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.