# Euler-Bernoulli beam element versus continuum beam element

I am using OpenSees to model a simply supported beam with a point load in the middle. The model is in consistent units. The beam is made up of bilinear quad elements. I have used 30 elements along the length of the beam and 1 element along the height of the beam.

The material is isotropic with the following properties:

$E = 80000$

$\nu = 0.0$

The loading $P = -10$. The model is 2 dimensions and 2 DOF's per node, although the software allows for input of element thickness in the 3rd dimension. The elements are $1$ unit by $1$ unit and the image does not reflect this (not to scale).

From basic structural mechanics the deflection at the base middle of the beam is given by

$$u_{max} = \frac {PL^3}{48EI}$$

which in this case equals $-0.84$ units.

Running a static analysis on the numerical model however yields a result of $-0.56$ units. This is very different.

Why does the beam modelled by continuum elements not reflect the true displacement for such a simple problem? What could be going wrong here?

• Are you refering to 2D or 3D elements as continuum elements? – nicoguaro Jun 10 '17 at 15:53
• The domain is 2D with 2DOF per node. But the software allows the user to input an element thickness even for 2D (I'm not sure why) see opensees.berkeley.edu/wiki/index.php/Quad_Element – user32882 Jun 10 '17 at 16:05