Hi all,

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.

Decription of my problem is as follows. 

Hi all,

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.

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.  

Hi all,

I have a doubt as follows.

"Why stress based Finite Element Analysis / Method is not popular compared to displacement based FE?"

I request you those who has some idea about this to comment.

With regards,

- Ramdas

Hi all!!!

In Finite Element Method (FEM), Hermite interpolation functions are used for interpolation of dependent variable and its derivative.

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. I couldn't find.

I am looking for the origin (basically the derivation) of Hermite interpolation functions. Kindly help me.

Thanx in advance and regards,

In imechanica when a blog is posted, we get good response / discussion (or sharing ideas, knowledge etc) from members. This happens many times.

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???

Hi all!!!

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.

Sigma_zz, sigma_xz and sigma_yz are out of plane stresses which cause delamination failure of laminated composite structures.

Hi all,

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.

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).

Thanks in advance,

- Ramdas

Hi all!!!

I have a very basic question in Fracture Mechanics. The question is as following.

"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?"

I request to give some thoughtful explanation.

With regards,

- Ramdas

Hi all,

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.

With regards,

- Ramdas (rd_mech@yahoo.co.in)

Hi all!

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?

Y = Yiled stress, sigma ij = stress ij, epsilon ij = strain ij. and espsilon Y = Yield strain = Y/E,   E = Young's modulus

Any thoughtful comments???

With regards,

- Ramdas

Hi all!

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"

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.

 I request somebody to explain why is it so??

 Thanks and regards,

- Ramdas

Hi all!

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"

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.

 I request somebody to explain why is it so??

 Thanks and regards,

- Ramdas

Hi all!

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"

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.

 I request somebody to explain why is it so??

 Thanks and regards,

- Ramdas

Hi all!

I have a very fundamental question as follwing.

In Nonlinear FE formulations, we use rate equations (virtual work), but, in linear FE we don't use rate equations. Why???

Is it because Nonlinear solution is iterative solution (time may be virtual time).

I request those who have an idea to give some explanations.

Thanks in advance,

Regards,

- Ramdas

Hi all,

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.

Thanks in advance,

Regards,

- Ramdas

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.

Now my queries are as following.

[1] Do we have strain compatibility equations for non-linear strain-displacement relations?

[2] Do we follow stress based approach in non-linear solid mechanics.

For me it looks like it is difficult (may not be possible also) derive strain compatibility equations in nonlinear  solid mechanics.

Hi all!!!

Could anybody please give some examples of materials possessing cubic symmetry (these materials need three independent elastic material properties).

Thanking you,

- R. Chennamsetti 

Hi all,

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).

We define potentials for gravitational force, electrical force etc...

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).

You may kindly explain this.

Thanks in advance,

With regards,

- Ramdas

Hi all,

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.

- Thanks & regards,

- Ramdas

Hi all,

I just want to know how do we calculate the RMS wave front in frontal solver...

Thank you,

- Ramdas

Hi!!

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.

[a] Any odd order governig equations ? If so, you may please write.

[b] Say, it has a functional also, then, what's the order of that differentiation?

[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.

Hi all,

[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

[2] In the above equations we assume that there are no body loads.

[3] The form of solution we assume for displacements is harmonic

[4] Plug these three displacements, u1, u2 and u3 in the equilibrium equations stated in [1].

[5] We end up with an Eigenvalue problem. This is nice.

[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.

Hi all!

I have a small doubt in the assumptions made in thin plate theory.

We make some of the following assumptions in thin plate theory (Kirchoff's classical plate theory) (KCPT).

[1] The normal stress (out of plane=> sigma(z)) is zero. and

[2] The vertical deflection 'w' is not a function of 'z' => dw/dz = 0

Hi all!

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.

Thanks in advance.

- R, Chennamsetti

Hi all!!

Where can I get literature on Mesh free methods (basics)?

I am suggested Dr. Liu's book.

Please suggest me some more good literature (some web sites, text books etc), assuming that I am zero in mesh free methods.