Help with 1D Stress FE Model Analysis

In summary, the conversation discusses a book on finite elements and stress analysis which the speaker believes contains mistakes. The speaker also shares images from the book and asks for opinions on the author's methods. They also mention that the number of nodes used in the calculations can affect accuracy and the stiffness of the matrix. The main confusion is about the author's use of different node positions in the calculations and how this affects the accuracy of the answers.
  • #1
Jonny6001
20
0
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.
 
Last edited by a moderator:
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  • #2
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:
  • #3
i understand that,but how can his answers be correct if they don't satisfy the simultaneous equations?
 

Related to Help with 1D Stress FE Model Analysis

What is a 1D Stress FE Model Analysis?

A 1D Stress FE Model Analysis is a numerical method used to simulate and analyze the stress distribution in a one-dimensional structure under different loading conditions. It is commonly used in engineering and scientific research to understand the behavior of structural components and make predictions about their performance.

What are the advantages of using a 1D Stress FE Model Analysis?

One of the main advantages of this type of analysis is its ability to accurately predict the stress distribution in a structure without the need for physical testing. It also allows for faster and more cost-effective design iterations, as well as the ability to simulate different loading scenarios and evaluate the effects on the structure's stability.

What factors affect the accuracy of a 1D Stress FE Model Analysis?

The accuracy of a 1D Stress FE Model Analysis depends on factors such as the quality of the input data, the complexity of the structure, and the assumptions made in the analysis. It is important to carefully select appropriate material properties, boundary conditions, and element types in order to obtain accurate results.

What are some common applications of 1D Stress FE Model Analysis?

1D Stress FE Model Analysis is used in a variety of fields, including civil engineering, mechanical engineering, and aerospace engineering. It is commonly used in the design and analysis of structures such as bridges, buildings, and aircraft components.

Are there any limitations to the use of 1D Stress FE Model Analysis?

While 1D Stress FE Model Analysis is a powerful tool, it does have its limitations. It is most suitable for analyzing simple structures that can be modeled as one-dimensional, such as beams and trusses. It is also important to validate the results of the analysis with physical testing to ensure accuracy.

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