solid mechanics

Notes for students who are preparing for the final.

1. 时间:上午9点15分,星期四,2006年1月18日。地方:年代ever Hall 206. No notes or books. Calculators are allowed.
2. 会有be 3 hours and 5 problems.
3. Exam problems will mostly draw uponhomeworkand parts of thelecture notescovered 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 deformationandstrings 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

Notes are attached. Return to theoutline of the course.

Find attached my powerpoint presentation and my report.

The notes are part of thecourse on advanced elasticity.

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,

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

Return to theoutline of the course.

A word file is attached.

Return to theoutline of the course.

3论文对于亚当的国际泳联可能有用l project (attached)

As promised, no homework for Thanksgiving :)

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

Return to theoutline of the course.

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.

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.

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.

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.

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).

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.

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.

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.