall of the heart. Myocytes are mechanically coupled to each other by desmosomes, and are electrically coupled to each other by connexins. These connections are extremely important in assuring the heart beats synchronously.

Adrian Podpirka's picture

ES 240 project: Stress and Vibration Analysis of a Golf Driver

In this project, I will attempt to analyze the stresses and vibrations produced by a stroke of a golfer on the club in order to determine the drivers “sweet spot.”  The sweet spot is the spot on the clubface, which causes the lease amount of vibration and force transfer to the golfers hand thus giving the golfer the best energy transfer, feel and therefore, the best drive. (Cross, The Sweet Spot of a baseball bat  Anyone who plays golf can quickly approximate the location of the sweet spot so I will attempt to verify its location through finite element analysis.

Vibrations of a Cantilever Beam

I found this paper on Vibrations of a Cantilever Beam.  Thought I would share it with the rest of the class.  

http://em-ntserver.unl.edu/Mechanics-Pages/Scott-Whitney/325hweb/Beams.htm

 

Cheers.

Nanshu Lu's picture

ABAQUS Computer Assignment #2 (Due Nov. 20)

CA #2 Natural frequency problem

Due on Monday (Nov. 20) in class

Joost Vlassak's picture

ES 246 projects

Each student creates a project that addresses a phenomenon or issue in plasticity theory, and presents it in class after the winter break. The scope of the projects is very wide: experimental, computational, or a critical discussion of one or more papers. The project contributes 30% of the grade, distributed as follows:

  • 5%: November 30 Thursday. Post your project proposal in iMechanica.
  1. Title. ES 246 project: e.g. Plastic buckling of plates.
  2. Tags. Use the following tags: ES 246, plasticity, Fall 2006, project
  3. Body. (i) Describe the project. (ii) Cite at least 1 journal article.
  • 5%: December 7 Thursday. Post a comment to critique the project proposal of at least 1 classmate.
Nanshu Lu's picture

Notes for Computer Assignment #1 Q5

The notes mentioned in the problem (Rice, Solid Mechanics, pp65-68) is attached.

Zhigang Suo's picture

Waves

A file on elastic waves is attached.

Return to the outline of the course

Zhigang Suo's picture

ES 240 Solid Mechanics Project

Updated on 11 October 2008.  Each student creates a distinct project that (a) addresses a phenomenon, and (b) involves a serious use of ABAQUS.   To get some inspiration, see projects of students who took this course in the past.

The project contributes 25% to the grade, distributed as follows.

Zhigang Suo's picture

Solid Mechanics Homework 34-38

34. Surface acoustic wave device
35. Approximate a rod as a 2DOF system
36. Soft tissues: large difference in velocities of longitudinal and transverse waves
37. A general approach to determine body waves
38. Reflection and refraction of a transverse wave

Return to the outline of the course

Nanshu Lu's picture

ABAQUS Tutorial and Assignment #1

1-1 ABAQUS Tutorial: Schedule & Proceedings

1-2 Learning ABAQUS: Begin with ABAQUS Command

1-3 Computer Assignment #1: Plate with circular hole

1-4 CAE Example: Having a sense of ABAQUS CAE

 

Zhigang Suo's picture

Trusses

Notes on the stiffness matrix formulation, used for ES 120, Introduction to the Mechanics of Solids, a sophomore course. This material will not be covered in ES 240, but might provide helpful reading if you do not have this background.

Return to the outline of the course.

Zhigang Suo's picture

Solid Mechanics Homework 31-33

31. A machine on a cantilever
32.  A beam on simple supports
33. Vibration of piano strings

Return to the outline of the course.

textbook

Though not that original, I want to recommend Timoshenko. Since many people have mentioned it already, I will discuss a Brief on Tensor Analysis by James Simmonds. Though not always useful, I sometimes use it to remember tensor rules that I have forgotten. The book is divided into chapters as follows:

 

I: Vectors and Tensors

II: General Bases and Tensor Notation

III: Newton's Law and Tensor Calculus

IV: Gradient, Del Operator, Covariant Differentiation, Divergence Theorem

Again, sometime it is not that useful and you spend your time trying to read it while not learning much, but it does come in handy sometimes. You can see the amazon link:

Amazon

Nanshu Lu's picture

For those who attended office hour today (Oct. 26)

After discussion with Xuanhe, I believe that B=0 for Q21 because there's no cut-and-weld operation here. Then the solusion is exactly the Lame Solution in Cylindrical Shape as in Q8.

What do you think?

Xuanhe Zhao's picture

Elasticity: Theory, Applications, and Numerics by Martin H. Sadd

I would like to recommend "Elasticity: Theory, Applications, and Numerics" by Prof. Martin H. Sadd as a reference for ES240. The book, as its name indicated, is mainly focused on elasticity theory and its applications, but also discusses numerical methods such as finite element method and boundary element method.

Prof. Martin H. Sadd, organized the book into two parts: I. foundations, and II Advanced topics. In part I, the book clearly outlines the basic equations of elasticity, i.e. strain/displacement relation, Hooke's law, and equilibrium equation. The other context of part I is devoted to the formulation and solution of two-dimensional problems. This structure matches the progress of our class very well.

The second part of the book begins with the discussion of anisotropic elasticity, thermo-elasticity, and micromechanics. These topics are complementary to the notes of ES240, and helpful in solving homework problems. In its last chapter, the book introduced finite element method and boundary element method.

Question 16

Book Title: Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue (Second Edition, Third Edition released earlier this year)

Author: Norman E. Dowling

Amazon.com Review Link

The book starts with a general overview and introduction to the mechanics of materials, but later emphasizes deformation, fracture and fatigue of materials. The following is a list of the chapters in the second edition:

(1) Introduction- Discusses types of material failure, design and materials selection, technological challenges, and the economic importance of fracture.

Zhigang Suo's picture

Vibration

“An Introduction to the Mechanics of Solids” by S. H. Crandall, N.C. Dahl, and T. J. Lardner

“An Introduction to the Mechanics of Solids” by S. H. Crandall, N.C. Dahl, and T. J. Lardner

As the title explains, this book shows very basics of the solid mechanics. The book has a good coverage of the concepts of primary elements of mechanics, the three equations, some environmental effect, and examples of torsion, bending, and buckling. This book elaborately explains/proofs several important equations, whose procedures tend to be skipped in many courses due to time limitation. Various case studies/problems accompanied with suitable figures have always helped me to get better senses. It is also easy to find what I am looking for in the book with neatly sorted tables and index. And most importantly, I like this book since the book discusses engineering applications and the limitations of these models.

The materials given in ES240 exceed the range that this book can cover, but this book still is a good resource to go back to when I forget the basics since my sophomore year when I used as our textbook for the materials and structures.

Zhigang Suo's picture

Solid Mechanics Homework 26-30

26. Stress-strain relations under the plane strain conditions
27. Getting weak: derive weak statements from differential equations
28. Potential energy and Rayleigh -Ritz method
29. Constant strain triangle
30. Gaussian quadrature

Return to the outline of the course.

Adrian Podpirka's picture

Textbook Recommendation

So besides using Timoshenko (which is basically the bible of solid mechanics), I have been using Slaughter's The Linearized Theory of Elasticity which I came across in the Gordon McKay Library.

Unlike some of the other textbooks, there is a big focus put on the theory and the idea behind the examples while still having many worked out problems. The first few chapters give a big refresher course on mathematics and lay the groundwork for what is to be taught later on.

I came across this book in particular for the in depth coverage of Airy Stress Functions.

The book is broken into 11 chapters:

Review of Mechanics of Materials
Mathematical Preliminaries
Kinematics
Forces and Stress
Constitutive Equations
Linearized Elasticity Problems
2D Problems
Torsion of Noncircular Cylinders
3D Problems
Variational Methods
Complex Variable Methods

Recommend books

If you prefer to learn tensors in solid mechanics, Nye's book is recommended.
The author covers most of the physical properties in various crystal structures. Some handy tables are included in the book. However, he uses ONLY tensors to derive the properties. If you prefer to write down equations one by one, this would not be a suitable book to start.
Timoshenko's book is also recommended too. As a beginner, this book explains not only the problem, also the meaning behind it. It clearly describes the fundamental questions.
Some books

Zhigang Suo's picture

Solid Mechanics Homework 21-25

21. A fiber in an infinite matrix
22. Anti-plane shear
23. Saint-Venant's principle for orthotropic materials
24. Plane problems with no length scales
25. More scaling relations: a half space filled with a power-law material

Return to the outline of the course.

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