# How to use a linear spring element?

## Description

In the interest of computation speed, it may sometimes be advantageous to replace a spring by a linear element. This element is defined by two end points, a material, and a geometry property that represents its cross-sectional area.

If we consider the Tutorial 1 example, we see that several finite elements are necessary to represent the prestress rod.

Replace the prestress rod section with a set of lines:

The lines at 45° are necessary to prevent spurious modes in the elements to the left and right of the rod (due to the sudden change in cross-sections in the model).

Then, apply material STEEL1 to the new lines:

Also apply the material STEEL1 material to the surface regions at the left and right of the linear spring element (since the initial surface was broken up, material and boundary conditions definitions are lost).

Use the boundary conditions toolbox to apply the desired cross-sectional area (the value is in m^2):

It is only when this condition is applied that a line is recognized as a linear spring element. Do not forget to apply the line constraint for the problem symmetry:

IMPORTANT NOTE: Do not apply the constraint to the linear spring elements.

At this point, the stiffness of the linear spring is simply defined by k = E × A / L where E is the Young's modulus of the elastic material (from the material assignment), A is the cross-sectional area (from the boundary condition assignment), and L is the length (from the geometry).

To define a similar stiffness than the rod in Tutorial 1, use 0.000008m^2 for the cross-sectional area. Note that because the problem is 2D axisymmetrical, the cross-sectional area represents only 1/2pi of the actual cross-section of the rod.

Finally, make sure that the spring elements are meshed with single linear elements. This can be forced by using the Meshing | Structured Mesh | Lines function, and by applying 1 subdivision to the spring elements.

After running the computation, the results should be essentially identical to those of Tutorial 1.

Note that the use of the linear spring element is the same in 2D and 3D models.

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