OS-E: 0710 Application of a GENEL Element

GENEL elements can be used to define kinematic responses between two nodes.

The GENEL element is defined with Grid ID's and a 12 by 12 matrix in the Basic system. Associated degrees of freedom are the three translations and three rotations at both nodes.

Model Files

Refer to Access the Model Files to download the required model file(s).

The model file used in this example includes:

Beam_vs_GENEL.fem

Model Description

The model includes two beam elements and one GENEL element. CBEAM elements (ID's 1 and 2) have identical beam sections.


Figure 1. Model and Beam Sections
The material properties for Element 1 are:
Property
Young’s Modulus
1MPa
Poisson's Ratio
0.3
The material properties for Elements 2 and 3 are:
Property
Young’s Modulus
210 GPa
Poisson's Ratio
0.3

The only purpose of Element 1 is to provide visualization in HyperView. The GENEL element is also applied between grids 1 and 2. The GENEL element is defined using the Euler-Bernoulli beam theory, which does not consider shear deformation like the Timoshenko-based beam used in OptiStruct. The beam is clamped at the left end and four subcases are defined for each, including a single force or moment component at the right end. The beam length is 100mm and shear deformation is rather insignificant. Element 2 is slightly more flexible in bending load cases than GENEL.

Beam element stiffness maxtrix can be defined as follows:


Where,
E
Young's modulus
A
Cross-sectional area
L
Length
I
Second moment of inertia
G
Shear modulus
J
Polar moment of inertia
a, b, …, h
Populated in the 12 by 12 stiffness matrix (see Figure 2, left).


Figure 2. Beam Element Stiffness Matrix, 78 Coefficients for Symmetric Matrix, GENEL Element Bulk Data Card for Stiffness Matrix

Results

Figure 3 shows the GENEL and beam element displacements in the bending load case.


Figure 3. GENEL and Beam Element Displacement in Bending