# Newmark's method to solve a system of spring elements

by mina1363
Tags: newmark's method
P: 14
Hi,

I have been trying to solve a system consisting of 3 linear spring elements using the Newmark's method to find displacement, velocity and acceleration in Matlab. I followed the instructions shown on page 5 of the paper attached and my code does not seem to be working as the displacement values keep increasing. Does anyone know whether the instructions I am using are correct....??? Also does anyone know a similar system for which a code has been written already so that I can compare my results.

p.s. I've aslo attached the equation of motionfor a single element. Effectively I have similar system including 4 by 4 mass and stuffness matrices and 4 by 1 displacement and acceleration matrices.

Any hints and tips would be appreciated.

Many Thanks!
Attached Thumbnails

Attached Files
 Dynamics Analysis by Numercial Integration.pdf (212.5 KB, 330 views)
P: 2
As far as I remember (it was 2 years ago), I relied on the same document and I think that I had the same issue with it.

I have attached a draft of mine that I found were you can have at least another version of the algorithm. Actually this part is based on another thesis.

You can also check Bathe's "Finite Element Procedures" where there's a another version.

Let me know if you still have problems...
Attached Files
 chapter.pdf (148.4 KB, 242 views)
 P: 14 Thank you for your reply. I think the steps shown in the document you attached are essentially the same only that they are for a free vibration system with no damping...rather than a forced one... I'm going to chekc out the other one you mentioned now.
 P: 14 Newmark's method to solve a system of spring elements Hi, Thank you for mentioning Bathe's book. So I used Newmark's algorithm from : Bathe, K.-J., (1996), Finite Element Procedures, Prentice-Hall International, page 781 and I did example 9.4 using the simple code I wrote and I got the answers. But I only managed to get the answers because when calculating the effective load, I calculated it for time 't' rather than time 't+deltat' . If I used 't+deltat' I would get really big displacement values. Do you have any idea why this is happening???
 P: 5 @ mina 1363 hi,i have been doing a similar problem and encountered an exactly similar hurdle.of displacemnts increasing continuoulsy.Can you tell me how you handled this problem
 P: 14 Hi, The example in Bathe, K.-J., (1996), Finite Element Procedures is applied to a case with a cosntant force. Unfortuantely I haven't done one for a vairable force yet. Regards,
 P: 5 I had a small doubt.Coincidently even I did my initial matlab code using the algorithm you used initially ;from the document you have attached.Is there any problem with it?Is it wrong?
 P: 14 I'm not sure to be honest but at least with the one form the Finite Element Procedures book you can check your algorithm (for a constant force) by doing the example in the book. If you don't have access to the book try www.scribd.com
 P: 5 @mina1363 hey thanks a lot!!that definately helped..Seems the initial algorithm has a problem.But I am getting correct value till around 6 "delta t"...not till 12 as given..any clue..why......hey if its possible for you can you send me the matlab code you have written..maybe i m somewhere wrong with the code...my email id is.... prashastpjain@gmail.com
 P: 14 Hi, I don't have access to my code right now. If you wish send me your code and I'll have a look at it by all means.
P: 5
I m sending you the code in both the ".txt" nd ".m" format....do let me know if there's any error.Your help will mean a lot.
Attached Files
 newmark beta method.txt (672 Bytes, 162 views) newmark_B.m (672 Bytes, 145 views)
 P: 5 hello mina... i hvnt heard from you.Any luck with the code???do let me know..
 P: 14 Hi, I'm sorry I've not had chance to look at it yet. I will look at it this afternoon and will let you know asap.
 P: 14 Hi, I had a look at your code. Everything seems fine. Althought I'm not familiar with the choleski function in Matlab as I just wrote my own algorithm. So make sure that the function gives you L and D. The other thing that I didn't use is the substitution function. Again I'm not sure how that works but make sure that you use backward and forward substitution. Best of Luck.
 P: 1 How we can apply Newmark Method for Multiple degrees of freedom
 P: 1 Hi, I'm working on "numerical solving the coupled thermoelasticity equation". for time integratio I use newmark method, but I have problem with boundary conditions. Does anyoe know, when should I impose boundary conditions?

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