FEM:A simple stiffness matrix problem

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Discussion Overview

The discussion revolves around a homework problem related to forming a stiffness matrix in the context of finite element analysis (FEM). Participants explore the appropriate approach to constructing the stiffness matrix, the relevance of stress stiffening, and the implications of torsional springs in the analysis.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • The original poster expresses confusion about forming the stiffness matrix and whether to consider stress stiffening in their analysis.
  • Some participants suggest that a 4x4 stiffness matrix is sufficient for the problem, while a 6x6 matrix may be unnecessary.
  • One participant notes that torsional moments may not be present in the frame due to the nature of the loads involved, which are primarily axial and bending.
  • Another participant cautions against considering stress stiffening unless specifically requested, highlighting that it could complicate the analysis by making it non-linear.
  • The original poster acknowledges the advice and plans to refer to a book that contains a similar problem for further guidance.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether to consider stress stiffening, with differing opinions on its necessity and implications for the analysis. There is also a lack of agreement on the appropriateness of using a 6x6 matrix versus a 4x4 matrix.

Contextual Notes

Participants mention simplifying assumptions in the stiffness method that maintain linearity, indicating that deviations from these assumptions could lead to non-linear problems requiring iterative solutions. The original poster's understanding of torsional springs is also noted as being influenced by a lack of information regarding the material property "G."

Who May Find This Useful

Students and practitioners in the field of finite element analysis, particularly those dealing with stiffness matrix formulation and linear versus non-linear analysis considerations.

arifgokcen
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Homework Statement





Homework Equations



1-Stiffness matrix?
2-When i am doing the deformation,should i consider stress stiffenning or just solve the problem as is

The Attempt at a Solution



I tried to form the necessary stiffness matrix but couldn't understand how should i approach the problem.I place two axial springs and one torsional spring at 1st end.However in the question "G" is not given so i shouldn't use torsional spring(as my prof. said.He just explained this part that i shouldn't use torsional spring).

then i formed a new 4x4 matrix for the first element and third element.
This matrix has 3 axial columns and 1 bending column with 2nd column being a bending column.

and for 2nd element i formed a 6x6 matrix with u_2,u_3,v_2,v_3,w_2,w_3

I know its trivial but still having problems.Very new to the topic so please elaborate

Thanks
 
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I recommend the book, 'Applied Finite Element Analysis', 2. ed., by Larry Segerlind.

Here is a link to a pdf copy:

ftp://161.53.116.242/Predavanja_vjez...0Segerlind.pdf

This book will show you step-by-step how to set up a stiffness matrix and solve it. Given the nature of your problem, a 6x6 element is not required. A 4x4 element should be sufficient.

Given the loading and construction of the frame, I cannot see that any torsional moments are present. Remember, torsion is twisting of a beam about its longitudinal axis. Your frame has only axial loads and bending loads.
 
What about the second part of my question.

Should i consider stress stiffenning.

I have downloaded book and problem 19-4 looks very similar as you said it shows 4x4 so i will try to solve that part again.

Thank you for you help
 
I'm not sure what you mean by 'stress stiffening', but unless you are specifically requested to do so, I would not.

There are certain simplifying assumptions implied in the stiffness method which keeps the analysis linear. If these assumptions are not applied, then instead of finding a direct solution to the stiffness equations, the problem becomes non-linear, and iterative methods of solution are required.
 

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