iMechanica - Beam Theory - Comments

Jagadish, I will suggest

Wenbin Yu — Fri, 19 Sep 2008 12:27:32 -0400

Jagadish,

I will suggest you to read Nonlinear Composite Beam Theory by Prof.Hodges at Georgia Tech

You will get ideas how to write the energy expression and how to handle large deflection correctly.

Wenbin

Generalized Timoshenko Model

Wenbin Yu — Fri, 19 Sep 2008 12:21:50 -0400

Dear Zishun and Sandyg,

In fact you don't have to assume constant shear over the beam height (equivalently section remains plane althoug not normal) to take advantage of the merits of the Timoshenko beam model. And the warping due to flexure contributes meaningfully to the shear energy. That is why we need a shear correction factor to compensate for this. A generalized Timoshenko model [1, 2] has been developed by carrying out an asymptotical dimensional reduction from 3D elasticity equations to a 1D model in the form of Timoshenko theory. The Timoshenko model constructed this way can reproduce the flexure problem of the elasticity theory. And also there is no need to assume how the section should deform and no need to introduce shear correction factors.

[1] Yu, W.; Hodges, D. H.; Volovoi, V. V.; and Cesnik, C. E. S.: "On Timoshenko-Like
Modeling of Initially Curved and Twisted Composite Beams," International
Journal of Solids and Structures, Vol. 39, no. 19, 2002, pp. 5101-5121. (pdf)

[2] Yu, W. and Hodges, D. H.: "Elasticity Solutions versus Asymptotic Sectional
Analysis of Homogeneous, Isotropic, Prismatic Beams," Journal of Applied
Mechanics, vol. 71, no. 1, 2004, pp. 15-23. (pdf)

Wenbin

Timoshenko's theory of beams. By one picture

siarheiarlou — Sun, 01 Jun 2008 18:46:26 -0400

Hi Sandyg,
At first, S.P.Timoshenko and G.M.Gere - world super stars of Applied Mechanics.

There is one little difference - shear deformations that we added to Euler bending. More particulary we understand that we have a bending angle and deflection as deformations at beam bending process. But accuracy requires to add a shear angle to bending angle. Then we have a little more total angle than bending angle only.

This example is reproduced in the school laboratory of one of technical Universities of Belarus. The experiment confirms brilliantly the improved theory of S.P.Timoshenko, taking into consideration the shear deformations. The parameters of cross-section area correspond to the flange beam ¹12 (GOST 8239 - 72 Russian Standard).

Vertically configured cantilever

Redentor S. Rojas — Sun, 01 Jun 2008 12:20:39 -0400

Hi to all! I am new to this forum and I just want to ask if there is a difference on the mathematical description of a horizontally and vertically configured cantilever. i am doing a research which requires vibration measurment and analysis, and I used a hacksaw blade and strain gages to do these. The hacksaw blade is coupled to the vibrating body, and the vibration is measured via the strain gages mounted on the hacksaw blade which is positioned vertically.

I hope somebody would answer this question. Thanks in advance!

Vibration

RidzaSmart — Sun, 01 Jun 2008 05:08:37 -0400

Is there a book that i can check for the stiffness matrix for vibration of beam allowing for effect of slip..?

large deflection of timoshenko beams?

jagadish.Gunda — Wed, 02 Apr 2008 10:13:32 -0400

I am trying to solve a vibration problem of timoshenko beams by considering the effect of geometric non-linearity with von-karman type strain-displacement relations. I have three variables which are theta, u and w. I am getting correct linear value but non-linear some thing wrong with energy expression it seems.

Can any body suggests some tips to write the strain energy of timoshenko beams due to axial, shear and bending loads considering the geomentric nonlinearity of von-karman type? Looking forward to your valuable comments.

Regards

Jagadish

(IISc,Bangalore)

Stepped beam

lagouge tartibu — Sun, 25 Nov 2007 05:40:44 -0500

Hi all

I have developped a finite element MATLAB program for a stepped beam

*with selectable number of portion of stepped beam and

*selectable size of beam.

The output of this program is the flap-wise and edge-wise natural frequency. Everything work perfectly.

My problem is that, i would like now to add the area moment of inertia of each portion of my stepped beam as a variable because the first portion of my stepped beam will be a "hollow beam".

I would like to find some interested information about MATLAB program of a stepped beam in order to improve the way i will input my data.

hope to get some advice and link soon!

lagouge TARTIBU

Researcher

Mechanical Engineering

Cape Peninsula University of Technology

Cape Town

South Africa

lagouge TARTIBU

Researcher Mechanical Engineering

Cape Peninsula University of Technology

Cape Town

South Africa

Ravitej Kommana IIT

Ravitej K — Sat, 03 Nov 2007 00:32:28 -0400

Ravitej Kommana
IIT Kanpur
INDIA.

i want the mid point deflection in case of "four point bend test" on a
specimen of length 140mm, width of 40mm and thickness of 10mm.

Problem is that, beam theory is valid if the cross-sectional
dimensions are less than axial dimensions. Here this condition is
violated. i had modeled the specimen in Abaqus and the diffection at
mid point is almost double that of the actual diffection calculated
from beam theory.

how can i find the theoritical difflection at mid point in this case?

i had one option, using timoshenko beam theory and applying larger
deflection theory. will it be a reasonable approximation in this case?

Ravitej

Dear Biswajit, Thanks for

mafarooqi — Mon, 11 Jun 2007 00:16:56 -0400

Dear Biswajit,

Thanks for your suggestion. Let me try this to implement to my problem first n then I'll get back in case I got stuck up.

Mohammad

Conversion to Abaqus format

Biswajit Banerjee — Sun, 10 Jun 2007 18:36:17 -0400

The route that I have taken in the past is as follows:

Assume that each pixel/voxel is one element.
Arrange the pixel data into a format that you can easily convert into Abaqus format.
Write a program to create an Abaqus input file from the pixel data.
Create an odb file after reading in the Abaqus input file.

An example of such an approach can be found here.

In the example, I start off with a pixel file called <>.sub and then run createAbaqus to create the Abaqus input file <>.inp and the element and node files <>.ele and <>.nod. The code generates ASCII files for 2D situations. You can easily take the idea and apply it to your situation. My work was done many years ago and used Abaqus 6.3. For refinement you can also use createAbqRefine to refine the mesh by dividing each pixel into 4 elements - but not much more.

People who work with Abaqus on a regular basis will probably be able to provide a better solution.

How to import a complex geometry created in Matlab

mafarooqi — Sat, 09 Jun 2007 19:23:13 -0400

Hi all,

I have visited quite a number of blog sites and such discussion boards, most of them full of trashy discussions--time wastage! However, in here, both the problems and comments are scholarly and pretty useful. I dont know if my problem is upto the mark or not. But please care to respond. Thanks

I am working on modelling of composites. I took a 2D bitmap image of a composite, opened in matlab, converted it into pixel coordinates (file format: .mat) . Now the dimension of the matrix of pixel coordinates is around 20000x2. My objective is to export this image data into ABAQUS for diffusion analyses. Could anyone please let me how to import this huge image matrix into ABAQUS or create a geometry? I am thinking on converting or reformatting the .mat data file into abaqus .odb file. So the second question is, what is the format of .odb file that can be used in ABAQUS.

Thanks,

Mohammad

PLATE THEORY

Alan Tan — Mon, 07 May 2007 15:58:09 -0400

Dear Sandyg,

I did a research (for my masters) about thin and thick plates which also includes large deformations. I used FEM for that. I will try to find the FEM code.

regards,

alan

That is right. You may refer

zishun liu — Thu, 15 Mar 2007 21:06:57 -0400

That is right. You may refer my colleagues Prof. CM Wang and Prof. JN Reddy's paper on this problem. I am sorry I can't remember the details, but you can find it from Prof. CM Wang's publications.

Modelling in ABAQUS

zishun liu — Thu, 15 Mar 2007 20:58:54 -0400

Dear Ramesh,

If MATLAB is not suitable for your problems, I suggest that you may use COMSOL software to solve it. This is more flexible for solving your problem. As you are familiar with MATLAB, it should be no any problem for you to use COMSOL. Of course you may try to use ABAQUS to solve it, in my opinion, it may have more credit for your research.

Zishun

Coding ABAQUS user element in C/C++

vh — Thu, 15 Mar 2007 07:27:40 -0400

Sai,

One can code the user element in Fortran or in C/C++. For writing the user element in C/C++ you can refer to the following webpage

http://abaqus.custhelp.com/cgi-bin/abaqus.cfg/php/enduser/std_adp.php?p_faqid=737&p_created=1041881581

V. Hegadekatte, University of Karlsruhe, Germany

Beam Theory

sandyg — Wed, 28 Feb 2007 21:00:40 -0500

What is the advantage of using Timoshenko beam theory over other beam theories? Also what is the
differnce between a Beam, a thick plate and a thin plate. Iam new to
this area so these questions may sound stupid to you. Also i want to know
that if a plate is thick then what will be the solution approach and same
for a Beam and thin plate. lets say we have to find deflection in all cases
(Beam, thick and thin plate)Thanx Sandyg