# The 8 Mode Shapes of a plane finite element

• Trying2Learn
In summary, the conversation was about obtaining the eight mode shapes and eigenvalues for a single plane stress or strain finite element. The speaker mentioned seeing them 30 years ago and writing a FORTRAN code to obtain them. They also saw them in a book but couldn't remember which one. The eight mode shapes were described as stretch in 1, stretch in 2, a horizontal and vertical shear, and one other. The speaker is currently trying to write a MATLAB code to produce them but is getting strange results. They are looking for a site that has the eight shapes and are not interested in an eigenvalue analysis on a mesh. The other person suggests using Abaqus, which shows the desired mode shapes with no boundary conditions applied.
Trying2Learn
TL;DR Summary
What are the eight mode shapes
I recall, about 30 years ago, seeing the eight mode shapes (and eigenvalues) of a single plane stress (or strain) finite element.

Also, years ago, I wrote a FORTRAN code to obtain them (using IMSL libraries)

I know there are eight (because the plane quad element had 8 degrees of freedom)

I also saw them in a book somewhere (but I do not remember the book).

There were eight mode shapes: stretch in 1, stretch in 2, a horizontal shear, a vertical shear and one other. THen there were three zero eigenvalue modes (free translation in two directions and a free rotation)

I am trying to write a MATLAB code to produce them, but I get strange results taht make no sense and am confusing myself (I do not know what Matlab is doing -- or maybe I am coding it wrong).

Can anyone point me to a site that has the eight shapes?

I am NOT looking for a eigenvalue analysis on a mesh (all my google searches bring up modal analysis on a mesh--I do not want that). I am looking for the analysis on ONE element

So, you are looking for mode shapes of a first-order quad element with no boundary conditions applied? Here's what I got in Abaqus (outline of the underformed shape is shown for each mode for reference):

berkeman
EXACTLY! That was what I remembered. I KNEW there is something wrong with my Matlab code. Now I must find the error.

THANK YOU VERY MUCH!

## 1. What are the 8 mode shapes of a plane finite element?

The 8 mode shapes of a plane finite element refer to the different patterns of deformation that a two-dimensional structure can undergo when subjected to external forces. These include bending, twisting, and stretching modes.

## 2. How are the mode shapes determined for a plane finite element?

The mode shapes are determined through mathematical calculations using the finite element method. This involves dividing the structure into smaller elements and solving for the displacement and stress at each node.

## 3. What is the significance of the 8 mode shapes in structural analysis?

The 8 mode shapes are important in structural analysis as they represent the different ways in which a structure can deform. By understanding these modes, engineers can design structures that can withstand various types of loading and ensure structural stability.

## 4. Can the 8 mode shapes change for different types of structures?

Yes, the 8 mode shapes may vary for different types of structures depending on their geometry, material properties, and boundary conditions. However, the fundamental concepts and principles behind the mode shapes remain the same.

## 5. How do the 8 mode shapes affect the behavior of a structure under different loading conditions?

The mode shapes can affect the stiffness, strength, and stability of a structure under different loading conditions. For example, a structure with a high bending mode may be more susceptible to bending forces, while a structure with a high twisting mode may be more resistant to torsional forces.

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