ramdas chennamsetti's blog
http://imechanica.org/blog/1470
enTheory of Representations for Tensor Functionsâ€”A Unified Invariant Approach to Constitutive Equations
http://imechanica.org/node/15438
<p>
Hi,
</p>
<p>
I am looking for the following paper.
</p>
<p>
Theory of representations for tensor functions - A unified invariant approach to constitutive equations - Q -S Zheng, Applied Mechanics Reviews, 47(11), 545-587, 1994.
</p>
<p>
If anyone has this paper, I request you to share.
</p>
<p>
Thanking you,
</p>
<p>
Best regards,
</p>
<p>
- Ramadas
</p>
<br class="clear" />http://imechanica.org/node/15438#commentsSun, 06 Oct 2013 10:04:14 -0400ramdas chennamsetti15438 at http://imechanica.orgiMechanica app in a smart phone
http://imechanica.org/node/15332
<p>
Hi all,
</p>
<p>
I am thinking that it is a good idea to have 'iMechanica' smart phone app (like facebook, twitter etc). We can post/check blogs using a smart phone. I request moderators and imechanicians to comment on this.
</p>
<p>
Best regards,
</p>
<p>
- Ramadas
</p>
<br class="clear" />http://imechanica.org/node/15332#commentsWed, 18 Sep 2013 12:16:55 -0400ramdas chennamsetti15332 at http://imechanica.orgStrain energy density function of a Transversely Isotropic Material
http://imechanica.org/node/13299
<p>
Hi all,
</p>
<p>
I was going through Constitutive Modeling in Continuum Mechanics. I came across the Transversely Isotropic Materials (TIM). I have a couple of doubts, which are listed in the attached pdf file. I request the Continuum Mechanicians to clarify.
</p>
<p>
Thank you in advance,
</p>
<p>
Best regards,
</p>
<p>
- Ramadas
</p>
<p>
</p>
<p>
</p>
<br class="clear" />http://imechanica.org/node/13299#commentsFri, 28 Sep 2012 12:13:45 -0400ramdas chennamsetti13299 at http://imechanica.orgLecture slides on some topics in Advanced Solid Mechanics
http://imechanica.org/node/13152
<p>Normal<br />
0</p>
<p>false<br />
false<br />
false</p>
<p>EN-US<br />
ZH-TW<br />
TH</p>
<p>MicrosoftInternetExplorer4</p>
<p class="MsoNormal">
<span>Hi all,</span>
</p>
<p class="MsoNormal">
<span>I have<br />
attached some slides (in pdf format), which I have prepared when I offered the<br />
course on 'Advanced Solid Mechanics'. These may be useful to some members. </span>
</p>
<p class="MsoNormal">
<span>With best<br />
regards,</span>
</p>
<p class="MsoNormal">
<p>Normal<br />
0</p>
<p>false<br />
false<br />
false</p>
<p>EN-US<br />
ZH-TW<br />
TH</p>
<p>MicrosoftInternetExplorer4</p></p>
<p class="MsoNormal">
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<p class="MsoNormal">
<span>Ramadas</span>
</p>
<p> <br />
</p>
<p>
</p>
<p>/* Style Definitions */<br />
table.MsoNormalTable<br />
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mso-hansi-theme-font:minor-latin;}</p>
<p>Normal<br />
0</p>
<p>false<br />
false<br />
false</p>
<p>EN-US<br />
ZH-TW<br />
TH</p>
<p>MicrosoftInternetExplorer4</p>
<p>/* Style Definitions */<br />
table.MsoNormalTable<br />
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mso-hansi-font-family:Calibri;<br />
mso-hansi-theme-font:minor-latin;}</p>
<br class="clear" />http://imechanica.org/node/13152#commentsTue, 18 Sep 2012 12:13:47 -0400ramdas chennamsetti13152 at http://imechanica.orgANSYS-LSDYNA Tutorials
http://imechanica.org/node/13011
<p>
Hi all,
</p>
<p>
I am looking for ANSYS-LSDYNA tutorials. If anybody has, I request him/her to kindly share or post the links.
</p>
<p>
Thanking you,
</p>
<p>
With best regards,
</p>
<p>
- Ramadas
</p>
<br class="clear" />http://imechanica.org/node/13011#commentsMon, 27 Aug 2012 00:49:34 -0400ramdas chennamsetti13011 at http://imechanica.orgLinear and non-linear buckling
http://imechanica.org/node/10083
<p>
Hi all,
</p>
<p>
When we do a non-linear buckling analysis, initially we introduce some imperfections (mode shapes of mode 1, 2 etc) from eigen buckling analysis. Then we multiply the load with eigenvalue of the first mode. This load is applied on the structure having imperfections. Now put on non-linear geometric option and run the analysis. At bifurcation point we get non-linear buckling load. Non-linear buckling load comes close to eigen buckling value.
</p>
<p>
Decription of my problem is as follows.
</p>
<p>
I have a big structure say 10 m length, 3 m width and 0.02 m (=20 mm ) thick. It is subjected to a complicated loading and constriants. When I do a linear buckling analysis, local buckling is taking place (mode shape is confined to an area of 1m X 0.2 m). Buckling factor is 1.3. I used the corresponding mode shape to introduce imperfection, mutiplied load by 1.3 and then arryied out non-linear buckling analysis. The load factor computed is 2.3. The whole structure (globally) is undergoing deformation.
</p>
<p>
My questions/statements are as follows.
</p>
<p>
1. When a local buckling takes place in a structure, the load factor obtained in non-linear buckling analysis is not in the close to the load factor obtained in linear buckling analysis. Correct or not?
</p>
<p>
2. If the above statement is not correct, what could be the probable mistake that I am commiting in carrying out non-linear buckling analysis?
</p>
<p>
3. What checks shall I carry out?
</p>
<p>
I request to give a thought on these issues.
</p>
<p>
Thanks in advance and regards.
</p>
<p>
- Ramadas
</p>
<br class="clear" />http://imechanica.org/node/10083#commentsTue, 12 Apr 2011 23:40:34 -0400ramdas chennamsetti10083 at http://imechanica.orgNon-linear buckling analysis - complex loading
http://imechanica.org/node/10014
<p>
Hi all,
</p>
<p>
I have attached a single slide ppt file with this blog. In this slide, there is a hollow cylinder subjected to internal pressure and non-uniform axial load. All the translations at the bottom of the cylinder are fixed. As a whole the cylinder is subjected to a complex loading. The cylinder is modeled using SHELL elements in ANSYS. Now I know how to carry out non-linear buckling analysis in ANSYS.
</p>
<p>
There is one more sketch in the slide. A column is subjected to a compressive load and also an infinitesimal lateral load to give perturbation. After carrying out non-linear buckling analysis on this column, we plot axial load vs lateral deflection. Here we get a non-linear load-deflection curve. This is clear.
</p>
<p>
I have the following fundamental questions in case of a cylinder, which is subjected to a complex loading as discussed above.
</p>
<p>
(a) To plot load-deflection curve what nodal points shall I take for load and deflection?
</p>
<p>
(b) Load direction is axial and deflection is radial - correct???
</p>
<p>
(c) Insted of point loads (F1 and F2), if I have axial pressure applied over the thickness, in elemental solution (/post26) I can get the force. How can I convert this to pressure to get the critical buckling pressure?
</p>
<p>
I request some body to calrify the above doubts.
</p>
<p>
With regards,
</p>
<p>
- Ramadas
</p>
<br class="clear" />http://imechanica.org/node/10014#commentsTue, 29 Mar 2011 14:19:03 -0400ramdas chennamsetti10014 at http://imechanica.orgStress based FE is not popular. Why?
http://imechanica.org/node/7445
<p>
</p>
<p>
Hi all,
</p>
<p>
I have a doubt as follows.
</p>
<p>
"Why stress based Finite Element Analysis / Method is not popular compared to displacement based FE?"
</p>
<p>
I request you those who has some idea about this to comment.
</p>
<p>
With regards,
</p>
<p>
- Ramdas
</p>
<br class="clear" />http://imechanica.org/node/7445#commentsMon, 25 Jan 2010 12:51:14 -0500ramdas chennamsetti7445 at http://imechanica.orgHermite interpolation functions
http://imechanica.org/node/6852
<p>
<font color="#000080">Hi all!!!</font>
</p>
<p>
<font color="#000080">In Finite Element Method (FEM), Hermite interpolation functions are used for interpolation of dependent variable and its derivative. </font>
</p>
<p>
<font color="#000080">In FEM books, Hermite interpolation functions are directly written in terms of Lagrange interpolation functions. No derivations are given. I searched in Numerical methods books also for derivation of Hermite interpolation functions.</font> <font color="#000080">I couldn't find.</font>
</p>
<p>
<font color="#000080">I am looking for the origin (basically the derivation) of Hermite interpolation functions. Kindly help me.</font>
</p>
<p>
<font color="#000080">Thanx in advance and regards,</font>
</p>
<p>
<font color="#000080">- Ramdas</font>
</p>
<br class="clear" />http://imechanica.org/node/6852#commentsTue, 29 Sep 2009 21:42:38 -0400ramdas chennamsetti6852 at http://imechanica.orgIf there is no response.....then.....
http://imechanica.org/node/6813
<p>
In imechanica when a blog is posted, we get good response / discussion (or sharing ideas, knowledge etc) from members. This happens many times.
</p>
<p>
If there is no response for a particular blog even after many days...then....what? It may be updated (because some members might have missed it). Even then also if there is no response, what may be done???
</p>
<br class="clear" />http://imechanica.org/node/6813#commentsWed, 23 Sep 2009 21:10:39 -0400ramdas chennamsetti6813 at http://imechanica.orgDelamination mode failure
http://imechanica.org/node/6808
<p align="justify">
<font color="#0000ff">Hi all!!!</font>
</p>
<p align="justify">
<font color="#0000ff">General theories of failure of laminated composites are Tsai-Hu, Tsai-Hill, Maximum stress and maximum strain. These thoeries do not specify which component (fiber or matrix) of lamina fails. </font>
</p>
<p align="justify">
<font color="#0000ff">Sigma_zz, sigma_xz and sigma_yz are out of plane stresses which cause delamination failure of laminated composite structures. </font>
</p>
<p align="justify">
<font color="#0000ff">I am looking for exclusive theories of failure which govern delamination failure in laminated composites. I request those who work in this area to help.</font>
</p>
<p align="justify">
<font color="#0000ff">Thanx in advance,</font>
</p>
<p align="justify">
<font color="#0000ff">Regards,</font>
</p>
<p align="justify">
<font color="#0000ff">- Ramdas</font>
</p>
<br class="clear" />http://imechanica.org/node/6808#commentsTue, 22 Sep 2009 12:16:59 -0400ramdas chennamsetti6808 at http://imechanica.orgFourth order tensor
http://imechanica.org/node/6771
<p>
Hi all,
</p>
<p>
I have a fundamental question on Tensors. The length of a vector (firts order tensor) is independent of the reference co-ordinate system. In case of second order tensor (stress/strain), the invariants (I1, I2, I3) are independent of the co-ordinate system.
</p>
<p>
If I consider 4th order tensor (of course 3rd order also), say Cijkl, what parameters are constant? (Like length in vector and invariants in second order tensors).
</p>
<p>
Thanks in advance,
</p>
<p>
- Ramdas
</p>
<br class="clear" />http://imechanica.org/node/6771#commentsSat, 12 Sep 2009 21:34:18 -0400ramdas chennamsetti6771 at http://imechanica.orgHigh SIF in plane stress
http://imechanica.org/node/5563
<p>
Hi all!!!
</p>
<p>
I have a very basic question in Fracture Mechanics. The question is as following.
</p>
<p>
"Stree Intensity Factor (SIF) is more in plane stress problems (plasic zone size is big) than in plane strain problems (plasic zone size is small). How do we explain this, without refering or invoking energy conecpt?"
</p>
<p>
I request to give some thoughtful explanation.
</p>
<p>
With regards,
</p>
<p>
- Ramdas
</p>
<br class="clear" />http://imechanica.org/node/5563#commentsWed, 03 Jun 2009 06:08:49 -0400ramdas chennamsetti5563 at http://imechanica.orgSpectral Element
http://imechanica.org/node/4620
<p>
Hi all,
</p>
<p>
I have just started learning (working) on spectral element method for modeling elastic wave propagation. I wrote a small code for bar spectral element. There is some problem in reconstruction of signal. If anybody is working in this area may write back. I will send my code. If anybody is having a sample code, I requet them to kindly share.
</p>
<p>
With regards,
</p>
<p>
- Ramdas (<a href="mailto:rd_mech@yahoo.co.in">rd_mech@yahoo.co.in</a>)
</p>
<p>
</p>
<br class="clear" />http://imechanica.org/node/4620#commentsSat, 10 Jan 2009 04:27:09 -0500ramdas chennamsetti4620 at http://imechanica.orgTheories of Failure in Strain space
http://imechanica.org/node/4440
<p>
Hi all!
</p>
<p>
In theories of failure (e.g von-Mises, Tresca, Max. principal stress etc), yield funcion, f(sigma ij, Y) = 0 is plotted in principal stress space (sigma 1, sigma2 and sigma 3). Why shouldn't we express the same yield function, f(epsilon ij, epsilon Y) = 0 and plot in principal strain space?
</p>
<p>
Y = Yiled stress, sigma ij = stress ij, epsilon ij = strain ij. and espsilon Y = Yield strain = Y/E, E = Young's modulus
</p>
<p>
Any thoughtful comments???
</p>
<p>
With regards,
</p>
<p>
- Ramdas
</p>
<br class="clear" />http://imechanica.org/node/4440#commentsFri, 05 Dec 2008 23:35:42 -0500ramdas chennamsetti4440 at http://imechanica.orgComplementary Strain Energy - Non-linearity
http://imechanica.org/node/4371
<p>
Hi all!
</p>
<p>
I read that the "cmplementary starin energy of a structure is not equal to sum of the complementary strain energies of it's components, if there is non-linearity like geometric"
</p>
<p>
That means for e.g. if I consider a truss stucture subjected to loading so that it undergoes geometric non-linearity, then the sum of the complementary strain energies from members is not equal to complementary strain energy of the structure.
</p>
<p>
I request somebody to explain why is it so??
</p>
<p>
Thanks and regards,
</p>
<p>
- Ramdas
</p>
<br class="clear" />http://imechanica.org/node/4371#commentsMon, 24 Nov 2008 21:53:16 -0500ramdas chennamsetti4371 at http://imechanica.orgComplmentary Strain Energy - Nonlinearity
http://imechanica.org/node/4317
<p>
Hi all!
</p>
<p>
I read that the "cmplementary starin energy of a structure is not equal to sum of the complementary strain energies of it's components, if there is non-linearity like geometric"
</p>
<p>
That means for e.g. if I consider a truss stucture subjected to loading so that it undergoes geometric non-linearity, then the sum of the complementary strain energies from members is not equal to complementary strain energy of the structure.
</p>
<p>
I request somebody to explain why is it so??
</p>
<p>
Thanks and regards,
</p>
<p>
- Ramdas
</p>
<br class="clear" />http://imechanica.org/node/4317#commentsMon, 17 Nov 2008 21:57:12 -0500ramdas chennamsetti4317 at http://imechanica.orgComplementary strain energy - Non-linearity
http://imechanica.org/node/4299
<p>
Hi all!
</p>
<p>
I read that the "cmplementary starin energy of a structure is not equal to sum of the complementary strain energies of it's components, if there is non-linearity like geometric"
</p>
<p>
That means for e.g. if I consider a truss stucture subjected to loading so that it undergoes geometric non-linearity, then the sum of the complementary strain energies from members is not equal to complementary strain energy of the structure.
</p>
<p>
I request somebody to explain why is it so??
</p>
<p>
Thanks and regards,
</p>
<p>
- Ramdas
</p>
<br class="clear" />http://imechanica.org/node/4299#commentsThu, 13 Nov 2008 05:01:04 -0500ramdas chennamsetti4299 at http://imechanica.orgWhy rate equations in Nonlinear FE?
http://imechanica.org/node/4072
<p>
Hi all!
</p>
<p>
I have a very fundamental question as follwing.
</p>
<p>
In Nonlinear FE formulations, we use rate equations (virtual work), but, in linear FE we don't use rate equations. Why???
</p>
<p>
Is it because Nonlinear solution is iterative solution (time may be virtual time).
</p>
<p>
I request those who have an idea to give some explanations.
</p>
<p>
Thanks in advance,
</p>
<p>
Regards,
</p>
<p>
- Ramdas
</p>
<p>
</p>
<br class="clear" />http://imechanica.org/node/4072#commentsFri, 17 Oct 2008 08:12:34 -0400ramdas chennamsetti4072 at http://imechanica.orgPolar decomposition
http://imechanica.org/node/3814
<p>
Hi all,
</p>
<p>
I went through a topic on polar decomposition of deformation gradient. I understood the mathematics. I would like to know the physical significance and application of this. I request somebody to explain this.
</p>
<p>
Thanks in advance,
</p>
<p>
Regards,
</p>
<p>
- Ramdas
</p>
<br class="clear" />http://imechanica.org/node/3814#commentsMon, 08 Sep 2008 23:04:45 -0400ramdas chennamsetti3814 at http://imechanica.orgStrain compatibility equation in non-linear solid mechanics!!!
http://imechanica.org/node/3771
<p>We have six strain compatibility equations, which are obtained from strain-displacement relations by making an assumptions 'small strains'. Strain compatibility equations ensure a single valued and continuous displacemnet filed. These equations are used in stress based approach.</p>
<p>
Now my queries are as following.
</p>
<p>
[1] Do we have strain compatibility equations for non-linear strain-displacement relations?
</p>
<p>
[2] Do we follow stress based approach in non-linear solid mechanics.
</p>
<p>
For me it looks like it is difficult (may not be possible also) derive strain compatibility equations in nonlinear solid mechanics.
</p>
<p>
I request that somebody may through light on the above by giving main focus on 'Strain compatibility equations in nonlinear solid mechanics'
</p>
<p>
Thanks in advance,
</p>
<p>
With regards,
</p>
<p>
- R. Chennamsetti.
</p>
<p>
</p>
<br class="clear" />http://imechanica.org/node/3771#commentsMon, 01 Sep 2008 08:22:48 -0400ramdas chennamsetti3771 at http://imechanica.orgCubic symmetry
http://imechanica.org/node/3332
<p>
Hi all!!!
</p>
<p>
Could anybody please give some examples of materials possessing cubic symmetry (these materials need three independent elastic material properties).
</p>
<p>
Thanking you,
</p>
<p>
- R. Chennamsetti
</p>
<br class="clear" />http://imechanica.org/node/3332#commentsFri, 13 Jun 2008 08:32:11 -0400ramdas chennamsetti3332 at http://imechanica.orgPotential for Strain energy
http://imechanica.org/node/2025
<p>
Hi all,
</p>
<p>
When a conservative force does work, it is independent of the path, we define the potential and work done is given by - (change in potential).
</p>
<p>
We define potentials for gravitational force, electrical force etc...
</p>
<p>
Assuming the body is linear elastic, internal forces, cause stresses in a body, are also conservative forces, whose work (strain energy) is independent of the path. Can we define potential for such internal forces? If so, we can calculate strain energy = -(change in potential).
</p>
<p>
You may kindly explain this.
</p>
<p>
Thanks in advance,
</p>
<p>
With regards,
</p>
<p>
- Ramdas
</p>
<br class="clear" />http://imechanica.org/node/2025#commentsMon, 01 Oct 2007 01:22:57 -0400ramdas chennamsetti2025 at http://imechanica.orgBody couples
http://imechanica.org/node/1889
<p>
Hi all,
</p>
<p>
We come across body loads such as gravitational, cenrifugal, magentic etc. Similary do we have body couples? If so, I request you to throw some light.
</p>
<p>
- Thanks & regards,
</p>
<p>
- Ramdas
</p>
<br class="clear" />http://imechanica.org/node/1889#commentsFri, 07 Sep 2007 00:02:37 -0400ramdas chennamsetti1889 at http://imechanica.orgRMS Wave front
http://imechanica.org/node/1878
<p>
</p>
<p>
Hi all,
</p>
<p>
I just want to know how do we calculate the RMS wave front in frontal solver...
</p>
<p>
Thank you,
</p>
<p>
- Ramdas
</p>
<br class="clear" />http://imechanica.org/node/1878#commentsMon, 03 Sep 2007 02:05:47 -0400ramdas chennamsetti1878 at http://imechanica.orgOdd order governing equation - FE formulation
http://imechanica.org/node/1799
<p>
Hi!!
</p>
<p>
We generally encounter governing equations of even order. In FE formulation we get a symmetric coefficient matrix 'A' (AX = B). I have a few doubts as follwing.
</p>
<p>
[a] Any odd order governig equations ? If so, you may please write.
</p>
<p>
[b] Say, it has a functional also, then, what's the order of that differentiation?
</p>
<p>
[c] For even order (n) differential equations (DE), when we use weak formulation approach, we bring down the order to n/2. This finally gives us a symmetric coefficients matrix 'A' (weighting function and shape function are same). But, for odd order DE, when weak formulation is used, then, what's the reduction in the order. I think it may not be n/2.
</p>
<p>
You may plese throw some light on the above questions.
</p>
<p>
- Ramdas
</p>
<br class="clear" />http://imechanica.org/node/1799#commentsSat, 11 Aug 2007 07:03:14 -0400ramdas chennamsetti1799 at http://imechanica.orgBody loads in wave propagation..
http://imechanica.org/node/1681
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<strong>Hi all,</strong>
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[1] In solids, the wave propagation equation is obtained from stress equilibrium equations. We make use of constitutive and strain-displacement relations to convert these equations in terms of displacements
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[2] In the above equations we assume that there are no body loads.
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[3] The form of solution we assume for displacements is harmonic
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[4] Plug these three displacements, u1, u2 and u3 in the equilibrium equations stated in [1].
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[5] We end up with an Eigenvalue problem. This is nice.
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[6] If body loads are present, then, it will no more an Eigenvalue problem. I haven't seen any test book /literature dealing with such problem.
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Has anybody tried solving the wave equation with body loads. If so, you may please write me and suggest me some literature on this.
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Thanks in advance.
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- Ramdas
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<br class="clear" />http://imechanica.org/node/1681#commentsThu, 12 Jul 2007 04:33:39 -0400ramdas chennamsetti1681 at http://imechanica.orgThin plate theory...
http://imechanica.org/node/1461
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<font face="times new roman,times" size="2">Hi all!</font>
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<font face="Times New Roman" size="2">I have a small doubt in the assumptions made in thin plate theory.</font>
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<font face="Times New Roman" size="2">We make some of the following assumptions in thin plate theory (Kirchoff's classical plate theory) (KCPT).</font>
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<font face="Times New Roman" size="2">[1] The normal stress (out of plane=> sigma(z)) is zero. and</font>
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<font face="Times New Roman" size="2">[2] The vertical deflection 'w' is not a function of 'z' => dw/dz = 0</font>
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<font face="Times New Roman" size="2">Now there are three stress components sigma(x), sigma(y) and sigma(xy). The other three stress components sigma(z), sigma(xz) and sigma(yz). This is like a plane stress.</font>
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<font face="Times New Roman" size="2">But, from the second assumption ez=0 (strain in z-direction) and from the above exz=0 and eyz=0. </font>
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<font face="Times New Roman" size="2">Then, this leads to plane strain. </font>
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<font face="Times New Roman" size="2">From the constitutive equation for 'ez' => sigma(x)+sigma(y)=0</font>
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<font face="Times New Roman" size="2">But, this doesn't happen.....I am looking for explanations ...</font>
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<font face="Times New Roman" size="2">Thanks in advance.</font>
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<br class="clear" />http://imechanica.org/node/1461#commentsThu, 24 May 2007 14:13:12 -0400ramdas chennamsetti1461 at http://imechanica.orgSpectral Finite Elements
http://imechanica.org/node/1455
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Hi all!
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I just strated using Spectral FE technique for wave propagation applications. I am looking for some example code (for bar/beam or any geometry). If anybody has, I request them to kindly send me.
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Thanks in advance.
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- R, Chennamsetti
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<br class="clear" />http://imechanica.org/node/1455#commentsWed, 23 May 2007 08:31:31 -0400ramdas chennamsetti1455 at http://imechanica.orgMesh free methods - literature
http://imechanica.org/node/1074
<p>Hi all!!</p>
<p>Where can I get literature on Mesh free methods (basics)?</p>
<p>I am suggested Dr. Liu's book. </p>
<p>Please suggest me some more good literature (some web sites, text books etc), assuming that I am zero in mesh free methods.</p>
<p>Thanking you.</p>
<br class="clear" />http://imechanica.org/node/1074#commentsFri, 16 Mar 2007 11:42:31 -0400ramdas chennamsetti1074 at http://imechanica.org