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