Help with 1D Stress FE Model Analysis

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    1d Model Stress
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SUMMARY

The forum discussion centers on the challenges faced in performing a 1D stress finite element analysis as presented in a specific book. The user expresses confusion regarding the sign convention and displacement calculations between nodes, particularly the transition from (u1-u2) to (u4-u3). The author of the book uses four nodes for approximation, with u1 as the fixed end, u4 as the free end, and u2 and u3 as intermediate nodes. The user questions the validity of the author's results, noting that they do not satisfy the simultaneous equations required for accurate analysis.

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  • Understanding of finite element analysis (FEA) principles
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  • Knowledge of sign conventions in mechanics
  • Basic proficiency in solving simultaneous equations
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This discussion is beneficial for engineering students, finite element analysts, and professionals involved in stress analysis who seek to deepen their understanding of 1D modeling techniques and the implications of node selection on analysis accuracy.

Jonny6001
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Hello, I am reading a book about finite elements with regards to stress analysis. I'm pretty sure the book is full of mistakes, which makes following and doing the examples fairly difficult.
I have posted a 1D analysis from the book, I'm not even sure how he comes up with some of the numbers in the calculations.

I do understand the method but what hasn't exactly "clicked" is the sign convention or the displacement of each node equating to the change in element length. The author has (u1-u2), then on the last element he switches to (u4-u3), is there a reason for this or is it because u4 is the last node?

Would someone mind having a really quick look at the images I posted to give their oppinion. But definitely his answers do not satisfy the simulataneous equations.

Thanks a lot for your time.

http://img2.imageshack.us/img2/3816/scan0001xo.jpg
http://img203.imageshack.us/img203/8407/scan0002r.jpg
http://img242.imageshack.us/img242/3311/scan0003e.jpg
http://img43.imageshack.us/img43/5510/scan0004al.jpg

I'm sorry, I've posted this in the general maths forum too but thinking about it, I think this area is more relevant.
 
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looks right to me. The author is specifying 4 nodes for his approximation.
u1 being the fixed end, u2 and u3 averaged in between, and u4 being the free end. Really, you can use as much nodes as you want, the more nodes, the more accurate. Although, The more nodes, the more stiffness k to calculate and a larger matrix to solve.
Also, your calculating with the element (eg. u2-u1), not the single node position
 
Last edited:
i understand that,but how can his answers be correct if they don't satisfy the simultaneous equations?
 

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