# Plates¶

Plates in Pynite can capture both out-of-plane (bending & shear) behavior and in-plane (membrane) behavior. There are two types of plates available to work with in Pynite, each with its own advantages and disadvantages.

`Rect`

Plate Elements¶

`Rect`

plate elements must be rectangular. Trying to make them any other shape will invalidate the analysis. These elements are based on a 12-term polynomial formulation for out-of-plane bending. This leads to accurate out-of-plane bending and shear stress results as long as the plates are not overly thick.

`Quad`

Plate elements¶

`Quad`

plate elements do not have to be rectangular. They can be generic quadrilaterals. These elements are isoparametric elements based on the popular MITC4 formulation, and are well suited to thick and thin plates. Out-of-plane bending stresses calculated for these elements are very accurate at the plate centers, but at the corners they tend to report center stresses. Pynite helps minimize this problem by “smoothing” plate stress results when displaying contours, which averages stresses from all plates connecting at a node. Smoothing does not help much at fixed supports, where there is no adjacent plate to average stresses with. Another workaround is to remember that while plate corner *stresses* are rough estimates for the MITC4 element, plate corner *forces* are highly accurate. One can obtain the plate corner stresses from the corner forces by dividing by 1/2 of the plate’s edge length.

## In-Plane (Membrane) Stresses¶

In-plane stresses (tension, compression, and in-plane shear) are accurate for both elements. The formulations for both the `Rect`

element and the `Quad`

element is based on an isoparametric formulation that is pretty accurate.

## Orthotropic behavior¶

One useful feature in Pynite is the ability to model orthotropic behavior in plates. This allows the user to specify a stiffness modification factor `kx_mod`

and ky_mod` for each direction of a plate. This can be very useful for modeling stiffness reductions due to cracked concrete. A stiffness reduction factor of 0.35 would reduce the axial stiffness in the local y-direction by 65%.

Note that right now the stiffness modification factor is always applied in the plate’s local axes. If a surface contains plates with unaligned local axes it probably doesn’t make sense to use this feature.

## Meshing¶

Pynite provides several meshing functions to help generate some commonly used basic meshes like rectangles, cylinders and cones. Duplicate/coincident nodes and plates generated by meshes are automatically merged when a model is solved.