The support stiffness values which are in-built in the calculations of COADE program are 10e6 kg/mm or so . Has this value been arrived at based on some experiments or logic ? Obviously the value has to be high enough to represent a real rigid support. But is there any specific logic for the value ? Is it that the same value is used by other softwares equivalent to CAESARII like Autopipe , CAEPIPE etc. ?
Regards,
Sunil

Mr. Godbole

In Finite Element analysis ,Modelling of fixed degree of freedom is done in two ways.

If you use the principle of minimum potential energy, where first you write an expression for the potential energy as sum of strain energy and work potential, then take the partial derivatives w.r t the degrees of freedom, to arrive at the equilibrium equation

[P]=][K][Q]

you will fnd that the coefficients for fixed degree of freedoms are no longer there when taking the partial derivatives. This results in a reduced stiffness matrix, displacement and load vectors.

The other method is to consider a spring of very rigid stiffness at the fixed degree of freedoms . This does not require elimination of rows and columns corresponding to fixed degree of freedoms.

This is preciously the method used by CAESAR II and other standard softwares The stiffness of the restraint is what is given by 1e12.

There is a strong mathematical basis for arriving at what should be the optimum value of this spring stiffness.Something which requires an elaborate discussion for which discussion forum is possibly not the right platform.

To my knowlegde the other softwares you have mentioned probably use in that range only.

If you want a more detailed discussion you can contact me at my e-mail address:

abhattac@bechtel.com

A.Bhattacharya

Stress analyst

Bechtel corporation

One small correction. I wanted to write "precisely ", which by slip has resulted in "preciously".

Anindya

Sunil,

I think there was some problem in you receiving my e -mail. So I am furnishing a detailed answer to your question in the discussion forum.

The equation

[P]=[K][Q]

is solved by Gaussian elimination method.

Now two types of solution errors arise. One is the truncation error and the other one is the round off error.


To define these terms in a simple manner: Truncation error is the term used to signify the reduction in no. Of digits in the stiffness co efficients and loads present in the actual [K] and [Q] stiffness matrix and load vector respectively, due to machine constraint. This is known as precision requirement.


Round off error is due to continuous” chopping off “ digits in the subsequent steps of Gaussian elimination.


Total error = truncation error + round off error.


The value of restraint spring stiffness is a result of lot of trial and error to strike a balance to minimize truncation and round off errors.


The main cause of truncation error is when the absolute values of the terms in the [K] matrix vary a lot. The main cause of round off error is when a small value of a diagonal term (Kii ) is used which will result in a higher multiplication factor for the pivot row at the time of decomposition ( LDLT ) .


This is quite an interesting topic in Numerical Analysis, all of which possibly cannot be discussed in the discussion forum.

If you are interested, I can refer two excellent texts books to you on this topic:


1) Numerical Methods in Finite Element Analysis- K.J. BATHE and E.L.WILSON

2) Finite Element Procedures:-- K.J.BATHE


A.Bhattacharya

Stress Analyst

Bechtel Corporation