Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Regarding Stiffness Matrix & Element Nodal Forces

Regarding Stiffness Matrix & Element Nodal Forces

Regarding Stiffness Matrix & Element Nodal Forces

Hello Everyone, I am calculating stiffness matrix for a hexahedron element using C code and I am using gauss points. However if I compare my output with the stiffness matrix output by Abaqus, I see some differences ? Is it normal ?

Also I am trying to transfer element nodal forces from one mesh to another. The transfer has to be conservative, so what is the best way to acheive this ?

RE: Regarding Stiffness Matrix & Element Nodal Forces

If your element has the same formulation as the Abaqus element (or is intended to have the same formulation), then it should give almost exactly the same results. If it doesn't, it won't.

Doug Jenkins
Interactive Design Services

RE: Regarding Stiffness Matrix & Element Nodal Forces

8-node hex elements often have all sorts of different formulations because the basic textbook one is quite terrible. Several programs seem to use identical formulations for 10-node tets though. 20-node hex is also more likely to be the same.

Other things to check:
  • Make sure you have the same number of Gauss points. It might be 1 or 8.
  • Make sure the row order is the same. It might be ordered by the element's node numbering or by the global node numbers or arbitrarily mixed up in some other way.
  • See if the non-zero structure is the same.
  • Check for correctness by summing the rows. Each row should sum to zero.
Not sure how you'd transfer node forces to a different mesh. I guess the most correct way would be to first find a continuous (ie. not discrete) force field that the node forces define, and then apply that distributed load to each element in the new mesh by integrating it over the element's face. For that second stage, you could use Gauss points to sample the field, but there's no guarantee they'll capture all the details if it's very non-uniform. You could use a much larger number of integration points to sample it more accurately. If you already know the field that the node forces represent then that will take care of the first stage which I have no idea how to do otherwise.

That's a very complex job. If you a dirty shortcut, maybe just sum them to find the net force then apply a uniform force that's the same? That might cause the wrong moment though.

RE: Regarding Stiffness Matrix & Element Nodal Forces

Thanks Doug and Whitwas for your suggestions.

@whitwas, The row sum came to be zero. I will try your suggestions and update. Thanks a lot.

RE: Regarding Stiffness Matrix & Element Nodal Forces

Hello Everyone, I found why there was a difference in results when cmpared to Abaqus. For Hex8, Abaqus does both Full Integration using 8 Gauss Points plus Reduced Integration using 1 Gauss point. The stiffness term is split into two parts - dilational and deviatoric (dont know the exact meaning).

RE: Regarding Stiffness Matrix & Element Nodal Forces

try google ...
"dilational" ... relating to "dilation" (oh, great !) ... "or compression" ... ok, that's more helpful.

another day in paradise, or is paradise one day closer ?

RE: Regarding Stiffness Matrix & Element Nodal Forces

Dilational typically refers to stresses that change the volume, though I usually hear it referred to as hydrostatic, not dilational. However, dilational is probably the better term since hydrostatic indicates water is involved which doesn't have to be the case.

For dilational stresses, think of a balloon floating in a chamber of gas. As the pressure in the surrounding gas goes up, the balloon shrinks in size. If you slowly increase the pressure the balloon will keep shrinking in size, but is unlikely to pop. Dilational stresses usually aren't what cause material failure, though they still cause strain. Deviatoric is more like shear stresses. They cause materials to fail. If you tried to cut that balloon with scissors after it shrank it would definitely pop. The scissors are introducing mostly deviatoric stresses.

In reality, both of these are derived from the typical stress tensor. When you add the two together it should give you back your typical stress tensor.

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members! Already a Member? Login


eBook - Integrating the Engineering Ecosystem
Aras Innovator provides multiple options for integrating data between systems, depending on the scenario. Utilizing the right approach to meet specific business requirements is vital. These needs range from authoring tools, federating data from various and dissimilar databases, and triggering processes and workflows. Download Now
Research Report - Simulation-Driven Design for SOLIDWORKS Users
In this engineering.com research report, we discuss the rising role of simulation and the paradigm shift commonly called the democratization of simulation. In particular, we focus on how SOLIDWORKS users can take advantage of simulation-driven design through two analysis tools: SOLIDWORKS Simulation and 3DEXPERIENCE WORKS. Download Now
White Paper - Industry 4.0 and the Future of Engineering Education
With industries becoming more automated, more tech-driven and more complex, engineers need to keep their skills and knowledge up to date in order to stay on top of this wave—and to be prepared for the Industry 4.0 future. The University of Cincinnati offers two online Master of Engineering degree programs designed specifically for practicing engineers. Download Now
eBook - The Design Gridlock Manifesto
In this eBook, you’ll learn 6 ways old CAD technology slows your company down and hear how design teams have put those problems to rest. “The Design Gridlock Manifesto” shares first-hand modern CAD experiences from 15 companies around the world. Download Now

Close Box

Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

Register now while it's still free!

Already a member? Close this window and log in.

Join Us             Close