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Expectation of higher order moment (Bayesian Stats)

I am taking a course in Bayesian statistics, which is off my field. In the lecture notes, the instructor showed

E[X^2n] = (2n-1) σ^2n

and E[X^3 . Y] = E[Y^3 . X] = 3.ρ.σ^4  

where  σ = variance

E = expectation

X is a random variable.

ρ = cor(XY) = E[XY]/σ^2

Can anyone kindly explain how these equations were derived or atleast point me towards some text where I can understand this? Is this to do with the moment generating function?

Marginal Probability Density Function of Stochastic Process

I was solving the following question and I derived the Auto correlation function and proved that it is a WSS process. However, I am not sure how to go about finding the Marginal probability density function. Should I find joint probability of a and b and then find marginal probability of each random variable?

Limitations of using Reliability, Availability & Maintainability software applications for engineering asset management

Does anyone have experience in using RAMs software applications?

I am working on a paper that looks at the limitations of managing risk and improving reliability of engineering assets by using RAMs software applications but I have no experience in using any RAMs software application.

von Mises or Equivalent stress for Beam Elements

Are there analytical expressions for computing von Mises or equivalent stress at any point for Beam elements similar to the ones in continuum elements? I would like to design a structure with beam elements and ensure that the equivalent stress is within bounds (yield stress etc) for the structure to be safe.

Zhigang Suo's picture

Rigid-plastic flow

The attached notes are written for a course on plasticity.  When I update the notes, I will post a link on my twitter account:  https://twitter.com/zhigangsuo.

ahmedettaf's picture

Newmark Lecture 2014

Dear Colleagues,

Prof. Ole Sigmund from the Technical University at Denmark: http://www.topopt.dtu.dk/ was the presenter of the 2014-2015 Newmark Distingusihed Lecture which was given in the Civil Engineering Department at the University of Illinois Urbana Champaign. His presentation was titled: Topology Optimization: State of the art and future perspectives. You may find a link to the video lecture here

Open Pit Model Abaqus

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Hi guys, 

I'm new on iMechanica, well at least writing on it, I've been working on a project about geomechanics in order to get my mechanical engineer university degree. The thing is that I'm felling like I can't get all this stuff together, so I would like to ask some questions about my project (Abaqus model of an open pit mining scenario):

Bayesian inversion.

Can anyone kindly recommend any books or papers to read to learn the basics of Bayesian inversion methods?

Thank you very much.  

Zhigang Suo's picture

Nonlinear viscosity

The attached notes are written for a course on plasticity.  When I update the posts, I will write a note on my twitter account:  https://twitter.com/zhigangsuo.  

interaction of stress intensity factor for perpendicular cracks

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pls sugguest ur ideas and i need ansys procedure for this

interaction of stress intensity factor for perpendicular cracks

hai friends,

me doing engineering design... my project tite is "interaction of stress intensity factor for perpendicular cracks" this is y final yr project....pls guide me finding problem & knowing about the fracture mechanics and the purpose of stress intenssity factor..i really need the ansys analysis procedure for creating perpendicular cracks... pls help me friends ...send some link or web page ..

 PLS send details to my mail id    ashwin.prabhu1990@gmail.com  

contact no: 8015180689

thank you!!

2015 Summer Biomechanics Bioengineering and Biotransport Meeting

<p>Please join us at the Summer Biomechanics, Bioengineering and Biotransport Conference (SB3C2015), to be held at beautiful Snowbird Utah, July 17-20, 2015 (http://www.snowbird.com). The theme of the conference this year is <strong> Synergy of Modeling and Experiments in Biomechanics, Bioengineering and Biotransport </strong>.

DEFORM 3D- HOW TO APPLY BLANK HOLDER FORCE

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Free Tags: 

Hi guys,

I am all new user to deform 3d. from the past month i managed to learn a bit of that. now i can deform a sheet into a cup using a punch and die set. problem is there are wrinkles on the cup. how to apply blank holder force. Can any body explain in detail. plz help me so that i can finish my project.

abedford's picture

Book on elastic wave propagation

Our book Introduction to Elastic Wave Propagation, originally published by Wiley in 1994, is now in the public domain. The book is attached. We intended it to be suitable for a one-semester course or for self-study by students needing background on elastic waves. (The solutions to the exercises are included.) Chapter 1 can also be used as a concise introduction to linear elasticity.

Anthony Bedford (abedford@mail.utexas.edu)

Douglas S. Drumheller (dsdrumh@q.com)

Zhigang Suo's picture

Viscosity

The attached notes are written for a course on plasticity.  I will update new posts on my twitter account:  https://twitter.com/zhigangsuo.  

Zhigang Suo's picture

Strain hardening

The attached notes are written for a course on plasticity.  I will update new posts on my twitter account:  https://twitter.com/zhigangsuo.  Rheology is the science of deformation. This science poses a question for every material: given a history of stress, how do we find the history of strain?

Please anyone help me to answer these questions.

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1. Justify if a stick of different length (same mass) is easier to be balanced with your hand with longer or shorter lengths. Calculation of inertia. Justify with calculations.

 

2. Definition of DOF and calculate them for a basic suspension, like double wishbone. Identify all the joints used.

Zhigang Suo's picture

Plasticity

I am teaching this course this semester.  I'll post notes as I write them.  Links to the notes are listed in this post.  I will also notify updates on twitter:  https://twitter.com/zhigangsuo

Zhigang Suo's picture

Basic Equations in Fluid Mechanics

I wrote these notes as a background for teaching elasticity and plasticity.  Even in this most basic formulation, the dilation of the fluid is viscoelastic.

oliver oreilly's picture

A (Possibly Free) Primer on the Finite Element Method

For those of you interested in a terse introductory guide to the Finite Element Method, you might find the latest book by my colleague at U.C. Berkeley, Tarek Zohdi, to be helpful:

SPLIT HOPKINSON PRESSURE BAR

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Hi all,

oliver oreilly's picture

Constraint Moments and Constraint Forces in the Mechanics of Rigid Bodies

For those of you preparing to teach a course on Lagrangian Mechanics of Rigid Bodies in the forthcoming semester or quarter, you may be interested to read a new expository paper by Arun Srinivasa at Texas A&M and myself:

 A Simple Treatment of Constraint Forces and Constraint Moments in Rigid Body Dynamics, ASME Applied Mechanics Reviews, To Appear (2014).  

Joost Vlassak's picture

Tenure-track Faculty Position in Materials Science and Engineering

HARVARD SCHOOL OF ENGINEERING AND APPLIED SCIENCES

Tenure-track Faculty Position in Materials Science and Engineering

Abaqus 6.13 Help needed - Subroutine UHYPER

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Hello all, I am in a desperate need of some expert help

For a newbie at Abaqus with subroutines,

After months of trying, finally installed Abaqus, verified results all passed.

(Abaqus 6.13, Microsoft Visual Studio 2010, Intel Parallel Studio XE 2013)

 Couple of questions-

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