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ES 240

Zhigang Suo's picture

Final Exam: ES 240 Solid Mechanics

Notes for students who are preparing for the final.

  1. Time: 9:15 am, Thursday, 18 January 2006. Place: Sever Hall 206. No notes or books. Calculators are allowed.
  2. There will be 3 hours and 5 problems.
  3. Exam problems will mostly draw upon homework and parts of the lecture notes covered in class. The exam intends to test your understanding of the material covered in the course, not your creativity.
  4. For the last two topics covered in class, finite deformation and strings and elastica, there was no homework, but some exercises are scattered in the notes. They may appear in the final.
  5. For equations, you will need to memorize the most basic ones, such as equilibrium equations, Hooke's law, and strain-displacement relations. But for anything that you cannot remember, you should be able to derive.

Grade distribution

Madhav Mani's picture

Powerpoint + Report

Find attached my powerpoint presentation and my report.

Madhav Mani's picture

citation

I guess it's time that I cite some papers that are relevant to what I am looking at. A paper byL.Mahadevan et al.: Elements of draping
and another one
Confined elastic developable surfaces: cylinders, cones and the elastica,

Zhigang Suo's picture

Solid Mechanics Homework 43-46

43. Energy loss
44. Zener model and relaxation test
45. Zener model and cyclic-load test
46. Vibration of a viscoelastic rod

Return to the outline of the course.

Zhigang Suo's picture

Solid Mechanics Homework 39-42

39. A circular transverse wave
40. Creep and recovery
41. Temperature dependence and Mr. Arrhenius
42. A loose nylon bolt

Return to the outline of the course.

ES 240 project: Analysis of Resonance in Wine Glasses

We studied in class the phenomenon of resonance in forced, damped oscillators.  The mass and stiffness of a one-dimensional oscillator give rise to a natural frequency of oscillations known as the resonance frequency.  With no damping, energy input at this frequency accumulates and the amplitude of vibrations increases.

The phenomenon of resonance generalizes to linear elastic materials with many more (ie infinite) degrees of freedom: energy input at a natural frequency of vibration will accumulate and result in increasing amplitude of vibration.  The natural frequency in this case is determined by material properties (ie Young's modulus) and the geometry and dimensions of the object (ie a wine glass).  With so many degrees of freedom, the resonance frequency of common objects may be impossible to calculate exactly and it may be necessary to use the finite element method to investigate resonance.

ES 240 project: Deformation of the Sarcolemma

The cardiac myocyte is the basic contractile unit of the heart. In addition to potentiating contraction through chemical and electrical means, each myocyte is a complex sensor that monitors the mechanics of the heart. Through largely unknown means, mechanical stimuli are transduced into biochemical information and responses. Such mechanotransduction has been implicated in the etiology of many cardiovascular pathologies [1]. One such mechanical parameter that the myocyte most likely monitors is the hydrostatic pressure in the myocardium.

Xuanhe Zhao's picture

ES 240 Project: Finite-element modeling of nano-indentation of thin-film materials

Measuring mechanical properties of materials on a very small scale is a difficult, but increasingly important task. There are only a few existing technologies for conducting quantitative measurements of mechanical properties of nanostructures, and nano-indentation is the leading candidate. In this project, we simulate the nano-indentation tests of thin film materials using finite element software ABAQUS. The materials properties and test parameters will be taken from references on nano-indentation experiments [1, 2]. Therefore, the model can be validated by comparing its predictions with experiment results. In addition, we will change 1) the thickness of the thin film and 2) the material of the substrate (for the thin film) in the model, in order to study substrate's effects on nano-indentation tests.

Madhav Mani's picture

ES 240 Project: Draping of a thin elastic sheet

Everyone has seen how a table cloth hangs over the edge of the table. The way in which the excess material is accomodated, that is, the nature of the wrinkles, may depend on the material properties of the table cloth, the angle which the edge of the table is making (a right angle in the case of most tables but one can imagine the wrinkles of a table cloth draped over a circular table, or for that matter any shaped table).

If you aren't quite sure what I am talking about then take a scarf or any isotropic homegenous material and just susupend it of the corner of your desk.

I don't have any article to cite. I don't know if any work has been done on this. My aim is to read Landau Lifshitsz and attack this problem from first principals.

I would also like to use Abaqus to see if I can simulate the system. And then vary things likes E and poisson's ratio etc. And also the angle of the corner makes etc.

ES 240 Project: Numerical calculation of stresses and displacements on buckled square thin membranes with FEM

Please see the attached PDF document for ES240 project proposal.

Please see the attached documents for the presentation and report files for this project (updated on 12/16/2006).

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

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

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