×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Contact US

*
*
*
*

Thanks. We have received your request and will respond promptly.

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!
*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

References for Equivalent Nodal Force Computations

thread727-493806

References for Equivalent Nodal Force Computations

References for Equivalent Nodal Force Computations

(OP)
Is anyone aware of any worked examples for the computations of Equivalent Nodal Forces for partial loading normal to a shell element?
I have a few of the books noted in the FAQ here that I have started working through namely:
Zienkiewicz - Volumes 1 and 2
Finite element procedures by K J Bathe
A First Course in the Finite Element Method by Daryl L Logan
Programming the Finite Element Method by Smith and Griffiths

I admittedly need to work on my calculus so don't have a full grasp yet on the body and traction force integrals, but none of the books appeared to directly address loadings of this type and in general don't provide many examples for the equivalent nodal forces.



A secondary question is for the body and traction force integrals are these typically done based on the actual element geometry or the isoperimetric formulation? Seems you could use the isoperimetric shape functions and jacobian and just need to work out the load function change of variable from x,y to eta,xi (for many cases this would appear to be a direct substitution).

I'm making a thing: www.thestructuraltoolbox.com
(It's no Kootware and it will probably break but it's alive!)

RE: References for Equivalent Nodal Force Computations

Check also "Concepts and Applications of Finite Element Analysis" by Cook.

RE: References for Equivalent Nodal Force Computations

(OP)
Thanks for the recommendation FEA way, have been eyeing a few copies of that one on Ebay for a few weeks.

I'm making a thing: www.thestructuraltoolbox.com
(It's no Kootware and it will probably break but it's alive!)

RE: References for Equivalent Nodal Force Computations

There might be some information in "The finite element analysis of shells by Chapelle and Bathe". You can refer any FEA of shell book which may have information you need.

RE: References for Equivalent Nodal Force Computations

The integrals are done using reference elements, as you mentioned, and often using isoparametric mapping, i.e., polynomial order of the element (e.g., linear) is the same order as the polynomial order of the element (linear representing piecewise linear, e.g., triangle, shapes). In practice, often a 1D integration scheme is used in two orthogonal directions in the reference element.

To express the integral of a typical element using a reference element, you will need the Jacobian (for scaling when changing "dxdy" to "dXidEta") and also to transform the gradient using the chain rule (in 2 dimensions); then, choose a quadrature scheme and implement it.

Note that Reissner-Mindlin plates suffer from shear locking unless a rather complicated mathematical trick (not just reduced integration as for a Timoshenko beam) is applied, so I would advice to start from the classical plate model - or better yet, to let commercial software provide a reliable and general plate solver.

RE: References for Equivalent Nodal Force Computations

(OP)
Thanks NRP99, I'll give that text a look.

Thanks for the explanation centondollar.

I'm making a thing: www.thestructuraltoolbox.com
(It's no Kootware and it will probably break but it's alive!)

RE: References for Equivalent Nodal Force Computations

(OP)
FEA Way: thanks again for that recommendation the Cook book has an excellent section on the equivalent nodal forces was able to grab a copy of the third edition for under $5 off of Abe Books.

I'm making a thing: www.thestructuraltoolbox.com
(It's no Kootware and it will probably break but it's alive!)

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

Resources

Low-Volume Rapid Injection Molding With 3D Printed Molds
Learn methods and guidelines for using stereolithography (SLA) 3D printed molds in the injection molding process to lower costs and lead time. Discover how this hybrid manufacturing process enables on-demand mold fabrication to quickly produce small batches of thermoplastic parts. Download Now
Design for Additive Manufacturing (DfAM)
Examine how the principles of DfAM upend many of the long-standing rules around manufacturability - allowing engineers and designers to place a part’s function at the center of their design considerations. Download Now
Taking Control of Engineering Documents
This ebook covers tips for creating and managing workflows, security best practices and protection of intellectual property, Cloud vs. on-premise software solutions, CAD file management, compliance, and more. 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