Design of pipeline

[billu]

hello everyone:)
I am working on modeling a buried pipeline in Opensees Based on BNWF(beam on non-linear Winkler Foundation). I have a question that what should be minimum element length while constructing a pipeline? whats the criteria for judging it?? because its a problem of soil-structure Interaction...Please if someone knows about it, guide me with this.
Thanks all. Waiting for the response.

[skamalzare]

Are you performing static or dynamic simulations? Is your solution system implicit or explicit?

* In FE analyses to represent a traveling wave accurately about 10 nodes per wave length are required. Fewer than 10 nodes can lead to numerical damping as the discretization misses certain peaks of the wave (Preisig and Jeremic, 2005).

I usually reduce the size of my elements to a level that smaller elements won't change my results.

[billu]

Hi thanks for replying
I am performing dynamic simulations.actually i am stuck in finding the minimum element length for now. I have to find flexural wave propagation speed if for example i am applying impact load in the range 0f 3kHz to 6kHz. Is there any formula or equation to find flexural wave propagation speed along the beam??? Can u guide with this please????

[billu]

And also if i consider for example total length of pipeline (which i am assuming it a beam) to be 100m.

[skamalzare]

Wave speed is a material property. Depending on what material you are using, you will have different wave speeds. It is calculated as: V = (elastic property / density)^0.5.

You can calculate the element length as: L <= (Vmin / (10*fmax)). Where, "L" is the maximum element length, "Vmin" is the lowest wave velocity along the material, "fmax" is the maximum wave frequency. I usually filter my waves to know what is my max frequency.

A good reference for your problem is: "Nonlinear Finite Element Analysis of Dynamic Soil-Foundation-Structure Interaction" by Preisig and Jeremic (2005).

Bests,
Soheil

[billu]

Hi soheil :_) thanks for ur kind reply it was really quite important piece of information.
Actually i am considering flexural waves along the beam, so if i am using steel pipeline I have to to put its young,s modulus but as i am considering flexural waves so they will be bending along the beam. Do u think within formula of Wave speed, we also have to account moment of inertia factor???

[skamalzare]

I did a quick Wikipedia check on speed of flexural waves, and it turned out that it is a function of material property and geometry. Therefore, you need to find the correct equation that includes both these factors. Note that this is not the case for body waves (i.e. shear and pressure waves).

[billu]

Yes you are right and i have found the equation.

[billu]

The governing equation for flexural wave propagation is derived for one dimensional wave equation in an infinite medium. Bernoulli-Euler theory of beam is considered, i.e. only pure bending is considered. So if the material of the beam is considered as homogeneous, then the motion in the vertical direction (y direction) can be given by (Graff, 1975)
a^2=EI/pA
where, E = modulus of elasticity; I = moment of inertia; p = mass density; A = cross sectional area.If a harmonic wave is propagating, then the flexural wave velocity, c can be found by,
a=(a)^1/2 * (EI/pA)^1/4
where, ω = angular frequency.