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large deformation of beam element
Sat, 2013-09-14 12:50 - mjalilych1
hello
my name is mohamad. I am phd student in mechanical engineering. I want to use of total lagrangian formulation for analysis of a cantilever. my difficulty is on implementation of newton raphson method and incrementing load. my code does not converge. can you help me. if there is a simple code I was wondering if someone aware me.
thanks in advance.
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nonlinear beam finite element
thank you.
some things to look at
You may wish to look at some of the following links
http://people.wallawalla.edu/~louie.yaw/nonlinear/ExIm_analysis.pdf
These next two have detailed algorithms written out for a corotational analysis using Newton-Raphson iterations under the case of load control. The second link also contains a displacement control algorithm. Both have references which would be helpful to you regarding nonlinear analysis control concepts that include Newton-Raphson iterations.
http://people.wallawalla.edu/~louie.yaw/Co-rotational_docs/2Dcorot_beam.pdf
http://people.wallawalla.edu/~louie.yaw/Co-rotational_docs/2Dcorot_truss...
You may also benefit from looking here
http://www.colorado.edu/engineering/cas/courses.d/NFEM.d/
regards,
Louie
3D corotational beam
Hi Prof. Liu
As a part of my PhD, I need to implement a slender beam dynamic in 3D with displacement control
I have read your very well explained papers regarding 2D corotational bar and beam static analysis for large rotation and displacement (load control)
I would like to know if you have a same paper for del with large rotation andisplacement for 3D
I will be very grateful to read your code because when I tru to implement the displacement control problem in 3D using bar elments an beam element
I have still some errors.
Best Regards
Ausberto Rivera
some sources for you to look at
Ausberto,
I have not implemented a 3D corotational beam formulation. It is something I want to do and have been working on from time to time for my own learning purposes. However, I will provide a list of sources for you to look at that look good to me for learning about 3D corotational beam formulations.
1 http://www.diva-portal.org/smash/get/diva2:9068/FULLTEXT01
2 http://www.scribd.com/doc/111444818/A-Consistent-Co-rotational-Formulati...
3 http://kth.diva-portal.org/smash/get/diva2:526302/FULLTEXT02.pdf
4 http://link.springer.com/article/10.1007%2Fs00466-006-0029-x#page-1
5 http://www.ufpa.br/nicae/integrantes/remo_souza/TrabPublicados/TesesDiss...
6 Krenk, Steen, "Non-linear modeling and analysis of solids and structures", Cambridge, 2009.
7 Crisfield, "Non-linear Finite Element analysis of solids and structures - Advanced Topics", vol II, Wiley, Chichester, 1997.
The above sources should give you a good start. After a lot of study the approach by Crisfield [2][7] seems quite messy. I'm getting to the end of working through his paper on 3D beams[2]. I haven't gone through much of it yet, but the book by Krenk[6] seems to be cleaner. Also, the source [3] is the most recent and looks promising. You will have to look over these and see what you think.
I hope that helps,
Louie
Thanks for this post Dr. Yaw.
Thanks for this post Dr. Yaw.
About the Newton Raphson Method
Hello,
The Newton Raphson Method is used to find the Optimum of an N-Dimensional Function since it uses the first and second derivatives. It has the Problem in Selecting the Starting Point because it May Not Converge to the Solution. You have to check your Formulation if it corresponds to the Described Method because there are Several kinds of Newton Methods. However you can find a Wide Variety of Search Methods to Reach the Solution in Optimization (Maximization or Minimization case). The Form of the Analyzed Function (Modal or Multimodal, .....) is also important for the Applied Method. An Efficient Method is the " Pattern Sequential Simplex Method " which uses a Geometrical Search in N-Dimensions. It Requires to Construct a Simplex (Triangle, Tetrahedron, ......) with (N+1) Vertices in the N-Dimensional Space. The Method Allows the Search of a Local Solution with Constructing a New Simplex at each Step Until the Optimum is Surrounded. The Method Converges if the Optimum Exists and is Unique.
Mohammed Lamine
thanks you for your
thanks you for your responses.
displacement control
hello Dear Scientists
I want to study nonlinear behavior of williams toggle frame by finite element method. I use of load control approach in newton raphson. my results are a little different. is it reasonable that I convert my program to displacement control. if ok please help me about useful literature in this topic.