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.
Blog posts
Are notes and textbooks a higher priority than journal clubs?
I registered for iMechanica a few days ago, and found many postings instructive. Here is my first blog entry.
The topics being studied today by mechanicians are very difficult (what I often call "dirty problems"). In fact, often the mechanical theories (actually coupled mechanics, biology, chemistry) required to gain improved understanding are still in their infancy. Mechanicians that have entered fields such as mechanics of biological structures have gotten up to speed by paying the price (hopefully an enjoyable time on a learning curve) of reading large numbers of papers and discipline-based books. Many of these papers are cryptic and, while they may be of high scientific quality, they do not have significant pedagogical value to those entering the field (graduate students for example).
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.
A method to analyze dislocation injection from sharp features in strained silicon structures
Stresses inevitably arise in a microelectronic device due to mismatch in coefficients of thermal expansion, mismatch in lattice constants, and growth of materials. Moreover, in the technology of strained silicon devices, stresses have been deliberately introduced to increase carrier mobility. A device usually contains sharp features like edges and corners, which may intensify stresses, inject dislocations into silicon, and fail the device. On the basis of singular stress fields near the sharp features, this letter describes a method to obtain conditions that avert dislocations.
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.
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.
Mechanics of climbing and attachment in twining plants
In a recent article in Physical Review Letters, Alain Goriely and Sébastien Neukirch offer a mechanical model of how the free tip of a twining plant can hold onto a smooth support, allowing the plant to grow upward. The model also explains why these vines cannot grow on supports of too large a diameter. Read more.
The mechanics involves large deflection and bifurcation of a rod. I hope to hear opinions from people who know about the mechanics of plants.
Delamination in Patterned Films
When the dielectric constant of an insulator in an interconnect is reduced, mechanical properties are often compromised, giving rise to significant challenges in interconnect integration and reliability. Due to low adhesion of the dielectric an interfacial crack may occur during fabrication and testing. To understand the effect of interconnect structure, an interfacial fracture mechanics model has been analyzed for patterned films undergoing a typical thermal excursion during the integration process.
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).