FEM - 2D finite element - rotational stiffness along local z axis (normal)

Introduction

This chapter is to provide a closer information about the behaviour of 2D elements connected in one single point with 1D elements.

Rotational stiffness of 2D element along normal (local z axis)

2D structural finite elements (FE)utilized by SCIA solver have practically no stiffness (very little for numerical stability) in rotation along normal (local z axis of these FE). If 1D member is connected to 2D element in a single point, the area to transfer rotation along 2D FE normal is infinitely small, and causes singularities. This solution is not correct, as shown on the examples below. It is up to the user to define the region in which these rotations will be transferred, based on the specific task what is being modelled and corresponding engineering assumptions. This must be always handled by the user and no universal approach (automation by SCIA) is feasible, due to very specific nature of each of these cases. Users are recommended to use rigid links or line rigid arms in order to model these regions properly.

Example 1) - 1D member perpendicularly connected to 2D plate

Below, two examples #A (wrong model)and #B (correctly modelled structure) are provided.

Finite element models differ in defined line rigid arm in case of the model #B. Both are loaded by a torsional moment of 1 kNm applied at the top of the column.

Results of 1D deformations - rotation along local x axis of 1D members:

The rotations are transferred into 2D element rotation along local z axis if not properly modelled in case #A:

Singularities are in internal forces (and stresses), for example:

Example 2) - 1D member connected to 2D plate in its plane

Below, two examples #C (wrong model)and #D (possibly correct model) are provided.

Finite element models differ in defined line rigid arm in case of the model #D. Both are loaded by a a force of 1 kN applied at the end of cantilever.

Results of 1D deformations - rotation along local y axis of 1D members:

The rotations are transferred into 2D element rotation along local z axis if not properly modelled in case #C:

Singularities are in internal forces (and stresses), for example:

Note: This behaviour of 2D elements is as expected. It is up to the user to define the size of the region where the rotations are transferred from 1D to 2D elements. Line rigid arms or rigid links might be feasibly used to model this (or possibly some dummy 1D elements).