## General Mechanical

#### Changing young’s modulus in linear elastic 2D model

• ali.ismail
Subscriber

Hello,

does anyone know why I get the same stress with different displacements when I change Young's modulus in a linear elastic 2D model? and how does Ansys calculate the displacements or stresses?

• peteroznewman
Subscriber

Please describe your model in more detail if you want a better answer. I want to see the geometry, mesh, loads, supports, and material  definition.

What do you mean by 2D?  Do you mean a 2D analysis such as Plane Stress or Plane Strain?  Or do you mean you have planar surface in 3D?  Show me a copy of the Geometry Details window to confirm.

A special case where you can change the displacement and the Young's modulus and have no change in stress is the following. A straight beam with an axial displacement of 1 mm. Double the displacement and halve the Young's modulus and you will get the same stress, assuming a linear solution.

• ali.ismail
Subscriber

I meant a 2D plane strain analysis. There is only one material under only the influence of self-weighing and defined by Poisson ratio, density, and young's modulus.

Horizontal displacements are not allowed on both sides and vertical displacement from the bottom is not allowed.

The dimensions of the model are 120*120 m and the diameter of the hole is 12 m.

And I am calculating the results only at 3 points shown in the mesh.

The geometry, mesh, and supports are shown in the pictures.

• ali.ismail
Subscriber

I would also be grateful if you knew the equation in which Ansys determines the displacements depending on the Poisson ratio

• peteroznewman
Subscriber

Some students fail to make the proper settings in Workbench to begin a 2D analysis and end up with a 3D analysis of a surface in the XY plane which is not the same thing.  In Mechanical, if you click on Geometry and look at the Details window, it you don't see Analysis type is 2D and that you selected Plane Strain, then you are in 3D.

The 2D equations of elasticity, in terms of displacements u and v, including Inertia Forces on the RHS and Body Forces X and Y are:

where

• ali.ismail
Subscriber

Do you mean this?

• peteroznewman
Subscriber

That is a correct setup for 2D Plane Strain.

• peteroznewman
Subscriber

In this model, with gravity pulling down on the material, when you halve Young’s modulus, the displacement and strain doubles so you have no change in stress because stress = E*strain and the factors of 2 on E and strain cancel each other out.